Technische Universität Berlin
School VII Economics and Management
Analysis of Investments in Electricity Markets
vorgelegt von
Andreas Schröder
Von der Fakultät VII - Wirtschaft und Management
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Wirtschaftswissenschaften
Dr. rer. oec.
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Jun.-Prof. Dr. Stefan Müller (TU Berlin)
Berichter: Prof. Dr. Claudia Kemfert (Hertie School of Governance)
Prof. Dr. Christian von Hirschhausen (TU Berlin)
Tag der wissenschaftlichen Aussprache: 20.02.2013
Berlin 2013
D 83
II
Abstract
The ongoing structural transformation of power systems calls for a fundamental overhaul of
electricity infrastructure throughout all system components, be it power plants, grids, load
management technologies, storage systems or other elements. In the light of the massive changes
that the system is likely to undergo within the decades following 2012, it is interesting to study
the drivers of investment decisions into various infrastructures to support the power system
restructuring. Driven by the increased interest in the economics of power markets, the Thesis
performs analysis for investment appraisals to different infrastructure components of future
electricity markets. Applications cover a wide range of infrastructure elements such as electric
storage, smart grid elements, transmission lines and power plants. The Thesis starts with an
introduction into basic concepts of power market economics. Chapter 2 entails an analysis of the
use of storage and demand-side-management tools where the sizing of batteries and load control
systems is optimized. It follows an investigation of the business case of fast charging stations for
electric vehicles. Subsequently, the Thesis includes two chapters on the evolution of fossil-fired
power generation capacities where investment incentives under the current power market design
are investigated. Since power plant expansion is closely interlinked with grid development plans,
the last two chapters are dedicated to the analysis of the interdependency between transmission
grids, congestion and investment into generation capacity. Reference is made to recent plans of
transmission expansion projects in Germany and Europe.
In all parts of the Thesis, numerical optimization methods are used to approximate the
fundamental functioning of markets and derive appropriate investment decisions from these
models. Common to all chapters is the use of techno-economic power market analysis where
electricity dispatch is optimized in combination with or given some specific capacity decision.
The fundamental models are partly casted in complementarity format and some applications do
include stochastic elements. The various chapters of the Thesis adopt the perspective of private
agents, system operators or social welfare maximizers while the geographical coverage ranges
from distribution grid level to European markets.
Keywords:
Electricity, power, investment, grid expansion, power plants, storage, e-mobility
III
Zusammenfassung
Im Zuge der Energiewende ergibt sich in der Elektrizitätswirtschaft der Bedarf an einer
grundlegenden Erneuerung verschiedener Infrastrukturkomponenten. Von Kraftwerken,
Übertragungsnetzen, Laststeuerungstechnologien bis hin zu Speichersystemen wird eine große
Bandbreite an technischen Lösungen vorgeschlagen um die Systemintegration von erneuerbaren
Energien zu fördern. Vor dem Hintergrund der laufenden Umstrukturierung des Stromsektors
besteht bei Unternehmen, Politik und Gesellschaft ein erhöhtes Interesse an Analysen zur
Wirtschaftlichkeit verschiedener Lösungen. Motiviert durch dieses Interesse, beschäftigt sich die
vorliegende Dissertation mit der ökonomischen Bewertung von Investitionen in verschiedene
Infrastrukturkomponenten des Strommarktes. Nachdem Kapitel 1 der Arbeit Grundlagen zur
Elektrizitätswirtschaft vermittelt, werden im zweiten Kapitel der Betrieb und die
Dimensionierung von Speichern und Laststeuerungssystemen in einer Fallstudie optimiert und
die Wirtschaftlichkeit der beiden Technologien verglichen. Das darauf folgende Kapitel geht auf
die Rentabilität des Betriebes einer öffentlichen (Schnell-) Ladestation für Elektrofahrzeuge ein
und untersucht dabei mögliche Geschäftsmodelle für einen profitablen Infrastrukturbetrieb. Zwei
weitere Kapitel untersuchen im Folgenden Anreize für Investitionen in fossile Kraftwerke bei
Beibehaltung des heutigen Marktsystems mit Grenzkostenpreisen auf Großhandelsmärkten. Die
Analyse thematisiert somit die zukünftige Entwicklung des Kraftwerksparks in Deutschland und
Europa auch unter dem Aspekt von Unsicherheiten bei Brennstoff- und CO2-Preisen. Da die
Entwicklung des Kraftwerksparks nicht zuletzt auch im Zusammenhang mit den Plänen zum
Stromnetzausbau zu sehen ist, sind die letzten zwei Kapitel der Arbeit der Interaktion zwischen
Netz- und Erzeugungsausbau gewidmet. Dabei werden aktuelle Planungen zum deutschen und
europäischen Netzausbau explizit in die Analyse eingebunden.
Methodisch zeichnet sich die vorliegende Dissertation durch die Nutzung numerischer
Optimierungsmodelle in allen Kapiteln aus. Techno-ökonomische Modelle werden verwendet
um fundamentale Eigenschaften von Strommärkten nachzubilden und geeignete
Investitionsentscheidungen herzuleiten. Eine Gemeinsamkeit aller Kapitel ist die operative
Optimierung der Stromproduktion im zeitlichen Verlauf („Dispatch“) bei gegebener oder
endogen determinierter Kapazität. Dabei greifen einige Modelle mathematisch auf ein
Gleichgewichtsformat zurück und berücksichtigen teilweise stochastische Komponenten.
Modellanwendungen behandeln Investitionsentscheidungen aus der Perspektive verschiedener
Akteure, darunter private Investoren, Systembetreiber und die öffentliche Hand. Die
geografische Dimension deckt in den Anwendungen von Verteilnetzen bis hin zu europaweiten
Übertragungsnetzen mehrere Ebenen ab.
Schlüsselworter:
Elektrizität, Strom, Investitionen, Netzausbau, Kraftwerke, Speicher, Elektromobilität
IV
Acknowledgements
I am indebted to my thesis supervisors Professor Christian von Hirschhausen and Professor
Claudia Kemfert for their continuous support and inspiration. Special thanks go to Christian von
Hirschhausen for having introduced me to the research community on energy markets over the
last three years.
I thank my numerous co-authors for their fruitful cooperation. In particular, I thank my fellow
students from TU Berlin (“Studienprojekt”) with which I had a great time working. Several
chapters of my Thesis would not have been possible without their contributions. My thanks go to
co-author Thure Traber for fruitful discussions and his input into several chapters of this Thesis.
I also wish to express my gratitude to the DIW Graduate Center, and the entire DIW department
of Energy, Transportation and Environment for providing me with an excellent research
environment. The DIW Graduate Center supported my Thesis and numerous conference
participations with a 3-year-long scholarship.
V
Content
ABSTRACT II
ZUSAMMENFASSUNG III
ACKNOWLEDGEMENTS IV
CONTENT V
ABBREVIATIONS IX
LIST OF TABLES XI
LIST OF FIGURES XII
CHAPTER 1 - INTRODUCTION 1
1.1 Motivation and basic literature 1
1.2 Methodology 2
1.3 Applications 4
1.4 Thesis structure 10
1.5 Conclusion 13
1.5.1 Insights in economic and policy analysis 13
1.5.2 Insights in methodology 14
1.5.3 Perspectives for future research 14
1.6 Statement of contributions 15
CHAPTER 2 – STORAGE AND DEMAND-MANAGEMENT IN DISTRIBUTION SYSTEMS 19
2.1 Introduction 20
2.2 Model Description 21
2.3 Application to a simple distribution system 24
2.3.1 Generation 24
2.3.2 Demand 27
2.3.3 Load control 29
2.3.4 Storage 29
2.3.5 Grid 30
2.4 Results 31
2.5 Discussion 34
VI
2.6 Conclusions 34
2.7 Appendix 36
CHAPTER 3 – FAST CHARGING INFRASTRUCTURE FOR ELECTRIC VEHICLES 38
3.1 Introduction & Literature Review 39
3.2 Input parameters 40
3.2.1 Investment cost 40
3.2.2 General demand for fast charging 42
3.2.3 Use pattern 43
3.2.4 Electricity prices and tariffs 45
3.3 Method 46
3.4 Results 47
3.5 Conclusion 50
3.6 Appendix 51
CHAPTER 4 – AN INVESTMENT-DISPATCH EQUILIBRIUM MODEL WITH LONG-TERM
UNCERTAINTY 52
4.1 Introduction and literature review 53
4.2 Model 55
4.3 Application to the German Power Market 56
4.4 Results 57
4.4.1 Profits 58
4.4.2 Investment 59
4.4.3 Prices 60
4.4.4 Market form 60
4.5 Conclusions 61
4.6 Appendix 62
CHAPTER 5 – AN INVESTMENT-DISPATCH EQUILIBRIUM MODEL APPLIED TO
EUROPE 65
5.1 Introduction 66
5.2 Model 66
5.2.1 Regional resolution 66
5.2.2 Temporal resolution 67
5.2.3 Transmission 67
5.3 Scenarios 68
5.3.1 Demand and energy efficiency 68
5.3.2 Renewable energy 69
5.3.3 Conventional generation 69
VII
5.4 Results 71
5.4.1 Wholesale spot price projections 71
5.4.2 Emission market prices 72
5.4.3 Market-driven capacity evolution 73
5.4.4 Power consumption and generation mix 77
5.5 Conclusion 78
CHAPTER 6 – TRANSMISSION GRID CONGESTION ANALYSIS 79
6.1 Introduction 80
6.2 Methodology 81
6.3 Application 82
6.3.1 Electricity grid 82
6.3.2 Electricity demand 83
6.3.3 Renewable energies 83
6.3.4 Conventional electricity generation 85
6.3.5 Infrastructure cost 87
6.4 Scenarios 87
6.5 Results and discussion 89
6.5.1 Four representative weeks 89
6.5.2 Detailed results for one exemplary week 90
6.5.3 Welfare analysis 94
6.6 Conclusions 95
6.7 Appendix 96
CHAPTER 7 – INTERACTIONS BETWEEN GENERATION CAPACITY EXPANSION AND
GRID DEVELOPMENT 100
7.1 Introduction 101
7.2 Literature review 101
7.3 Model formulation 103
7.4 Data 106
7.4.1 Geographic coverage 106
7.4.2 Temporal coverage 106
7.4.3 Generation 107
7.4.4 Demand 108
7.4.5 Storage & DSM 108
7.4.6 Grid 109
7.5 Scenarios 109
7.6 Results 110
7.6.1 Generation 110
7.6.2 Investment 112
7.6.3 Congestion AC Grid 113
VIII
7.6.4 Congestion on HVDC lines proposed in the NEP 2012 114
7.6.5 Price differences 115
7.7 Conclusions 116
7.8 Appendix 118
REFERENCES 120
APPENDIX – SOURCE CODES 137
GAMS Code of the model in Chapter 2 137
GAMS Code of the model in Chapter 3 145
GAMS Code of the model in Chapter 4 154
GAMS Code of the model in Chapter 5 163
GAMS Code of the model in Chapter 6 168
GAMS Code of the model in Chapter 7 175
IX
Abbreviations
aCAES Adiabatic Compressed Air Storage
AC Alternating Current
AMM Advanced Metering System
BC Brown coal (lignite)
CAPEX Capital Expenditure
CC Combined Cycle
CCGT Combined Cycle Gas Turbine
CCS Carbon Capture and Storage
CHP Combined Heat and Power
CO2 Carbon Dioxide
CPU Central Processing Unit
CT Combustion Turbine
DC Direct Current
DCF Discounted Cash Flow
DSM Demand-Side-Management
EC European Commission
EEV Expectation with the ExV Solution
EEX European Energy Exchange
EMF Energy Modeling Forum
EPEC Equilibrium Problem with Equilibrium Constraints
EPI Expectation under Perfect Information
ESS Expected Value of the Stochastic Solution
EU ETS European Union Emission Trading System
EU European Union
EUR Euro
EV Electric Vehicle
EVPI Expected Value of Perfect Information
ExV Expected Value
GAMS General Algebraic Modeling System
GT Gas Turbine
HC Hard Coal
HVDC High Voltage Direct Current
IGCC Integrated Gasification Combined Cycle
X
IRR Internal Rate of Return
KKT Karush-Kuhn-Tucker Conditions
LCoE Levelized Cost of Electricity
LP Linear Problem
MCP Mixed Complementarity Problem
MPEC Mathematical Problem with Equilibrium Constraints
NEP Netzentwicklungsplan (Grid Development Plan)
NG Natural Gas
NLP Non-linear Problem
NPV Net Present Value
NREAP National Renewable Energy Action Plan
NTC Net Transfer Capacity
OPEX Operating Expenditure
PC Pulverized Coal
PhD Doctor of Philosophy
PTDF Power Transfer Distribution Factor
PV Photovoltaic
QCP Quadratically Constrained Problem
RES Renewable Energy Sources
ROI Return on Investment
ST Steam Turbine
TOU Time-of-use
TSO Transmission System Operator
TYNDP Ten-Year Network Development Plan
VSS Value of the Stochastic Solution
XI
List of Tables
Table 1: Overview of models in different chapters .................................................................................... 18
Table 2: Available capacity and projections of marginal generation cost incl. carbon cost in 2020. ......... 25
Table 3: Storage investment cost data compiled from various sources. ..................................................... 29
Table 4: Compilation of information on EV charging station cost............................................................. 41
Table 5: Literature overview in alphabetic order. ...................................................................................... 54
Table 6: Expected profits over the horizon 2010-2035. ............................................................................. 58
Table 7: Investment levels under perfect competition and with 9% discounting. ...................................... 59
Table 8: Nomenclature ............................................................................................................................... 63
Table 9: Technical and economic parameters ............................................................................................ 64
Table 10: Scenario overview ...................................................................................................................... 68
Table 11: Technological characteristics and fuel price assumptions .......................................................... 70
Table 12: Breakdown of RES generation capacities on Dena zones in 2030 in GW. ................................ 86
Table 13: Costs for fossil-based power generation including CO2 costs. ................................................... 86
Table 14: Overview welfare effects summed over four representative weeks. .......................................... 94
Table 15: Additions to the AC grid of 2030 versus today. ......................................................................... 99
Table 16: Additions to the DC grid of 2030 versus today. ......................................................................... 99
Table 17: Generation capacities in Germany in the reference scenario. .................................................. 107
Table 18: Wind and solar production 2005-2011 in Germany. ................................................................ 107
Table 19: Scenario overview. ................................................................................................................... 109
Table 20: Key results of scenarios. ........................................................................................................... 111
XII
List of Figures
Figure 1: Algorithm used for solving the two-stage problem. .................................................................... 23
Figure 2: Frequency and power output under different wind speeds (average 5.22 m/s). .......................... 25
Figure 3: Simulated diurnal profiles of mean wind speed and output in winter (right). ............................ 25
Figure 4: Feed-in and load of non-power-metered consumers in 2010 in NEW grid. ............................... 26
Figure 5: Sampled demand profiles in winter and summer. ....................................................................... 27
Figure 6: Convergence of sample demand mean with an increasing amount of scenarios. ....................... 27
Figure 7: Deterministic mean standard load profile. .................................................................................. 28
Figure 8: Stylized 5-node grid in a reference distribution grid................................................................... 31
Figure 9: Investment into storage and DSM under varying investment cost and EV market penetration.. 32
Figure 10: Storage operation, DSM operation and line flows in the course of a day in two scenarios. ..... 32
Figure 11: RES feed-in, original demand and load after storage and DSM shifts. .................................... 32
Figure 12: dneg and dpos for households and commercial units in kW during a day. EV profiles excluded. 36
Figure 13: Parameters affecting cost and revenue stream. ......................................................................... 40
Figure 14: How many EV can be fed through which charging infrastructure? .......................................... 43
Figure 15: Two synthetic weekly EV demand profiles at 62.5 kW station with 30 EV/day (600 kWh). .. 44
Figure 16: Exemplary retail tariffs and electricity cost profile used in the calculations. ........................... 46
Figure 17: Return on Investment under different investment cost levels. .................................................. 48
Figure 18: Operation of an on-site storage device of 30 kWh capacity and 30 kW power limit. .............. 49
Figure 19: Return on Investment with and without storage. ...................................................................... 49
Figure 20: Estimation of the load pattern of a single charging station over the course of one week. ........ 51
Figure 21: Generation and investment cost. ............................................................................................... 57
Figure 22: Scenario tree. ............................................................................................................................. 57
Figure 23: Price profile. .............................................................................................................................. 60
Figure 24: Regional resolution of EMELIE-ESY ...................................................................................... 67
Figure 25: Wholesale electricity prices EU-27 average ............................................................................. 72
Figure 26: Carbon emission prices ............................................................................................................. 73
Figure 27: Conventional capacity investments until 2050 [GWel net capacity]. ........................................ 74
Figure 28: Power generation in the EU-27 ................................................................................................. 76
Figure 29: Onshore wind generation: Reference vs. Strategic South Scenario. ......................................... 84
Figure 30: Proposal of DC lines. Dark circles indicate converter stations. ................................................ 88
Figure 31: Congestion index for all scenarios in weeks 14, 28, 41 and 51. ............................................... 90
Figure 32: Generation portfolio of week 51 in the reference scenario. ...................................................... 91
Figure 33: Net Input: Median of hourly import/export in German zones. ................................................. 92
Figure 34: Line congestion in three scenarios measured in terms of shadow value. .................................. 93
XIII
Figure 35: Variable generation cost.......................................................................................................... 108
Figure 36: Generation dispatch pattern in the reference scenario. ........................................................... 111
Figure 37: New generation capacity by 2030 in the absence of national HVDC lines. ........................... 112
Figure 38: Congestion patterns in the standard grid. ................................................................................ 113
Figure 39: Congestion on HVDC lines proposed in the NEP 2012 (reference scenario). ........................ 114
Figure 40: Comparison of congestion patterns on HVDC lines proposed in NEP 2012. ......................... 115
Figure 41: Prices in different scenarios. ................................................................................................... 116
Chapter 1 - Introduction
1
Chapter 1 - Introduction
1.1 Motivation and basic literature
The ongoing transformation of the energy system (named “Energiewende” in German) calls for a
fundamental overhaul of electricity infrastructure throughout all system components, be it
generation capacity, grid capacity, load management technologies, storage systems or other
elements. In the light of the massive changes that the system is likely to undergo within the next
decades, it is interesting to study the drivers of investment decisions into infrastructure to support
the system restructuring.
The increasing use of non-dispatchable Renewable Energy Sources (RES) is one of the major
challenges that future energy systems are to tackle. Uncertainty and intermittency
1
of RES feed-
in as well as temporal (Sinden 2007) and geographic misalignment (dena 2010) between
production and demand increase the need for flexible back-up resources such as storage devices,
load management or fast-cycling power plants. Requirements for investment into these sources
of flexibility strongly interact with the availability of transmission capacity. Market risks such as
fuel cost uncertainties add an additional layer of complexity to investment. All these interactions
together make investment analysis a complex question in which quantitative models may help to
obtain information on drivers and consequences of investment. All chapters of this thesis
contribute with numeric insights into investment valuations as an attempt to identify
infrastructure needs and to explain market behavior.
A further complication of investment decision-making and its implementation is the presence of
multiple agents in all decision processes. We should recall that although the energy
transformation as paradigm shift is a goal imposed by the public, it primarily remains the
responsibility of investors to implement the infrastructure in liberalized markets. Models must
therefore reflect the decision structures and incentives for private decision-makers. The Thesis
performs distinct investment appraisals from the perspective of private agents, system operators
and welfare maximizers with applications to different infrastructure components of the future
electricity markets. A fundamental question is that of a possible gap between investment
requirements and likely realizations. The current market design of liberalized ‘energy-only’
power markets is on the brink of being reformed so as to provide more incentives for capacity
expansion to private investors. Part of the problem is the nature of security of power supply as
public good. As users can hardly be excluded from security of supply their willingness to pay for
it is low (Stoft 2002). An elaborate overview on the discussion on power market design,
“missing money” and “resource adequacy” can be found in Hogan (2005) and Cramton and Stoft
(2005). Additionally, Joskow and Tirole (2007) and Littlechild (2006) analyze private sector
investment incentives in the light of regulatory instruments such as price caps or the possibility
of rationing, concluding that significant under-investment results from regulatory uncertainty and
tools such as price caps. Chapter 4 of this Thesis delves into incentives for generation capacity
expansion and the role of uncertainty.
Peculiarities of the power sector make investment analysis in electricity markets a specific
endeavor different to analysis in classical commodity markets. Short-term balancing
requirements as well as technical transmission constraints are among the factors which require
quantitative analysis particularly tailored to power markets. There exists a large body of
1
Uncertainty refers to the non-predictability of feed-in while intermittency designates the chaotic fluctuating pattern that feed-in
exposes.
Chapter 1 - Introduction
2
literature that presents introductions to basic concepts in the field of power market economics.
The lay reader may be referred to the basic introductory book of Kirschen & Strbac (2004)
which has an economic focus with a slight technical touch as it explains fundamental energy
engineering principles such as transmission network constraints, financial transmission rights
and nodal pricing. Their chapters 7 and 8 present concepts relevant for investment into
generation and transmission capacity where the authors present ways of defining optimal
capacities taking into account complicating factors such as retiring capacity, cyclical demand and
reliability constraints, amongst others. It thereby lays the foundations for much of what is
presented in this Thesis. The more advanced reader may be interested in Erdmann & Zweifel
(2008) who guide the reader through scientific and engineering basics of energy conversion and
the various power generation technologies as well as resource markets. Concepts of probability
calculations and some basic investment analysis key indicators (NPV, IRR, ROI, DCF)
2
are
presented, which are partly used in this Thesis. Adding to this, the American-based textbook of
Stoft (2002) covers key issues of power markets with strong economic focus. As it includes a
treatment of market power in the electricity sector in chapter 4 (pp. 337), it is interesting in the
context of this Thesis where equilibrium models are used. Theoretic explanations on market
power outlined in the Stoft textbook are thus implicitly addressed in this Thesis (e.g. Cost mark-
ups, Elasticity of demand, Lerner Index, Herfindahl-Hirschman-Index, Cournot Competition).
An advanced and in-depth treatment of equilibrium models - and thus market power - with
applications to the electricity sector can be found in Gabriel et al. (2013). The compilation
constitutes a good overview of the use of different complementarity model formats in energy
economics. While this Thesis does not go beyond the use of Mixed Complementarity Problems
(MCP), Gabriel et al. (2013) also present applications of MCP extensions for sequential games,
which require a format such as Mathematical or Equilibrium Problems with Equilibrium
Constraints (MPEC or EPEC).
Descriptions of the functioning of power markets with dominant technical or techno-economic
focus can be found in Konstantin (2007) and Strauss (2009). Konstantin (2007) sets itself apart
in that it includes some chapters on concepts relevant for commercial investment analysis and it
also entails an interesting chapter on Combined Heat and Power (CHP), a field with increasing
importance in future power markets. His chapter 7.2.5 (pp. 287) is highly relevant for this thesis
as it encompasses explanations on technical and economic key parameters affecting the
economics of power generation. While Konstantin (2007) and Strauss (2009) cover all
generation technologies with main focus on fossil-fired generation, Quaschning (2009) provides
an overview of renewable energy systems and their technical characteristics. The textbook can
be considered as reference work especially in the field of solar and wind energy. In this Thesis,
reference to Quaschning (2009) is made on several occasions for the derivation of wind and solar
power characteristics.
1.2 Methodology
A multitude of approaches help appraising investment decisions with quantitative models. The
Thesis concentrates on so-called ‘fundamental’ market models to approximate the functioning of
electricity markets. These do not merely replicate market behavior but they try to explain market
behavior by replicating fundamental relationships. Electricity market price modeling is a good
example to understand the difference between fundamental and other types of market models.
Fundamental models replicate the merit order and technology dispatch to explain the pattern of
2
NPV = Net Present Value; IRR = Internal Rate of Return; ROI = Return on Investment; DCF = Discounted Cash Flow.
Chapter 1 - Introduction
3
electricity prices while econometric types of models merely replicate prices as close as possible
without explaining the underlying technological processes.
The methodological leitmotif of this Thesis is to perform different quantitative applications of
infrastructure investment appraisals to case studies in the electricity market. All chapters make
use of numerical optimization and equilibrium models which fall into the category of
‘fundamental’ market models. Several parts of the Thesis deal with decision-making given
specific stochastic components, others perform simpler forms of analysis, so-called deterministic
optimizations. When categorizing model applications in this Thesis by the representation of
uncertainty and the number of model stages, the following methods are applied:
(One-stage) Deterministic expected-value problems – The simplest and most common
form of investment analysis is expected-value optimization. It forms part of the realm of
deterministic optimization, where uncertain developments are either condensed into
average parameters or considered in a separate scenario analysis. Most parts of this
Thesis use such simple evaluation models which allow for decent extensions into details
other than uncertainty.
Two-stage stochastic problems – Bi-level problems are used in sequential decision-
making to distinguish upfront investment decisions from subsequent operational
optimizations with stochastic input. A simple example of a two-stage stochastic problem
with operational choice between a forward (bilateral) and a spot (pool) trade can be found
in Conejo et al. (2010, p.38). When the problem is formulated with ‘scenario-variables’
(Conejo et al. 2010, p.38), decomposition methods can become particularly interesting to
this kind of problems. In some large-scale cases, separate multiple problems are easier to
solve in decomposed form rather than in the extensive expected-value form. Chapter 2
incorporates an example of bi-level optimization with Benders decomposition (Benders
1962) where second-stage uncertainties influence first-stage decisions.
Multi-stage stochastic problems – In contrast to single- and two-stage problems, multi-
stage optimization takes into account dynamics of uncertainty. Decisions follow a
specific sequential order. Constraints ensure that non-anticipativity is guaranteed and so
is the decision sequence (Conejo et al. 2010, p.41). A multi-period representation is
useful to account for the real options character of investment (Dixit & Pindyck 1994),
which confers to the decision agent the flexibility of dynamic adjustment. Multi-stage
analysis is thus a tool to scrutinize amount and timing of investment decisions. A major
selling point of multi-stage optimization with fundamental models as opposed to
econometric-based valuation is that it allows taking into account feedback effects
between investment and investment incentives (operational results). Chapter 4 of this
Thesis includes multi-period investment decision making under uncertainty.
Decision-making under uncertainty is a field which receives increased interest in applied
research due to its importance in real-life power markets. Managing risk and uncertainty in
investment decisions is of pivotal importance notably in electricity markets which are
characterized by a strong presence of intermittency and unpredictability in both, the long- and
short-term context. Over the coming decades, volatility at the production stage is expected to
become even more accentuated when electricity is increasingly produced through RES.
Stochastic optimization models are therefore suitable for economic analysis purposes in the
electricity market. A good overview of advanced methods of stochastic optimization with
applications to electricity markets can be found in Conejo et al. (2010). Seminal works on
stochastic optimization but without energy focus include Dixit & Pindyck (1994), Birge &
Louveaux (1997) and Kall & Wallace (1994). These textbooks complement Conejo et al. (2010)
Chapter 1 - Introduction
4
in the inclusion of mathematical proofs and some examples beyond energy markets while
explaining pretty much the same basic concepts.
Independent of the issue of uncertainty, the methodology used for numerical optimizations in
this Thesis can also be differentiated by the type of models used. Ventosa et al. (2005) provide
an overview of various decision and analysis support models and their possible applications that
may help carrying-out investment appraisals. A distinction is made between single-firm
optimization models, simulation models, and equilibrium models. The advantage of single-firm
optimization models – as used in most chapters of this thesis – is that they allow for representing
technical restrictions in great detail. Nevertheless, equilibrium models can also capture technical
details to some extent as proven in various applications in Gabriel et al. (2013). A comparison
between different forms of equilibrium models is done in Dye et al. (2002) who use the clearing
process of the power market model (centralized/decentralized) and the nature of interaction
among rival generators (from strong competition to collusion) to distinguish models. A rather
methodological way of categorization is to classify models along their problem type (linear, non-
linear, integer, complementarity). The problem types addressed in this Thesis are:
LP (Linear Problem) and NLP (Non-linear Problem) for simple cost minimizations,
hence single-firm optimization. Examples of system cost minimizations in power markets
can be found in the PhD Thesis of Haller (2012) and Nicolosi (2012). The work of
Burstedde (2012) also applies cost minimization and it is in many respects comparable to
the model of Chapters 6 and 7 here.
QCP (Quadratically Constrained Problem) for welfare maximization. The difference
between welfare maximization and cost minimization is the inclusion of consumer rents
in the social welfare function which makes the mathematical formulation non-linear.
However, results from welfare maximization should coincide with cost minimization in
perfectly competitive markets without market distortions. Examples of welfare
maximizing power market models can be found in Green (2007) and Leuthold et al.
(2012).
MCP (Mixed Complementarity Problem) for profit maximization with multiple players.
These types of models are especially interesting when the ability of market power
exertion is possible. Examples of applications to electricity markets can be found in
Traber & Kemfert (2011a; 2011b) and Weigt & Hirschhausen (2008).
1.3 Applications
In order to cover a wide range of topics within the field of electricity markets, the
aforementioned methods are applied to investment analysis in different settings within the
electricity market. Distribution grids are addressed as well as transmission grids, mobile and
stationary storage and load control, charging infrastructure for electric cars, power plant
capacities and transmission grids. These infrastructure components constitute one part of a
mosaic of measures to bring forward the energy transformation of the electricity sector.
3
They
form part of competitive and partially supplementary solution strategies for the integration of
RES into the system. In what follows, a short walk through these options is done one by one.
3
This list is non-exhaustive. Other flexibility elements could be e.g. curtailment of intermittent RES feed-in or grid congestion
management.
Chapter 1 - Introduction
5
In the beginning and the end chapters of this Thesis, electric storage systems are subject of the
analysis. Storage has received increasing attention in the electricity community due to its
promising role in the integration of RES by increasing temporal flexibility of production and
consumption. A broad range of storage technologies co-exist and compete with each other and it
remains to be defined which option is the most economic choice from a system perspective. A
technology classification can be made by the form in which energy is stored: Electrochemical
(batteries), kinetic (flywheels), or potential energy (pumped hydro storage and compressed air
storage) (Schill 2011). Other possibilities are the storage of power by the conversion in other
materials, for instance in the form of heat via CHP processes, or in the form of hydrogen via
electrolysis (Lipman 2011). In the recent past, there is increasing interest in the blending of
hydrogen into the existing gas grid (up to ca. 15% blending ratio feasible (dena 2012)) with
possible reconversion to power (Sterner 2009). In addition to Table 3 in Chapter 2, a recent
overview of storage technologies and possible developments in future can be found in Baker
(2008), Hall and Bain (2008), Ibrahim et al. (2008) and the PhD Thesis of Gatzen (2008). These
sources give details on technical characteristics as well as the possible evolution of economic
viability. Round-trip-efficiency and lifetime appear to be amongst the key technical
characteristics affecting economic viability and thus technology choices of investors. Power
density and weight are particularly important for mobile storage systems. The most cost-effective
options for stationary use currently include hydro pump storage systems, lead-acid and lithium-
ion batteries (Electricity Storage Association 2011). Together with the rather visionary concept
of Compressed Air Energy Storage (CAES), these storage technologies are treated in the last two
chapters of this Thesis. Besides the technology choice, there is also room for investors to play
with the sizing a storage system. Investors can modify power rating and storage capacity so as to
tailor the system to their needs. Chapter 2 of this Thesis includes a size optimization for a storage
system, yet, holding the capacity-power rating ratio constant for reasons of simplicity.
For the integration of RES, storage is one option next to others such as Demand-Side-
Management (DSM). DSM refers to the possibility of controlling consumption. Load shedding
and load activation are means of interfering with the consumption decision of the consumer with
the help of communication technology. Through DSM, consumers with production facilities can
be attributed a more pro-active role than in traditional power systems, creating some kind of
“prosumer”. While there is a lot of talk on ‘smart grids’ in the electricity community, its large-
scale roll-out lags behind expectations in several European countries (Eurelectric 2011, p.28).
Exceptions pertain to countries such as Italy and Sweden where regulation is particularly
supportive to smart metering roll-out. In most countries, roll-out of DSM systems is progressing
slowly in the domain of households and commerce, while load control in industry processes is
far more abundant. Paulus and Borggrefe (2011) adopt a system-wide perspective of investment
in DSM in a case study for Germany with focus on industrial consumers and they conclude that
technical and economic DSM potentials in the energy-intensive industries are promising.
However, costs for DSM equipment seem to be too high to compete with other solutions such as
flexible back-up power plants (EWI 2012, chap.4.1). In general, DSM may not be suitable for
coping with long-term RES intermittency or seasonal balancing but appears more promising for
addressing stochastic RES feed-in, i.e. the provision of balancing power (Schill 2011; Strbac
2008).
In the wake of increasing market penetration of Electric Vehicles (EV), it is interesting to
analyze possible investment options in this relatively immature market. While extensive analysis
has been carried-out on the attractiveness of pure and hybrid EV in comparison to conventional
cars (Skerlos & Winebrake 2010; Feng & Figliozzi 2012; Funk & Rabl 1999), little insights have
been gained in the economics of corresponding infrastructure. Only few project reports mention
costs and conduct commercial evaluations of charging infrastructure (Wiederer & Philip 2010;
Chapter 1 - Introduction
6
Morrow et al. 2008; Slater et al. 2009; Wietschel et al. 2009; PlanNYC 2010). Notably when it
comes to investment and operation of battery-swapping stations or fast charging systems,
virtually no in-depth analysis has been published besides some analysis of the company TEPCO
in Japan (Anegawa 2009; Anegawa 2010). One chapter in this Thesis attempts to contribute
insights on this behalf. Japan is currently on the forefront of implementing fast charging
infrastructure for EV with the United States following up rapidly. It remains to be seen, whether
and where this technology proliferates further. Regarding Germany, the process of market
diffusion of EV is mainly steered under the umbrella of the Forum ‘Nationale Plattform
Elektromobilitaet’. It publishes annual reports on the market situation. While the 2011 report
(NPE 2011, p.37) includes an estimate of fast charging facilities of around 250 stations by 2014,
the necessity of ca. 7000 stations is mentioned in the long-term vision of the 2012 report (NPE
2012, p.48). This is an ambitious target given barely 12 stations being available in Germany in
early 2012 (NPE 2012, p.56).
One strategy to support the integration of RES is seen in the expansion of flexible
(“conventional”) power generation capacity as sort of back-up facility. This is a rather
contentious option since new fossil-fired and nuclear power plants do by virtue of their
environmental implications contradict the goal of RES integration at first glance. Some often
industry-driven exports, though, purport the requirement of new capacities as back-up. In this
context, the BDEW Kraftwerksliste (2011) projects 23.5 GW of reliable capacity to be realized
in Germany with high likeliness. The same order of magnitude (19 GW) is indicated by Maurer
et al. (2012) as required minimum additional generation capacity for Germany. A report of EWI
(2012) projects investments into 44.5 GW gas, and 6.7 GW lignite-fired power plants until 2030.
Other sources talk of 8 GW (Knopf et al. 2011) or 10 to 14.2 GW new capacity by 2020 (dena
2008). For Europe, capacity expansion of gas-fired plants (139 GW), coal-fired plants (67 GW)
and little nuclear power is projected in the World Energy Outlook (IEA 2011d). EWI (2012)
project gas-fueled generation capacity investment to almost double to 55 new GW by 2030 while
investment in other conventional resources ought to decline. Two chapters of this Thesis are
entirely dedicated to the discussion of the likely evolution of power generation capacities in
Germany and Europe. They contribute to discussing the incentives for investment under the
current market design of so-called energy-only markets where market prices are marginal cost-
based and investors need to recoup investment cost through ‘ordinary’ power production and
sales (no capacity markets exist). It is often argued, that such market design does not provide for
sufficient incentives and thus needs some readjustment through some sort of capacity
instruments (Cramton & Stoft 2005; Agora 2012; Milstein & Tishler 2012) as implemented in
several electricity markets such as PJM
4
and some European countries (Matthes et al. 2012). A
compilation of arguments for and against the sufficiency of energy-only markets can be found in
Cramton & Ockenfels (2011) and Muesgens & Peek (2011).
Another question is the actual necessity of power generation capacity from a system perspective.
This topic can be addressed in technical assessments where system stability requirements and
load flows are considered (ENTSO-E 2009). As transmission grids and generation capacity are
two interlinked parts of the system, the last two chapters of this Thesis analyze interactions
between transmission grid expansion plans and generation capacity expansion.
The need for new transmission grid capacity is almost undoubted in the relevant research
community. The 3d energy package of the European Commission mandated the European
Transmission System Operators (ENTSO-E) to establish a Ten-Year Network Development Plan
4
PJM refers to a Transmission Operator in the North-Eastern United States. It operates a reliability-pricing model designed to
create long-term price signals to attract needed investments in reliability.
Chapter 1 - Introduction
7
(TYNDP) in which specific transmission projects are outlined. It is the first policy effort to bring
forward coordinated long-term planning processes for European power transmission
infrastructure. The German political situation is characterized by the implementation of the
TYNDP through the National Grid Development Plan (‘Netzentwicklungsplan’). The ongoing
process defines the need for additional transmission capacity within Germany for the next 20
years on a running yearly basis. The June 2012 proposal of the four German Transmission
System Operators (TSO) projects the need for around 28 GW of High-Voltage Direct Current
(HVDC) lines across Germany by 2032 on top of expansion plans in the Alternating Current
(AC) grid (TSO 2012). In the light of past proposals to expand electricity grids, different studies
have examined their suitability on an EU-wide scale (Troester et al. 2011; Leuthold et al. 2012;
Schaber et al. 2011) and national scale (dena 2010). This Thesis contributes to the discussion
with two chapters and it adds some new element in that it covers the most recent HVDC
proposals outlined by the German TSO. The plan of July 2012 (‘Netzentwicklungsplan’) is
criticized as being over-dimensioned according to Jarass and Obermair (2012). In late 2012, the
Federal Network Agency approved a plan (‘Bundesbedarfsplan’), where only 51 of the 74
proposed projects were confirmed, leaving corridor B of the HVDC lines unconfirmed. The 2012
plan now stipulates 2800 km of new lines and 2900 km renewal of lines (Sueddeutsche 2012).
In order to determine the effect of transmission grid expansion projects on the markets, there is a
need to apply sophisticated models of power flow simulation. Real world physical flows follow
Kirchhoff’s and Ohm’s laws.
5
Power does not necessarily flow across the shortest distance, but
rather it finds its way through the grid via the path of the least resistance. This nature of power
flows gives rise to so-called loop-flows in meshed grids. To account for these peculiarities of the
power flows, some chapters of this Thesis use a DC load flow approach (Schweppe et al. 1988)
for determining power flows in meshed grids. DC Load flow calculations consider only real
power equations and can reduce the problem size compared to more realistic AC load flow
models (Overbye et al. 2004; Stigler & Todem 2005). Due to the presence of non-linear and non-
convex terms in the AC power flow equation, AC load flow models extend a model’s calculation
time and they tend to have the problem of non-convergence (Groschke et al. 2009). The DC
approach aims at approximating real-world AC network flows with a set of linear constraints,
which are derived from a range of simplifying assumptions regarding voltage drops. The AC
problem is linearized by omitting reactive power flows, normalizing voltages and reducing phase
angles.
6
In a case study of the Midwest U.S. transmission grid, Overbye et al. (2004) prove that
differences between the DC- and AC-based approaches to nodal pricing are minor. Similarly,
Purchala et al. (2005) validate the DC load flow assumptions and testify a good performance but
with outliers on individual lines (Burstedde 2012).
Another concept closely related to DC load flow models is that of Power Transfer Distribution
Factors (PTDF). These PTDF describe the flow through any individual line in dependence of the
input of one unit of electricity at some specified hub. The flow on a specific line is thus
determined by all net inputs into all adjacent nodes. Baldick (2002) and Lui & Gross (2002) give
theoretical and empirical evidence in favor of the PTDF approximation while Duthaler et al.
(2007) highlight approximation errors in zonal models. Errors occur if zones are not defined in
line with the fundamental market congestion structure (Burstedde 2012). A further caveat of the
PTDF approach is that matrices have to be restated in the case of a change in the network
5
The Kirchhoff rules define the relation between electric tension and currents: At each node of a network the sum of in- and
outgoing flows equals zero and the directed sum of electrical potential differences (voltages) around any closed circuit (loop) is
zero. The Kirchhoff rules reformulate Ohm’s law which states that the current through a conductor is proportional to the potential
difference between two points.
6
These assumptions are more inaccurate for lower voltage levels and in case of high line usage (Burstedde 2012; Schweppe et al.
1988).
Chapter 1 - Introduction
8
topology. Examples of the use of PTDF can be found in a study on European congestion
management policies in Ehrenmann and Smeers (2004), in the PhD Thesis of Waniek (2010), in
an application to Re-Dispatch in Germany in Nuessler (2012) and in Linnemann et al. (2011)
who use a PTDF approach to incorporate “n-1” security constraints
7
into a re-dispatch model.
Overall, Waniek (2010) suggests that the PTDF approach remains popular in research and is
preferred to the NTC approach notably in welfare analysis. In this Thesis, the PTDF approach is
used in an international model application with welfare analysis in chapters 6 and 7.
An alternative to the AC, DC load flow and PTDF approach is a formulation of flows in a simple
piping model, where loop flows are not accounted for. Such approach is used in one chapter of
this Thesis, because no aggregated international data on transmission line characteristics (i.e.
reactance) was available to the authors. In that case, Net Transfer Capacities (NTC) – as
published by ENTSO-E (2012) - can be used as input data. The NTC-approach is a substantial
simplification omitting Ohm’s and Kirchhoff’s physical laws of power flows and its results are
not necessarily optimal in the real world. A seminal study which uses NTC values is PRIMES
(Capros 2011), the model used for the Energy Roadmap of the European Commission. A hybrid
model with both NTC and DC load flow elements (for international and national flows) is
presented in Burstedde (2012). The PhD Thesis of Nuessler (2012) tests all approaches: DC,
PTDF and NTC-based simulations.
Besides the nature of power flows, there are other peculiarities of the power sector which make
quantitative analysis complex. These include the various technical flexibility constraints that
come with the necessity of a permanent energy balance. In electricity systems, demand and
supply must balance at each instance in time for system frequency to hold. Due to this constraint,
the temporal dimension of the dispatch of power generation units is of great importance.
Technical constraints such as load gradient limits, start-up limits (Muesgens & Kuntz 2007;
Abrell et al. 2008) and economics considerations of ramping costs (Kumar et al. 2012; Lefton &
Besuner 2006) must thus be reflected in any economic consideration of power markets. All of
the models used in this Thesis do reflect system constraints to account for flexibility of
generation. While a realistic depiction requires complex non-linear elements to represent start-up
behavior, this Thesis uses the alternative of linearized operational constraints, as proposed in
some earlier work (Muesgens & Kuntz 2007; Abrell et al. 2008). A literature overview in
Schroeder et al. (2013) includes a compilation of technical and cost figures for power dispatch.
Model assumptions in some chapters were aligned with indications in that overview report.
8
Further issues influencing the model applications and their complexity are the temporal
resolution and the time horizon used. The representativeness of results significantly hinges on
the use of a fine time resolution and the inclusion of many time steps. To keep a model tractable,
representative type-days are often chosen to reflect typical combinations of load and RES feed-
in. All chapters of this Thesis use an hourly resolution at the dispatch stage and some
representative time horizon. Combined investment-dispatch models in Chapters 4 and 5 use such
simplification, as do other comparable investment studies (Nuessler 2012; Haller 2012). Since
the choice of a subset of times risks to neglect extreme events, a full year consecutive hourly
resolution is sometimes used to model the dispatch in detail (Gatzen 2008; Nicolosi 2012).
7
“n-1” Security constraints ensure that a system is in a “n-1” secure state. That means an outage of a single component may not
trigger cascading failures producing a possible black-out.
8
The literature review of Schroeder et al. (2013) produces insights into the most recent developments of technical and cost
parameters and their likely evolution in the future. CCS and nuclear power appear to be way more costly than assumed in many
relevant studies. Another striking fact is that solar power has become much cheaper than most recent studies assume. Regarding
the analysis of power plant flexibility, advanced coal- and lignite-fired power plants are almost as flexible as CCGT power
plants.
Chapter 1 - Introduction
9
Chapter 7 of this Thesis also uses such fine temporal resolution but compromises on the side of
the long-term representation of different years. Nicolosi (2012) demonstrates that the temporal
resolution heavily influences the results of investment models in systems with a high share of
RES feed-in.
As this Thesis is concerned with investment decisions, the lay reader might expect some
introduction into basic notions relevant for general investment analysis such as corporate finance
theories and common metrics used for investment appraisals (IRR, NPV, DCF etc.). Since such
investment metrics are not at the center stage of this Thesis and to avoid doubling, a short
briefing into these concepts is made in the individual sections where they are used.
Chapter 1 - Introduction
10
1.4 Thesis structure
The PhD Thesis has started with an introduction into a number of fundamental concepts relating
to electricity markets and methodological basics. In this section, an outline was given for the
motivation of the individual chapters and their content. The subsequent chapters of this Thesis
are linked by methodological similarities and their focus on investment in electricity
infrastructure. Nevertheless, all chapters constitute independent parts one from another. They are
enchained by chronological order of production unless otherwise stated.
Chapter 2 – Smart grids: Storage devices and demand control can contribute to reducing
electricity generation cost through inter-temporal substitution of production and demand in a
system with a large share of intermittent resources. Chapter 2 presents a model that helps
quantifying the related cost reductions in a simulation model of a simplified medium-voltage
grid (10kV) under uncertain demand and wind output. A storage and DSM investment decision
is considered in a two-stage stochastic program. The model maximizes total welfare and it
informs an optimal investment sizing decision as regards specific 'smart grid' applications such
as storage facilities and meters enabling load control. The yields vary according to the stochastic
realization of wind output and demand. Capacity is chosen to optimize overall expected yield.
With this example, the basic foundation of stochastic programming and the advantage of the
stochastic programming solution over deterministic approaches are illustrated. In the previous
introduction, the fundamental properties of these problems’ general class were summarized as
two-stage stochastic linear problems with recourse. The resulting problem has two decision
2
Smart grid applications in
distribution grids
3
E-Mobility charging
infrastructure
4
Power plant investment
stochastic model
6
Grid congestion
7
Power plants &
grid congestion
5
Power plant investment
in Europe
1
Introduction
Chapter 1 - Introduction
11
stages and a valuable property known as block separable recourse that allows for decomposition
approaches to speed up efficient solution. In this special instance, Benders decomposition
(Benders 1962) is used. Still, the problem is relatively simple since it forms a linear program, as
opposed to more complicated integer programs or complementarity problems, and
decomposition therefore happens to not reduce computation time. Furthermore, stochasticity is
represented in one single stage, hence the model is not dynamic and no long-term perspectives
are included. Later chapters of this Thesis expand on Chapter 2 with long-term dynamics being
included.
Topic-wise, chapter 2 deals with the complementarity of different flexibility options (storage,
DSM). Results of the stylized application indicate that central storage facilities are a more
promising option for generation cost reductions as compared to DSM. This is in line with results
from other research in that field and results are corroborated by the fact that large-scale roll-out
of metering systems lags behind expectations in most European countries (Eurelectric 2011,
p.28). Torriti et al. (2010) provide an overview of the status of demand-side projects in European
countries and conclude that DSM has been slow to emerge because of limited knowledge, high
costs, and infrastructure. Adding to this, demand shifting has tight time limits and is not suitable
for coping with long-term RES intermittency or seasonal balancing (Schill 2011). DSM
measures appear more promising for addressing stochastic RES feed-in, i.e. the provision of
balancing power (Strbac 2008). The analysis here performs sensitivity tests with respect to the
market penetration of uncoordinated plug-in EV which are found to strongly encourage
investment into load control equipment and slightly improve the case for central storage devices.
Chapter 3 – E-Mobility infrastructure: The next chapter deals with investment into recharging
infrastructure for EV. By now it is fairly uncertain which charging technology for battery-
powered EV is going to penetrate the European automotive market. Among the most prominent
and most debated solutions are fast-charging stations as well as battery-exchange stations,
alongside home-charging. Whilst the necessity of home-charging solutions is undoubted, little
knowledge has been spread on the usefulness and the economic rationale of fast chargers. The
presented analysis aims at providing a first insight into the economics of this technology which is
hitherto little explored research-wise. The work presents cost components, business models and
organizational structures of infrastructure management in the case of fast charging for EV. It
touches upon metrics used in investment analysis, such as Return on Investment and cost
annuities. Calculations of contribution margins allow for an insight into the economics of EV
fast charging systems in a short-term perspective. The equilibrium model Esymmetry (Traber &
Kemfert 2011a) is used to model the electricity market dispatch under oligopolistic competition
of Cournot type. It is used to replicate electricity market prices and to address the question
whether market power affects the attractiveness of station operation from the perspective of
electric utilities. The results are very pessimistic about the operational margins of station
operations and they suggest that charging stations must be complemented with other purposes
than pure power sales to generate profits.
Chapter 4 – Power plant investment under uncertainty: Chapter 4 presents an integrated
electricity investment and dispatch model with endogenous electricity generation expansion in
partial equilibrium format. A modified version of the electricity market equilibrium models
Esymmetry and Emelie (Traber & Kemfert 2011a; Traber & Kemfert 2011b) is used to
scrutinize power plant investment decisions. Investment analysis under uncertainty is often
conducted with options valuation methods. A shortcoming of real options valuation is that
interdependencies (feedback effects) between some variable, e.g. electricity market prices, and
the investment decision can hardly be modeled, notably in the presence of strategic actions in
markets with imperfect competition. In Chapter 4, where power plant investment and subsequent
variable dispatch decisions are scrutinized, there is a direct interdependency between fuel and
Chapter 1 - Introduction
12
thus market prices and investment decisions. A real option approach fails to model this link, so
another form of multi-period program must be undertaken. Chapter 4 reflects the (real) optional
structure of investment but applies a more profound analysis in the stage of the recourse
decision, here the dispatch. It hereby allows for modeling feedback of prices on investment in a
multi-period setting. Decisions occur at different points in time so that the problem can be
viewed as having multiple stages of observations and actions (Birge & Louveaux 1997). The
capacity expansion models optimal choices of the timing and levels of investments to meet
future power demands. Here, decisions are taken dynamically about additional capacity and
about the allocation of capacity to meet demand. The newly integrated model features an hourly
time resolution and incorporates long-term fuel price risk at the investment stage. Such
stochastic multi-period equilibrium model allows for an outlook on power plant capacity
expansion in electricity markets since it adopts the perspective of profit-maximizing electric
utilities and it replicates realistic wholesale market prices. The parameterization of an extended
model application to European markets is based on a literature review on technical and economic
parameters of power generation technologies (Schroeder et al. 2013). An application is done for
Germany over the horizon 2010-2035. The model is confined to the German electricity market
and it leaves out trade with international partners since the sole purpose of this model is to show
how investment behavior changes depending on the problem formulation as either stochastic or
deterministic model. The primary focus of the model application in chapter 4 lies on building a
stochastic model and the analysis of its properties. It aims at looking into the sensitivities of the
model with regard to certain parameters and assumptions and the model structure. A large-scale
application of the same model is performed in chapter 5.
Chapter 5 – Power plant investment in Europe: Chapter 5 presents an application of a multi-
period deterministic model on power generation capacity expansion in a European-wide context.
No uncertainties are considered and compromises are made regarding specific features of the
model (time scale, storage) in order to leave space for a large-scale application to Europe for the
horizon 2010-2050 where private investors optimize their generation capacity investment and
dispatch. Results give indications regarding the expected European power plant mix in the period
2010-2030. It is investigated how different climate policy regimes affect investment and dispatch
behavior of the European power markets. The model projects investment into Carbon Capture
and Storage (CCS) and nuclear technology to be way lower than comparable peer models do.
The model results also show a strict upward movement of wholesale market prices over time.
Yet, prices are not high enough to spur large investments into CCS-equipped and nuclear power
plants.
Chapter 6 – Grid congestion analysis: This chapter considers transmission grid congestion in a
case study of Germany and neighboring countries. After having analyzed incentives for power
plant investment (in the previous chapter), it remains to be analyzed how to connect power plants
to demand hubs. There has been much talk in recent years about transmission grid infrastructure
requirements to connect production and demand. In the light of policy proposals to expand
electricity grids so as to better incorporate RES into the system, there is increased interest in
quantitative analysis of the congestion situation. Chapter 4 picks up the network regulator’s call
for a transmission infrastructure plan and proposes solutions for the horizon 2030 with a focus on
the German grid, embedded in a European context. The purpose is to propose a stylized
application to European electricity markets. This chapter uses the DC load flow approach in a
welfare maximization regime.
Chapter 7 – Power plants & congestion: The literature on power plant placing models is rare.
Most model-based investment studies omit the geographical dimension within countries (EWI
2012; EWI et al. 2010) with few exceptions (Frontier & Consentec 2008; Dietrich et al. 2010).
Other studies are not model-based (BMU 2010) or capacity expansion is set exogenous (dena
Chapter 1 - Introduction
13
2008). Studies which identify the need for generation capacity as reserve capacities only
consider nations as autark power systems but they do not address flexibilities offered through
increased international market integration, storage and DSM (EWI 2012; Maurer et al. 2012).
The work here proposes the centralized planning of power plant expansion as solution to grid
congestion, supported by the increased use of storage, DSM, HVDC lines and international
transmission capacities. Dominant power plant technologies and their appropriate placement are
identified. The analysis quantifies the added value of centralized planning to overall welfare and
puts these into the context of massive grid expansion plans as outlined in the National Grid
Development Plan for Germany (TSO 2012). A central conclusion is that HVDC line projects
shall be prioritized, as done in the subsequent ‘Bundesbedarfsplan’ (BNetzA 2012).
1.5 Conclusion
This Thesis provides a contribution to the ongoing debate on the restructuring of electricity
markets. Quantitative assessments are used to analyze investment decisions into various
infrastructure components of the future power system. In what follows, I would like to point to
the main findings of the individual chapters, some fundamental policy conclusions and
methodological conclusions.
1.5.1 Insights in economic and policy analysis
The analysis of the second chapter demonstrates a case where investment into storage
capacity is likely to be less costly and more useful than DSM systems from an aggregated
system cost perspective. Main reasons are the higher flexibility that storage systems
allow for, e.g. inter-seasonal storage. When choosing the optimal flexibility tool,
investors are therefore likely to favour storage over DSM solutions. This finding is also
in line with indications in related work (EWI 2012; Schill 2011; Strbac 2008).
Chapter 3 on E-Mobility charging clearly shows that fast charging infrastructure can
hardly be operated profitably in these early days of EV adoption. Investment and
operation of such charging stations must therefore be motivated by other purposes than
direct power sales. Additional revenues could e.g. be generated from indirect sales such
as parking fees, sales of other goods, and marketing effects.
Chapter 4 produces insights into the effect of long-term market price uncertainties on
investment into fossil-fired power plants. The application is primarily of methodological
interest. It is shown that uncertainties have a strong impact on technology choice,
decision timing and amount of investment. All in all, uncertainties create expected losses
for private investors. Incentives for investment are low especially for oligopolies.
According to the results of chapter 5, the current market design is not likely to incentivize
high amounts of generation capacity investment in European markets. This finding
supports the call for a fundamental overhaul of the market design, as energy-only markets
appear not capable anymore of providing sufficient incentives for new capacity
investment to secure system stability.
Chapter 6 analyzes the transmission congestion effects of an organised positioning of
RES close to demand hubs and alternatively the installation of cross-country HVDC
lines. It is found that there continues to be a need for transmission capacity expansion by
2030. However, the strategic placement of generation resources and storage systems
could contribute to alleviating the need for large HVDC lines.
Chapter 1 - Introduction
14
According to the calculations in chapter 7, the HVDC expansion plans of the National
Grid Development Plan published in June 2012 appear to be questionable. Adding to the
critique of Jarass and Obermair (2012), chapter 7 suggests that the plan proposed by the
TSO omits the possibility of increased use of storage and demand-control and the
placement of back-up generation capacity. It therefore determines an increased amount of
transmission grid capacity requirements. Additionally, the Plan misses to prioritize
proposed HVDC projects. The calculations in this chapter demonstrate high differences
in the significance of individual HVDC lines. This finding calls for a prioritization of
lines. In an amendment to the National Development Plan – posterior to the publication
of this work -the Federal Network Agency did indeed reshuffle the list of expansion
projects and propose some priorities (BNetzA 2012).
1.5.2 Insights in methodology
Trials with the decomposition of a linear optimization problem proved hardly useful in
the context of a small model application as used in Chapter 2. Troubles to show the
advantages of decomposition in terms of computation speed were also stated in related
work from presenters at research conferences. If integer-type decisions are embedded in
the optimization process, there seems to be some use of decomposition according to
recent analysis of Goerner and Abrell (2011) as well as Gunkel and Kunz (2012).
Chapters 4 and 5 show that modeling markets with equilibrium models and market power
exertion under hourly dispatch with inter-temporal restrictions is hardly promising but
rather cumbersome computation-wise. Inter-temporal restrictions increase the
computation time of the problem dramatically while the market power assumption
heavily affects results and produces numerous outliers. The sensitivity of the results
regarding market power raises the question whether the actual (moderate) behavior of
market power exertion can be truly represented in simple Cournot competition models.
In chapters 6 and 7, I witnessed CPLEX to be a powerful solver for a large-scale
application to European power markets in a non-linear model. I also discovered the
usefulness of centralized computers (with parallel computing facilities). Advances in
computer technology make it possible to calculate increasingly complex and thus realistic
models.
Chapters 2 and 4 include some form of stochastic optimization. Challenging computation
owing to the ‘curse of dimensionality’ in dynamic programming (Birge & Louveaux
1997) limited model complexity and insights into stochastic optimization: However, I
have gained a basic understanding of the performance of stochastic models in comparison
to deterministic counterparts. This understanding can be useful when applying more
advanced methods of stochastic optimization in future.
1.5.3 Perspectives for future research
This Thesis provides the foundation for future work in several areas. For instance, the
model applied in chapters 6 and 7 would benefit from a revamp of the input data.
Essentially, the use of more distinguished datasets for countries else than Germany would
be needed to draw conclusions about investment behavior outside Germany. Weather-
dependent feed-in time series of solar and wind power are amongst the most important
datasets to drive results.
Chapter 1 - Introduction
15
A shortcoming of the works in chapters 2 and 4 is that uncertainty in several input
parameters is not represented in great detail. As the treatment of uncertainty is becoming
increasingly relevant in many contexts, it should ideally be taken care of with greater
sophistication. Extensions of the models could be some more profound econometric
underpinnings of stochastic processes through simulated (jointly correlated multivariate)
time series and a quantifiable basis for transition probabilities between scenarios. Adding
to this, a reflection of risk aversion and particular risk management strategies would
make the model representation much more realistic.
1.6 Statement of contributions
The chapters in this thesis are the result of collaborations with the Thesis Supervisors Prof. Dr.
Christian von Hirschhausen, Prof. Dr. Claudia Kemfert and additional colleagues, as indicated
below. The author of this thesis has made substantial contributions to all chapters covering
conceptual design, data compilation, technical model development and writing. The
collaborations took on different forms as detailed hereafter.
Chapter 1 - The introduction has not been published elsewhere before. It is my own production.
Chapter 2 - I published chapter 2 as single author paper in Applied Energy. The publication is a
result of an earlier collaboration with the TU Berlin students Jan Siegmeier and Murk Creusen.
The development of an intial model version was done in collaboration with the TU students
while its final implementation and writing of a manuscript has been performed by me.
Chapter 3 - The work on chapter 3 was led by me. Dr. Thure Traber contributed to this work by
reviewing the text and assisting in the implementation of the ESYMMETRY model, which has
been previously developed by him and Prof. Dr. Claudia Kemfert.
Chapter 4 - The newly developed model is a modification and conjunction of two models
(EMELIE, ESYMMETRY) developed by Dr. Thure Traber and Prof. Dr. Claudia Kemfert
earlier on. Building on their earlier models, I developed a revamped model and application and
produced a paper out of it as single author. I was fully responsible for model programming and
implementation. Some input data was taken over from earlier publications of Dr. Traber and
Prof. Dr. Kemfert. Most of the input data was updated in accordance with own research.
Chapter 5 - This chapter has been lead-authored by me with significant input from Dr. Thure
Traber and Prof. Dr. Claudia Kemfert. Dr. Thure Traber provided the initial model code, also
used in chapter 4. While Thure was responsible in renewing some basic features of the model
code, I was main responsible for the implementation and analysis of model runs and the writing
of the manuscript. Thure and Claudia provided valuable input in fine-tuning the manuscript and
graphics as well as coding the model and eventually assisted in the model implementation. The
intern Lukas Schmid helped in coordinating with the Energy Modeling Forum (EMF 28).
Chapter 1 - Introduction
16
Chapter 6 - This work results from a study group at Technical University Berlin composed of
Jenny Boldt, Lisa Hankel, Lilian Charlotte Laurisch, Casimir Lorenz, Felix Lutterbeck, Pao-Yu
Oei, Aram Sander, Helena Schweter, Philipp Sommer and Jasmin Sulerz. I adopted a key role in
data compilation, model development, implementation and the writing of the final publication.
The work makes use of the ELMOD database on electric grid characteristics available at TU
Berlin/TU Dresden. The participating TU students contributed in updating the ELMOD database
and reviewing other key input data for the model as well as text writing. The development of a
model code from scratch lied in the main responsibility of Pao-Yu Oei and me.
Chapter 7 - The work on chapter 7 is a result of collaboration with Maximilian Bracke, with me
as lead author. The work builds in large parts upon the model developed with TU Berlin students
in chapter 6 and therefore relies on the ELMOD database of TU Berlin/TU Dresden. Major
modifications in model programming, input database and scenarios were performed by me.
Maximilian Bracke helped in compiling the literature review.
All chapters of the dissertation are linked to publications in different formats and media,
including SSCI-ranked scientific journals. An earlier version of Chapter 2 is published in the
Elsevier journal Applied Energy. An earlier version of chapter 3 has led to a published article in
Energy Policy. The fourth chapter on power plant investment has produced three publications:
One in the proceedings of the conferences EURO 2012, one at the Verein fuer Socialpolitik 2012
and one submission to the journal Energy Systems. A modified version of the text of chapter 5 is
submitted to a special issue in the journal Climate Change Economics in the Energy Modeling
Forum (EMF 28) framework. The text of the 6th chapter on transmission grid investment was
elaborated as policy-oriented paper which is brought to a broad audience through the magazine
Energiewirtschaftliche Tagesfragen, a TU Dresden Working Paper, a DIW Wochenbericht, as
contribution to the public consultations of the National Grid Development Plan 2012 and as
Energy Policy publication. One version of chapter 7 on the integrated planning of power plant
expansion and grid congestion is published in the proceedings of the IAEE European Conference
2012 and as DIW Discussion Paper. An overview of publications can be found in the following
table.
Chapter 1 - Introduction
17
Chapter 2
Schroeder,
Siegmeier,
Creusen (2011)
Modeling Storage and Demand Management
in Electricity Distribution Grids
DIW Discussion
Paper 1110
Schroeder (2011)
Storage and Demand Management in Power
Distribution Grids.
Applied Energy, 12,
4700-4712
Chapter 3
Schroeder, Traber
(2012)
The Economics of Fast Charging Infrastructure
for Electric Vehicles
Energy Policy, 43,
136–144
Chapter 4
Schroeder (2012)
An Electricity Market Model with Generation
Capacity Investment under Uncertainty
VfS 2012 and EURO
2012
Chapter 5
Schroeder,
Traber, Kemfert
(2013)
Energy Modeling Forum 28 model paper
DIW DP and Climate
Change Economics
subm. 01/2013
subm.
Chapter 6
Boldt et al.
(2012)
Renewables in the Grid – Modeling the
German Power Market of the Year 2030
TU Dresden WP-
EM-48
Schroeder et al.
(2012)
In Ruhe planen: Netzausbau in Deutschland
und Europa auf dem Prüfstand
DIW Wochenbericht
Nr. 20
Hankel et al.
(2012)
Stellungnahme zum NEP 2012 Strom
NEP 2012
Stellungnahme
Schroeder et al.
(2013)
The Integration of Renewable Energies into the
German Transmission Grid - A Scenario
Comparison
Energy Policy, 61,
p.140-150
Oei et al. (2012)
Szenarienrechnungen zum
Netzentwicklungsplan
Energiew.
Tagesfragen 9/2012
Chapter 7
Schroeder,
Bracke (2012)
Power plant expansion and grid congestion
DIW Discussion
Paper 1250
Chapter 1 - Introduction
18
Chapter
2
3
4
5
6
7
Type of model
LP
MCP
MCP
MCP
QCP/ NLP
QCP/ NLP
Objective function
Cost min
Profit max
Profit max
Profit max
Welfare max
Welfare max
Demand function
Linear elastic
Iso-elastic
Linear elastic
Linear elastic
Linear elastic
Linear elastic
Endogenous investment
Storage & DSM
-
Power plants
Power plants
-
Power plants
Competition
perfect
imperfect/ perfect
imperfect/ perfect
imperfect/ perfect
perfect
perfect
Uncertainty
Demand, RES prod.
-
Fuel prices
-
-
-
Grid
DC load flow
-
-
Piping model
DC load flow PTDF
DC load flow PTDF
No. nodes
5
-
-
15
41
41
No. lines
4
-
-
30
231+36
231+36
No. technologies
6
15
15
15+3
6
6
Storage
Pump, battery
-
-
-
Pump
Pump, battery, aCAES
DSM
Household
-
-
-
Household, Commerce,
Industry
Household, Commerce,
Industry
Time resolution
24h
168h
24h-120h
24h
4 x 168 = 672h
8760h
Reference year
2010
2010
2010
2010
2010
2011
Geo coverage
Local
Germany
Germany
EU27+CH+NO
Subset of Europe
Subset of Europe
Software/ Hardware
GAMS, 32-bit Windows
GAMS, 32-bit Windows
GAMS, 32-bit Windows
GAMS, 32-bit Windows
GAMS, 32-bit Windows
GAMS, 64-bit LINUX
Solver
CPLEX
PATH
PATH
PATH
CPLEX
CPLEX
Related Publications
Schroeder (2011)
Schroeder, Traber (2012)
Schroeder (2012)
Schroeder, Traber (2013)
Boldt et al. (2012)
Oei et al. (2012)
Schroeder et al. (2012)
Schroeder, Bracke (2012)
Journals
Applied Energy 88
(2011)
Energy Policy 43 (2012)
Verein fuer Socialpolitik
2012;
EURO 2012
Subm. to Climate Change
Economics EMF 28
Special Issue
Energy Policy forthcom.
DIW Wochenbericht
En. Tagesfragen 9/2012
DIW DP; Subm. to
Energy Systems
Table 1: Overview of models in different chapters
(Source: Own compilation)
Chapter 2 – Storage and Demand-Management in
Distribution Systems
Chapter 2 – Storage and Demand-Management in Distribution Systems
20
2.1 Introduction
Since electricity demand and the availability of output from RES are intermittent by nature,
system operators have to resort to relatively costly measures such as reserve energy and re-
dispatch to maintain system stability. Back-up capacities are set to become more relevant with
increasing shares of RES penetration. In this context, storage devices serve to store excessive
electricity generation and feed-in missing energy in times of need. An alternative concept of
better aligning demand and supply of electricity through two-way digital communication
technology is commonly referred to as 'smart metering'. Measures to manage demand with the
help of smart meters include demand response and direct load control. Recent legislation
obliges German grid operators and utilities to install smart metering systems in new and
refurbished dwellings. While legislative pressure spurs investment in smart metering, it may
imply a negative effect on investment incentives in storage.
This analysis scrutinizes load control and storage facilities as potential concurrent options
targeting at electricity generation cost reductions and it quantifies possible substitution
effects. Because of their common purpose, direct load control and centralised storage are two
competing or possibly complementary solutions from the perspective of a vertically integrated
power distribution system operator and utility. Moreover, it is tested whether storage and load
control could alleviate the need for grid reinforcements by avoiding capacity shortages. The
idea is that avoided shortage adds value to storage or DSM devices because of capacity
upgrade deferral and added electricity sales (Pudjianto et al. 2006). Additionally to these
issues, a methodological purpose of this work is to demonstrate how stochastic optimization
and Benders decomposition method can be sensibly applied to analyze and compare
investment options in a power distribution system setting. The focus lies on short-term
uncertainties and their impact on investment decisions.
There exists a broad range of literature dealing with storage sizing decisions. Diaf et al.
(2007), Arun et al. (2008), Kapsali and Kaldellis (2010), Martin et al. (2010) and Troncoso
and Newborough (2010) perform numerical optimizations in a deterministic setting.
Applications of stochastic patterns of generation and demand can be found in Ekren et al.
(2009), Ekren and Ekren (2009), Ekren and Ekren (2010) and Tan et al. (2010). Tan et al.
(2010) present a stochastic optimization model of battery sizing for demand control with
emphasis on outage probabilities which is not dealt with in this analysis. Roy et al. (2010)
apply stochastic wind generation patterns to a wind-battery system sizing model with
deterministic demand. IEA (2010) do likewise with Plug-in EV as storage facilities.
The combination of intermittency of RES and DSM is addressed in Moura and de Almeida
(2010) and Giannoulis and Haralambopoulos (2011). Concerning DSM, numerous research
publications were found on investment decisions into DSM or related operational questions as
in Manfren et al. (2011). Lee et al. (2007) assess investment into load management systems
for heating in a national case study for Korea. Paulus and Borggrefe (2011) adopt a system-
wide perspective of investment in DSM in a case study for Germany with focus on industrial
consumers. Neenan and Hemphill (2008) investigate investment from a societal perspective
while Strbac (2008) and Electricity Journal (2008) find that investment into DSM appliances
might not be all that profitable in general. It is intended to further investigate this claim in the
present analysis.
The contribution here is unique in that no study explicitly compares the cost saving potential
of storage and DSM in a comprehensive model including grid representation, endogenous
investment and factors of uncertainty. Whilst an 11kV distribution network representation in
combination with a benefit analysis for storage and demand response measures can be found
Chapter 2 – Storage and Demand-Management in Distribution Systems
21
in Wade et al. (2010), the present work complements their analysis by adding endogeneity to
the investment into storage devices and DSM appliances as well as uncertainty of demand and
wind generation. A further contribution consists in the application of Benders Decomposition
Method to the stochastic program. Decomposition methods can be applied to numerous bi-
level optimization problems in the energy sector, such as unit-commitment or capacity
expansion. To the author’s best knowledge, an application to evaluating storage and DSM
infrastructure investment is unprecedented.
The chapter is divided into a descriptive part, including the methodology and model
description, an explanation of parameters and scenarios applied. Subsequently, results are
outlined, discussed and final conclusions are drawn.
2.2 Model Description
A basic direct current (DC) load flow model (Leuthold et al. 2008) is adapted to a situation
with DSM and storage management. The model is designed as linear program under a cost
minimization regime with hourly time resolution of two exemplary holidays (winter/summer).
It is coded in General Algebraic Modeling System (GAMS) and can be solved with the solver
CPLEX (GAMS 2011). A vertically integrated system operator and utility is considered as the
cost minimizing agent. As explicated before, the aim of the operator is to reduce generation
cost by performing load management through storage and DSM. The agent can decide on
whether to invest in storage and DSM technology as well as how to operate it. Still, the
operator is able to shift the vertical demand curve left and rightwards through direct load
control. The extensive-form cost-minimisation objective reads as follows.
(2.1)
Objective
(extensive form)
The agent minimizes generation cost (cg · G) of each technology s as well as investment cost
of DSM (Id · cd) and storage (Is · cs). Besides generation and investment, the agent can
manipulate storage in- and outflow (Sin and Sout), shed or induce consumption (D) and transfer
electricity from one node to another (P), subject to constraints detailed below. All variables
are positive.
On the demand side, consumers are aggregated at each of the 10kV/0.4kV sub-station nodes
n. Thus, a diurnal pattern of consumer demand (without DSM and storage), denoted by q, can
be approximated using standard averaged load profiles weighted by the number of customers
at the respective node. A perfectly inelastic, hence vertical demand function is assumed. This
is a fundamentally different approach to demand response studies (Aalami et al. 2010;
Moghaddam et al. 2011) and suitable here, since the focus lies on the producer side. There is
no demand response. The consumer demand q is supplemented by contributions from DSM
and charging of a battery. Note that demand is treated as stochastic parameter and it thus
depends on the set sc.
Demand, supply and network flows constitute the energy balance constraint per node (2). It
incorporates the simultaneity of generation and consumption as well as the first Kirchhoff
rule.
Chapter 2 – Storage and Demand-Management in Distribution Systems
22
(2.2)
Energy balance
On the supply side, a setup is considered where each generation technology s
S at time t
T
and node n
N contributes an amount G to total electricity generation at marginal unit cost cg,
up to its capacity limit gmax, which is exogenous, time-dependent and treated as stochastic
parameter.
(2.3)
Generation limit
Ideally, investment decisions relating to DSM and storage should consider grid infrastructure
constraints because load shifting may serve as a mean to avoid capacity shortage and system
outage probability. Pudjianto et al. (2006) explicitly take into a ccount thi s “delaying capacity
replacement” value of DSM devices when appraising the worthiness of DSM. In the model
presented here, a number of grid-related constraints are included in order to study the grid
impact of storage and DSM operation. The topology of a lossless DC network with L lines is
described by the L x N network adjacency matrix lm, where lm = 1 means that line l
L starts
at node n, while lml,nn = -1 means that it ends at node nn. Weighting each line with the inverse
of its reactance x, the matrix h (4) can be obtained and thus the network susceptance matrix b
(5). If the phase angle of node n at time t is denoted by P, the flow along line l at time t is
given by equation 6, where the sign of lf depends on the direction of the flow. Since P is
defined relative to a reference bus, slackness conditions slack · P = 0 hold, and a slack(1) = 1
is chosen (that is, P = 0) to set node 1 as the reference node (8). Physical line capacity
constraints are included (7). In a DC network, only the thermal limit is relevant. If the grid
capacity constraint was violated -which turns out not to be the case in this specific
application- the operator would incur losses through foregone sales of electricity.
Additionally, the capacity shortage is fixed manually ex-post, a penalty cost is applied and the
model is re-run with new capacity figures.
(2.4)
Weighted Network Matrix
(2.5)
Network susceptance
(2.6)
Line flow
(2.7)
Line flow limits
(2.8)
Flow convention
The second set of constraints relates to DSM. Investments in load control infrastructure for
DSM have the benefit of allowing inter-temporal shifts of electricity demand. When direct
load control is made possible, parts of electricity consumption may be shifted to earlier or
later stages up to power limits dneg and dpos, respectively (9). The system operator does this
with the aim of saving cost. dneg represents the power limit of energy that can be saved at each
time by shifting load away to another period of the day. Accordingly, dpos is the potential that
can be added at each time. Note that both parameters are defined as positive numbers while
Chapter 2 – Storage and Demand-Management in Distribution Systems
23
contributions must balance to zero over time (10). The option for DSM is reflected in an
additional contribution to total demand, D.
DSM appliances may yield peak load reductions and thereby justify infrastructure
reinforcement deferral. However, it is disregarded that the installation of DSM appliances
could yield overall demand reductions. This is done not only because projections of demand
reduction through DSM devices appear to be fairly uncertain and consumer-specific, ranging
between zero and 20% (Papagiannis et al. 2008; EcoFys 2009; Moura & de Almeida 2010).
The focus is on direct load control exerted by the system operator. Demand response
measures and related consumption savings driven by consumer behavior are beyond the scope
of this operator´s cost-minimization model.
Storage facilities in the distribution network can take up a positive charge Sin at time t,
convert it (with some loss e) and subsequently provide positive amounts Sout, where the
overall balance is governed by capacity constraints (12) as well as input and output kW power
constraints, which are set equal to kWh capacity constraints for reasons of simplicity (13).
Note that energy capacity is set equal to power limit and that there is no continuation value of
left-over storage since the storage device is empty at the last time period (11).
(2.9)
DSM Limits
(2.10)
Constant total demand
(2.11)
Storage balance
(2.12)
Storage capacity limits
(2.13)
Storage power limits
(2.14)
Non-negativity
Figure 1: Algorithm used for solving the two-stage problem.
(Source: Own illustration)
The problem is formulated as two-stage stochastic optimization program, with initial
investment at the first stage and operative optimizations at the second stage, see Figure 1.
Benders Decomposition Method is applied with conflicting variables being initial investment
levels into storage and DSM (Birge and Louveaux 1997). The first-stage (master) and the
second-stage (recursive sub-problem) are successively solved in loops until convergence of
the upper and lower level objective is reached. In this case, the sub-problem objective
Chapter 2 – Storage and Demand-Management in Distribution Systems
24
represents the upper bound as a restriction of the initial problem and the master problem
yields a lower bound as a relaxation of the initial problem. The solution algorithm stops if the
difference between the minimum upper bound and the current lower bound is less than or
equal to a very small number; otherwise the algorithm continues. Benders optimality cuts are
added to the problem set of constraints after each iteration. Moreover, feasibility cuts ensure
that infeasibilities in the sub-problem due to misallocations in the master problem are ruled
out, see Figure 1. The Benders approach reduces computation effort as compared to solving
the extensive form expected-value-problem.
(2.15)
Master Objective
(2.17)
Sub objective
(2.18)
Fixing variables to results of
Master Problem
The relaxed master problem objective (15) includes α, the objective value of the sub-problem
and is restricted by the Benders cut (16). The recursive sub-problem objective function is
equation 17. Concerning the Benders cut, λd and λs correspond to the duals of the constraints
(18) which fix the variables Id and Is to their values resulting from the corresponding master
problem. αiter is a decision variable setting the lower bound to the recourse problem after each
iteration iter. Note that the iteration counter is added in the variable sets in equation 16 unlike
all previous equations.
2.3 Application to a simple distribution system
This section describes the application of the presented model to a simple five-node 10kV
medium-voltage-grid with characteristics representative for a typical distribution system
structure in sub-urban Germany. Assumptions regarding the application are detailed hereafter.
2.3.1 Generation
Nine technologies are part of the generation mix in this application: Six technologies – hydro,
nuclear, lignite, hard coal, gas and biomass – have generation capacities with full availability
at any time (up to a technical factor, e.g. due to maintenance requirements, taken from EWI et
al. (2010)). Three technologies have varying availability, with wind output being treated as
stochastic parameter. Small-scale heat-controlled CHP diurnal patterns follow an
approximation in Pudjianto et al. (2006) for both winter and summer and they are weighted by
a seasonal factor to account for higher heating demand (and thus more electricity supply)
during winter. Likewise, Photovoltaic power (PV) exposes different daily profiles by season
adapted to a central German location (Jahnke 2012).
(2.16)
Benders cut
Chapter 2 – Storage and Demand-Management in Distribution Systems
25
Available energy (per day, aggregated over all nodes)
demand peak [kW]
1100
Technology
Wind
PV
CHP
Biomass
Hydro
Nuclear
Lignite
Coal
Gas
Total
Type
Source
time-
dependent
time-
dependent
time-
dependent
flexible
flexible
flexible
flexible
flexible
flexible
installed capacity
(Germany 2020) [GW]
EWI et al.
(2010)
40.9
33.3
4
7.85
7.7
6.7
22.4
28.5
24.4
175.75
electricity generation
(Germany 2020) [TWh]
EWI et al.
(2010)
94
31
20
37
7.5
49.2
145.2
120.2
40.4
544.5
capacity utilization
(where relevant)
Calculation
10.6%
57.1%
technical availability
(where relevant)
EWI et al.
(2010)
88%
90%
93%
86%
84%
84%
installed capacity [kW]
(in model)
Calculation
537.44
437.57
52.56
103.15
101.18
88.04
294.34
374.50
320.63
2309.42
available energy, per day
[kWh] (in model)
Calculation
varying
varying
varying
2178.57
2185.51
1965.07
6075.27
7549.94
6463.81
31638.31
Technology
Wind
PV
CHP
Hydro
biomass
nuclear
lignite
coal
gas
Marginal cost [EUR/MWh]
0
0
0
0
0
10
40
38
70
Table 2: Available capacity and projections of marginal generation cost incl. carbon cost
in 2020.
(Source: Based on EWI et al. (2010))
Figure 2: Frequency and power output under different wind speeds (average 5.22 m/s).
(Source: Own production based on Roy et al. (2010))
Figure 3: Simulated diurnal profiles of mean wind speed and output in winter (right).
(Source: Own production)
Chapter 2 – Storage and Demand-Management in Distribution Systems
26
Figure 4: Feed-in and load of non-power-metered consumers in 2010 in NEW grid.
(Source: NEW Netz (2012))
It is assumed that generation capacities are distributed differently between the nodes of the
small network – while the bulk of power will be available via the grid supply point, some of
the CHP, PV and biomass capacity is located at the demand nodes. These assumptions are
summarized in the parameters gmax, specifying the maximum available power from each
generation technology per time slot and per node. Incremental generation cost is illustrated in
Table 2. The figures are independent from the utilization rate of a generation technology.
Special attention is given to generation data of wind power which is treated as stochastic
parameter. A Weibull probability distribution is used to create random samples of wind
speeds just as in Roy et al. 2010). Equation 19 includes w, the wind speed, r, a random
number uniformly distributed between 0 and 1, a scale and a shape parameter k and m. The
shape parameter equals 2 (typical for Central Europe) and the scale parameter varies by time-
of-day (Ekren et al. 2009; Roy et al. 2010; Giannoulis & Haralambopoulos 2011) and it is
calibrated to match a typical on-shore location in the center of Germany.
(2.19)
Inverse of the Weibull
cumulative distribution
function
Knowing that energy potential per second (the power) varies in proportion to the cube of the
wind speed (in m/s) it is then possible to calculate actual wind energy production in kWh. The
number of wind rotors and their conversion efficiency are calibrated so as to match a share of
wind energy in total production conform to projections in EWI et al. (2010). Cut-in, rated and
cut-out wind speeds are indicated in Roy et al. (2010). To align with the size of the model grid
the maximum wind power output is scaled down to 537.44 kW with 800 m2 of installed rotor
surface. The simulated random diurnal profiles (Figure 3) of wind output are validated against
observed data in Giannoulis and Haralambopoulos, (2011), Niederrheinwerke (2011) (Figure
4) and simulations in Roy et al. (2010). The fact that wind speed is simulated as a Markov,
non path-dependent, stochastic process may imply an over-valuation of investment into
flexible storage and DSM.
Chapter 2 – Storage and Demand-Management in Distribution Systems
27
Investment decisions into storage and DSM consider a long time frame and confront with
uncertainty about the future generation technology mix. Whilst an investment appraisal
should consider today’s investment cost, generation cost reductions accrue in the uncertain
future and should therefore be estimated accordingly. From the perspective of 2011, the year
2020 is a reasonable representative ‘average’ year regarding the penetration of RES over the
life-time of a storage or DSM investment. Therefore, a hypothetical generation limit of each
generation technology is derived from a forecast for the year 2020 given in EWI et al. (2010).
The available installed capacity in Germany is scaled down. The share of installed capacity
versus yearly peak demand in the model network corresponds to that of the national grid
(EWI et al. 2010). Optimized generation profiles are outlined in the results section.
2.3.2 Demand
360 dwellings are assumed to be connected per 10kV-0.4kV transformer. Each consumer unit
is equivalent to a 1.99-person household, a representative mix for Germany (EWI et al. 2010).
The share of commerce and households is 21% and 79% in the model. The industrial sector is
left out in the model because – by law - industrial consumers are already equipped with
appliances for DSM when yearly consumption exceeds 100,000 kWh.
Figure 5: Sampled demand profiles in winter and summer.
(Source: Own production based on BDEW (2010))
Figure 6: Convergence of sample demand mean with an increasing amount of scenarios.
(Source: Own production)
Chapter 2 – Storage and Demand-Management in Distribution Systems
28
Figure 7: Deterministic mean standard load profile.
(Sources: Own production based on BDEW (2010), Grein et al. (2009) and NEW Netz (2012))
A random sampling method is utilized for the simulation of demand realizations. Random
sampling techniques are popular in risk analysis and used in research on electricity topics
(Tan et al., 2010; Roy et al., 2010). Simulated stochastic demand values (Figure 5 and Figure
6) are drawn from a normal probability distribution with time-varying mean and standard
deviation under the assumption of independence between wind power output and demand.
The simulation creates 50 profiles which include the possibility of very extreme events. The
mean values of demand realizations are taken from BDEW (2010) and averaged over months
and types of day so as to create two single daily mean profiles per year with 24 hours each
(summer/winter) as indicated in Figure 7. Standard deviations of demand variability are
known to the optimizing agent based on empirical demand realizations at the EEX wholesale
intraday market (EEX 2012). Deriving medium-voltage demand variability from wholesale
market demand fluctuations is reasonable for model systems with aggregation of a high
number of consumers. The more consumers are aggregated, the less volatile is energy
consumption (Widen & Waeckelgard 2010). Fluctuating demand profiles outlined in
Giannoulis and Haralambopoulos (2011) and Grein et al. (2009), projected profiles for 2020
in Moura and de Almeida (2010) and empirical data in Widen et al. (2009) and
Niederrheinwerke (2011) were consulted for validation of the sampled demand profiles here.
Maximum and minimum sampled demand in the modeled system figures at 1,100 kW and
240 kW, excluding EV. This is a spread of factor five and a deviation of 60-90 % around the
average system demand (561 kW). Empirical data from 2010 in NEW Netz (2012) exposes a
spread of factor 4 between peak and lowest demand. For an isolated island with 90,000
inhabitants, Giannoulis and Haralambopoulos (2011) show that the spectrum of demand
values ranges 75-100% of the mean value either way while maximum and minimum yearly
demand differ by factor eight. The spread of demand simulations in the model system here is
thus comparable with empirical profiles at other distribution systems.
In this application electricity consumption of EV is incorporated into the stochastic reference
demand q. A load pattern is assumed with 8 hours domestic charging time at a rate of 1.6 kW,
referred to as Level 1 charging speed, see Figure 7. A full charge per night (12.8 kWh) would
correspond to a 100 km range. Note that EV are not equivalent to storage facilities in the
model. This implies no vehicle-to-grid technology is considered here. Uncontrolled EV solely
Chapter 2 – Storage and Demand-Management in Distribution Systems
29
behave as additional consumers whose load can be curtailed and shifted if DSM appliances
are installed. Charging behavior is under full control of the system operator if the EV is
connected to a smart meter. Different penetration rates of EV are tested from zero to 10%.
2.3.3 Load control
The DSM potential for average households and commerce is derived from a study report for
the City of Mannheim, Germany (Grein et al. 2009) and triangulated with Stadler (2008). EV
availability is added to the DSM potential. The resulting potential can be observed for each
time slice in Figure 7 and Figure 12. Figure 7 plots an average load profile for a household
with the corridor of maximum and minimum load when DSM appliances are installed.
Positive and negative shifts are possible and their potential is asymmetric. The potential to
increase energy load at each time, dpos, is generally larger than dneg.
The total cost of equipment for DSM figures in between 160 and 350 EUR per installed
system EcoFys (2009). The application here refers to the so-called Advanced Metering
System (AMM), which includes two-way communication via an integrated router gateway in
each dwelling. This system enables time-of-use pricing and direct load control up to the
capacities detailed in Figure 12. The cost figure includes investment into hardware such as
meter, gateway, router and its initial installation. In order to calculate lifetime cost, a 6.5%
annual discount rate is applied with a lifetime of 16 years (EcoFys 2009).
2.3.4 Storage
The model considers investment into a central large-scale stationary battery with endogenous
capacity and conversion efficiency factor of 75%. The focus is on batteries instead of
mechanical conversion systems (pumped hydro, compressed air storage) for batteries require
little up-front installation cost. To account for different battery technologies, the cost input
data is varied. Approximated cost data of equipment and installation is compiled in Table 3
for reference (Doughty et al. 2010; Electricity Storage Association 2011).
Conversion
Storage type
EUR/kWh
EUR/kW
Cycles (100%)
Efficiency
Mechanical
Supercapacitor
3,800-4,000
100-400
10,000-100,000
95-100 %
Flywheels
1,000-3,000
300
20,000-60,000
90-95 %
Pumped Hydro
60-150
500
20,000-50,000
70-85 %
Compressed Air
30-120
550
9,000-20,000
70–80 %
Electro-
chemical
Nickel-metal hydride
700-800
-
500-3,000
65 %
Nickel-Cadmium
350-800
175
1,000-3,000
60-70 %
Sodium-Sulfur
200-900
150
2,000-3,000
85-90 %
Lithium-Ion
200-500
175
3,000-6,000
95-100 %
Vanadium Redox-Flow
100-1,000
175
2,000-3,000
75-85 %
Zinc-Bromine
50-400
175
> 2,000
70 %
Lead Acid
50-300
175
200-1,100
75 %
Table 3: Storage investment cost data compiled from various sources.
Mechanical bulk storage included for reference but not considered in the calculations.
(Sources: EcoFys (2009), Doughty et al. (2010), Electricity Storage Association (2011))
Chapter 2 – Storage and Demand-Management in Distribution Systems
30
In the cost considerations, a life-time of 3,000 cycles is assumed at 80% depth of discharge
with one cycle being completed every three days, hence a life-time of 12 years. To facilitate
tractability and increase computation speed, the three dimensioning vectors of a storage unit –
capacity in kWh, charge rate and discharge rate in kW - are all set equal in this analysis. Such
assumption is justifiable in a setting with hourly time resolution where ramping constraints
and thus power limits are of secondary importance in contrast to capacity limits. In the real
world, actual batteries often feature hourly power limits as high as energy capacity limits.
This holds true notably for storage devices that serve as reserve for capacity markets.
2.3.5 Grid
A stylized configuration is simulated with characteristics that approximate realistic grids, as
illustrated in Figure 8 (Fletcher & Strunz 2007; Niederrheinwerke 2011). The grid
representation used in the case study here consists of five nodes, one of them the grid supply
point (GSP) and additionally demand nodes with 10kV/400V transformers. The nodes are
connected in line so as to simulate a ‘worst-case’ topology. The analysis restrains to the
10kV-level of a stylized distribution network. An application of the presented DC flow model
to a 400V level is delicate for the DC load model does not include reactive power. At 400V
level, voltage drop limits and reactive power are of high relevance. Large-scale generation,
including wind turbines and pump storage, is assumed to be connected at the 10kV level,
whilst DG and EV are part of the underlying 400V grid. 10kV overhead lines have a lateral
surface of 70 mm2 with associated capacity of 185 Ampere. In a 10kV DC setting this results
in a maximum capacity limit of 1,850 kW. A typical reactance of the 10kV network is around
0.4 Ohm/km (Pudjianto et al. 2006; Fletcher & Strunz 2007). Upgrade costs of overhead
circuits in a comparable 11 kV grid lie at 3,102 EUR/MW/km (Pudjianto et al. 2006). It is
assumed all lines are 2 km long and line flows do not incur transmission losses. Grid
reinforcements are not included as variable in the model equations delineated above but
calculated ex-post in case grid capacity represents a shortage.
Chapter 2 – Storage and Demand-Management in Distribution Systems
31
Figure 8: Stylized 5-node grid in a reference distribution grid.
(Source: Own illustration and based on Niederrheinwerke (2011))
2.4 Results
The linear problem is implemented in GAMS, using the solver CPLEX 9.0 (GAMS 2011)
with standard options. A 1.3 GHz CPU machine executes the stochastic linear program for
one exemplary day in between 2 and 8 minutes time, depending on cost parameter values. Up
to 20 iterations are needed. The deterministic model is solved within a few seconds time.
In Figure 9, optimal investment curves are interpolated from several mode runs. Storage
devices are found to pay off at investment cost below 850 EUR/kWh of capacity. For
instance, if costs amount to 300 EUR/kWh, storage devices are profitable up to a size of
roughly 0.5 MWh capacity (and MW power limit) in the framework of the model, depending
on the degree of EV penetration. That corresponds to about one fifth of installed generation
capacity (2,309 kW) and one half of peak demand (1,100 MW) in the system. In total, it is
found that less than 1% of aggregated electricity consumption is stored in most scenarios
(Figure 10). Summed over all nodes, there are 309 kWh storage capacity (left graph) and 807
of the 1,440 consumers have DSM appliances installed (right graph). A higher number of EV,
hence additional load, further improves the case for storage devices. Given these numbers, it
can be concluded that even relatively expensive technologies such as Nickel-Cadmium and
Nickel-metal hydride batteries seem to be profitable. In contrast, super-capacitors and
Chapter 2 – Storage and Demand-Management in Distribution Systems
32
flywheels need to severely cut their cost in order to become competitive. 2011 investment
cost lies between 2,000 and 4,000 EUR/kWh.
Figure 9: Investment into storage and DSM under varying investment cost and EV
market penetration.
(Source: Own illustration)
Figure 10: Storage operation, DSM operation and line flows in the course of a day in two
scenarios.
(Source: Own illustration)
Figure 11: RES feed-in, original demand and load after storage and DSM shifts.
(Source: Own illustration)
Chapter 2 – Storage and Demand-Management in Distribution Systems
33
Appliances for DSM prove hardly profitable in the deterministic model setting, which echoes
a finding of Strbac (2008) and Electricity Journal (2008). Likewise, the stochastic model
predicts DSM to be little beneficial in the absence of EV. Only if all-inclusive investment
costs boil down to 200 EUR per consumer, investment into load control technology may
become beneficial. Note that 2009 cost for AMM systems lies 260 EUR and projections for
2020 figure at a minimum of 160 EUR (EcoFys 2009). The break-even point (tolerance
threshold) for investment into DSM increases up to 700 EUR when 10% of consumers own
EV. Such strong shift clearly outlines that a high number of EV induces investment into load
control equipment. When in competition to each other at current cost, investment into storage
devices is thus clearly favored to DSM systems. This effect is minimal or partly reversed
when EV penetration is high. Obviously, storage devices offer more flexibility to load
management than does DSM.
The grid capacity is sufficient for a securely functioning system in all scenarios. Even with
high penetration of EV, grid capacity constitutes no severe shortage since line flows do not
exceed 60% of thermal capacity limits at any time slice and any scenario, as shown in Figure
10 (total limit 1850 kW). Moreover, alternative grid configurations such as a meshed grid
would rather improve the situation. It can be concluded that no grid reinforcements are
required at 10 kV level in the model setting. The grid representation constitutes a stylized grid
with realistic characteristics so as to be able to generalize conclusions to a certain extent.
While the stylized grid seems to be well equipped for additional future loads, this does not
mean grid extensions are not needed at 400 V low-voltage level. In order to undertake studies
at 400 V level, an AC network model would be appropriate. Such model would incorporate
reactive power and voltage drops which are of high relevance in low-voltage grids.
At specific hours in summer, the system exposes an over-supply of RES feed-in. In these
moments, DSM and storage operations are crucial. Figure 10 and Figure 11 illustrate how
load profiles are adapted to better align with RES feed-in. Overall, the system predicts
between 50 and 60% of demand to be covered by RES generation in the absence of storage
and DSM, which is more optimistic than future projections for Germany in EWI et al. (2010)
(34% RES generation by 2020). The use of storage and DSM slightly improves the coverage
through RES. Figure 10 illustrates how line flows narrowly coincide with storage use
indicating that line flows are to a great extent driven by storage operations. It is found that the
introduction of storage devices enhances line flows at certain moments, see Figure 10. This
implies a stronger capacity use rate than in the absence of storage, notably in peak periods, i.e.
midday. All in all, grid system reliability is not affected by storage and DSM operation since
line flows do not exceed a critical bound at any moment, neither with nor without storage and
DSM.
A sensitivity study regarding the presence of EV in the year 2020 is illustrated in Figure 9.
This is done to address the question of how EV modify the value of storage and load control.
Obviously, a high number of vehicle charging augments demand and uncertainty and
therefore strengthens the case for storage devices and DSM. If 10% of the consumers own and
drive EV, investment into DSM appliances is likely to rise by more than 50% as compared to
a world in absence of EV. All in all, results suggest that EV strongly induce investment into
load control facilities. This result pretty much reflects the trivial fact that most EV are sold to
home owners along with smart metering systems. A potential alternative to smart EV home
charging solutions could have been to install central storage devices and let EV owners charge
whenever they like (so-called dumb charging). However, the value of storage increases only
slightly in the EV scenario. This result indicates that installing DSM appliances for EV
owners to allow for smart charging is a much better solution than installing central storage.
Chapter 2 – Storage and Demand-Management in Distribution Systems
34
2.5 Discussion
The application has shown a case where investment into storage is more profitable relative to
DSM systems from an operator’s point of view. Practical and management aspects strengthen
the position of central stationary batteries for storage versus DSM systems. Central storage
devices are much easier to handle than a high number of dispersed DSM systems. The latter
also require decent communication systems for interaction between consumers and supply in
order to be fully effective (Wissner 2011). Furthermore, storage offers a constant load
potential at any time. When installing DSM systems, the availability of DSM potential is
dependent on the consumer and it may temporarily be very low. Thus, storage devices offer
more flexibility as compared to DSM systems. A drawback of storage is that it requires higher
upfront investment cost and it may not go with consumption reductions in general.
Consumption reductions can be reached through demand response programs and the offering
of variable tariffs with the help of DSM systems. This latter effect (demand response) is left
out in the analysis here. Furthermore, storage systems may be more vulnerable to fatigue and
self-depletion and their lifetime might be shortened depending on the charging behavior.
What is the point of using a stochastic model? Results of the deterministic model indicate a
tendency to under-invest as compared to the stochastic model’s outcome. Figure 9 indicates
that deterministic investment levels (dotted line) can be up to 50% lower than in the stochastic
model (continuous lines) for storage. For both, storage and DSM, investment levels are
consistently higher in the stochastic model. The value of the stochastic solution (VSS) is
estimated to figure at around 0.5% to 5% of total system costs, indicating a gain in efficiency
when using the stochastic model as opposed to the deterministic model. The VSS allows us to
obtain the goodness of the expected solution value when the expected values are replaced by
the random values for the input variables. It can be concluded that the cost of disregarding
uncertainty lies at around 0.5% to 5% of total generation costs. On the other hand, the
execution time of the stochastic model with a sample of 50 draws is roughly 15 times higher
than the deterministic model. Computation times largely vary depending on the cost input
data, though. All in all, the stochastic model is superior for it provides efficiency gains at
reasonable additional CPU effort. The deterministic model appears to induce wrong long-term
investment decisions and under-values the flexibility provided by storage and DSM.
The extensive form stochastic model solves in a slightly shorter time than the Benders
decomposition model. If the model was extended so as to diminish stylization, the Benders
model computation time should improve in comparison to the extensive form. This conjecture
is supported by the fact that Benders decomposition is most suitable for outsized problems
characterized by a capacious set of variables, nodes and parameters (Benders 1962). In these
conditions it may be valuable to isolate a group of decision variables and investigate the
problem partially with Benders method. The decomposition model presented here shall
constitute a basis for further models of larger size.
2.6 Conclusions
The analysis here presents a DC load flow model applied to investment in storage and DSM
facilities in a stylized medium-voltage grid. The model incorporates uncertainty in demand
and wind output and uses Benders Decomposition to distinguish the investment choices from
operative optimizations. It is shown how Benders Decomposition method can be
meaningfully applied to a small-scale investment problem in a network-constrained industry.
Chapter 2 – Storage and Demand-Management in Distribution Systems
35
The model is capable of reflecting multiple formats of short-term uncertainties in system
constraints at the operational dispatch stage. Nevertheless, computation time reductions were
not achieved in the small model application presented here.
The model results indicate that grid reinforcements at 10 kV level are not necessary in any of
the scenarios. Capacity utilization rates do not hit the 60% bound, which implies there is little
harm to system stability in the presented application.
Results in this application suggest that storage devices are beneficial at capacity cost of up to
850 EUR/kWh under the stipulated conditions. This implies that relatively expensive storage
technologies such as Nickel-Cadmium and Nickel-metal hydride storage are profitable at
current cost. Flywheels and large-scale capacitors are not competitive unless cost is reduced
to 25% of 2011 cost.
DSM is not beneficial in any scenario, particularly in the deterministic model. Investment is
beneficial up to an all-inclusive cost of roughly 200 EUR per consumer. This break-even
point (tolerance threshold) boosts when consumers own EV, implying that EV strongly
encourage investment into load control systems. The finding reflects the actual fact that most
EV are sold along with advanced (‘smart’) metering systems.
As a logical consequence, it is found that investment into storage is likely to crowd out
investment into DSM appliances in the model setting. Since both options are direct
alternatives for ener gy management, ‘smart meters’ seem to be of little economic value to the
system operator in the absence of EV. Unless governments strongly encourage DSM through
obligations (beyond current obligations) and financial incentives or the promotion of EV,
storage facilities are the better option for a vertically integrated distribution system operator
facing the conditions of this model. The present analysis aimed at modeling conditions that
would be representative for a section of a stylized distribution system in Germany.
It was shown, that the stochastic model produces more efficient solutions than its
deterministic counterpart. The cost of disregarding uncertainty lies at 0.5-5% of total
generation cost. The analysis demonstrates that a stochastic treatment of wind and demand
patterns significantly augments the case for the use of storage. The break-even point for
investment decisions into storage increases from 350 to 850 EUR/kWh when uncertainty of
wind and demand are taken into account. Hence, the deterministic model leads to
considerable under-investment into storage.
All in all, the results are highly sensitive to the assumed investment cost for storage and load
management devices. EV are another cause for variations, yet, to a lesser extent. The
calculations indicate that the value of storage strongly varies with the intermittency of wind
output. The value of DSM is less sensitive to wind but more sensitive to EV penetration.
There are a number of conceptual caveats to the analysis which constitute areas for
improvement. Energy saving through demand response is entirely factored out. The model
may therefore underestimate the value of DSM to a minor extent. Furthermore, the investment
cost for batteries is calculated on a diurnal basis with a fixed number of cycles per day. Fixing
the cycles is a necessary step to obtain an exogenous cost figure but somewhat arguable since
the cycles are endogenously determined in the model. Another drawback of this model is that
some potential business cases of batteries and DSM are not included. Besides peak load
reductions and network reinforcement deferral, Wade et al. (2010) point to other benefits of
using storage devices. For instance, balancing markets as potential business field for batteries
are not included in the present model. Other shortcomings are the stylized grid configuration,
the missing reactive power in the DC load flow model and the absence of ramping constraints
for storage. An application to a grid of larger size is an option for subsequent research.
Chapter 2 – Storage and Demand-Management in Distribution Systems
36
2.7 Appendix
Figure 12: dneg and dpos for households and commercial units in kW during a day. EV
profiles excluded.
(Source: Own production based on Grein et al. (2009) and Widén et al. (2009))
Chapter 2 – Storage and Demand-Management in Distribution Systems
37
Nomenclature
Set
n
node with subset nn (1-5)
l
line (1-4)
t
hour (1-24)
s
technology (wind,solar,PV,CHP,biomass,hydro,nuclear,hardcoal,lignite,gas)
sc
scenario (1-50)
iter
iteration (unlimited)
Variable
D(n,t,sc)
demand shifting (kWh)
Sin(n,t,sc)
storage inflow (kWh)
Sout(n,t,sc)
storage outflow (kWh)
G(n,t,sc,s)
generation (kWh)
Is(n)
investment in storage (both kW and kWh)
Id(n)
investment in a DSM system (absolute number)
P(l,t,sc)
phases angle difference (-)
Parameter
q(n,t,sc)
consumer demand (kWh)
gmax(n,t,sc,s)
maximum generation capacity (kWh)
cg(s)
variable generation cost (EUR/kWh)
cs
levelized investment cost for storage (EUR/kWh and EUR/kW)
cd
levelized investment cost for DSM (EUR/kWh)
e
storage efficiency (%)
dpos(t,n)
positive load shift capacity (kW)
dneg(t,n)
negative load shift capacity (kW)
lf(l,t,sc)
electricity flow (kW)
x(l)
line reactance (Ohm)
b(n,n)
network susceptance matrix (-)
h(l,n)
weighted network matrix (-)
lm(l,n)
incidence matrix (-)
lfmax(l)
maximal capacity for line flow (kW)
slack(n)
slack variable (-)
p(sc)
probability (%)
λs
dual of fixing storage investment in subproblem (EUR/kWh and EUR/kW)
λd
dual of fixing DSM investment in subproblem (EUR per dwelling)
α(iter)
sub-problem objective (EUR)
IsMasterProblem(n)
investment in storage from master problem (both kW and kWh)
IdMasterProblem(n)
investment in a DSM system from master problem (absolute number)
w
wind speed (meter/second)
k
Weibull scale parameter (-)
m
Weibull shape parameter (-)
r
random number with uniform distribution (0-1)
Chapter 3 – Fast Charging Infrastructure for Electric
Vehicles
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
39
3.1 Introduction & Literature Review
It is currently uncertain which charging technology for battery-powered EV will become the
de facto market standard. Besides home charging, the most prominent and most debated
solutions are fast-charging stations and battery-exchange stations. Whilst the necessity of
home-charging solutions is undoubted, little is known about the usefulness and economic
rationale of public fast chargers. The present chapter aims at providing an insight into the
economics of this technology, which is hitherto little explored research-wise but is widely
debated by the public. Public fast-chargers have the benefit of facilitating long-range drives
for EV, and thus could serve as a means to mitigate range anxiety, with EV users having the
opportunity to access public charging infrastructure at times when they are running low on
charge. This factor may be crucial to increase market penetration of EV. Fast charging attracts
EV users for it replicates the ease of conventional refueling and it attracts potential operators
for it appears as being the only type of charging station to potentially promise reasonable
returns. However, the technology has significant disadvantages as it may negatively affect
battery lifetime, electricity system reliability and RES grid integration. For this reason,
several stakeholders support night charging with smart grid applications, while others call for
fast-charging solutions stressing its crucial role as range-extender.
There is relatively little research addressing with EV charging infrastructure, particularly
when it comes to fast chargers. Åhman (2006) reviews public efforts to support EV
deployment in Japan, including charging infrastructure. Likewise, Skerlos and Winebrake
(2010) describe public policies in the United States that address EV, including charging
infrastructure. Brown et al. (2010) delve into EV standards used in the United States where
the infrastructure constitutes an important part of standardization. Nansai et al. (2001) conduct
a life-cycle analysis of charging infrastructure at different public locations in Southern
California with strong focus on environmental effects.
In general, a great deal of literature addresses optimized home charging, which is only a
secondary focus of this chapter. Some research papers also include charging profiles of public
EV stations. Kang and Recker (2009) conduct an activity-based assessment of EV energy
impact and thereby use 1 year travel data to derive a typical charging profile of a public
charging station amongst other findings. Other charging profiles can be found in Markel et al.
(2009), who analyze fuel displacement potentials of EV under various use rates of public
(fast) charging stations. Cost data for fast charging infrastructure can hardly be found in the
peer-reviewed literature but is exposed in project studies (Wiederer & Philip 2010; Morrow et
al. 2008; Slater et al. 2009; Wietschel et al. 2009; PlanNYC 2010).
The present analysis aims at shedding light on the economics of public fast-charging for EV.
An economic valuation that should provide insight in the investment decision for a single fast
charging station by estimating contribution margins is presented. The following research
questions are addressed: At which use rate do level 3 charging investments pay off? Which
markup would be needed? What would be the value of an on-site storage device to
complement the charging system? Results are ought to serve as a basis for an application of a
real options approach to EV charging infrastructure valuation in subsequent research work.
The article is divided into five sections. The introduction is followed by the model
presentation. Subsequently, contribution margins, which arise through the daily operation of a
charging station, are calculated. In this section, it is investigated how on-site storage can
improve the economics of charging stations. We close with a conclusion.
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
40
3.2 Input parameters
Figure 13 illustrates the composition of cost and revenues from the operation of an EV
charging station. The key drivers of turnover are the tariff (markup), power limit and
utilization rates, which in turn are estimated based on assumptions on EV charging and
driving behavior.
Figure 13: Parameters affecting cost and revenue stream.
(Source: Own illustration)
9
3.2.1 Investment cost
Investment cost is compiled for different charging station types in Table 4. Generally, the
industry distinguishes three charging levels. The range extends from level 1 chargers (low-
speed) which are commonly used for home-charging to level 3 chargers (high-speed). Due to
cost and thermal limits it is most efficient to deliver high-voltage electricity in direct current
(DC) directly to the vehicle's battery pack. Such high voltage and high-current charging is
called a DC Fast Charge (level 3) in contrast to less powerful AC charging levels 1 & 2 and 3-
phase AC charge (level 3). CHAdeMO is the first international standard for public Level 3
DC charging solutions. It originates in the Japanese market, is penetrating the United States
and may enter Europe. A large-scale fast charging station network has not been implemented
in Germany until 2010 and it is uncertain whether CHAdeMO or 3-phase AC power will
become the de facto standard for possible applications.
The cost figures compiled in Table 4 include carefully selected numbers. Since the various
sources suggest all different cost figures, the numbers given in Table 4 are merely educated
guesses, discussed with industry experts. The aim is to provide the model with thorough
parameters without any claim for exactness. Total cost of installation varies greatly depending
on the necessity for upstream grid reinforcement. Level 1 and 2 chargers usually require little
grid upgrade. The high power involved in Level 3 charging is beyond the capacity of most
utility transformers serving residential areas. Grid and transformer upgrades may therefore be
required. Additionally, maintenance of on-street charging furniture may also be significant.
As a rule of thumb, annual maintenance and repair figures at 10% of investment cost
according to industry experts. The life-length of a charging spot is estimated at 10-15 years
for level 3 chargers (Wiederer & Philip 2010).
The cost figures compiled in Table 4 include carefully selected numbers. Since the various
sources suggest all different cost figures, the numbers given in Table 4 are merely educated
guesses, discussed with industry experts. The aim is to provide the model with thorough
parameters without any claim for exactness. Total cost of installation varies greatly depending
on the necessity for upstream grid reinforcement. Level 1 and 2 chargers usually require little
grid upgrade. The high power involved in Level 3 charging is beyond the capacity of most
9
O&M = Operation and Maintenance
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
41
utility transformers serving residential areas. Grid and transformer upgrades may therefore be
required. Additionally, maintenance of on-street charging furniture may also be significant.
As a rule of thumb, annual maintenance and repair figures at 10% of investment cost
according to industry experts. The life-length of a charging spot is estimated at 10-15 years
for level 3 chargers (Wiederer and Philip, 2010).
Level 3 DC
public
Level 3 AC
public
Level 2
public
Level 1
public
Station lifetime (years)
10-15
10-15
20
20
Load limit (Volt)
500
400 (3 phase)
230 (1 phase)
230 (1 phase)
Load limit (Ampere)
125
96 (3·32)
32
16
Current
DC
AC
AC
AC
Power limit (kW)
62.5
50
7.3
3.6
Av. duration of 20 kWh charge cycle (min)
19
24
164 (2.74 h)
333 (5.6 h)
Max. number of 20 kWh charging EV/day
75
60
8
4
Calculation of 3-phase power: √ with as a standard value used here.
Material cost (EUR)
40,000
(40,000 – 75,000)
40,000
(40,000 – 75,000)
2,000
(2,000 – 7,500)
1,500
Grid reinforcement cost/civils (EUR)
14,000
14,000
1,000
500
Transformer cost if applicable (EUR)
0 - 35,000
0
0
0
Total CAPEX (EUR)
54,000
54,000
3,000
2,000
Maintenance and repair (EUR/ year)
Rule-of-thumb: 10% of material cost
4,000
4,000
200
150
Total OPEX (EUR)
40,000
40,000
4,000
3,000
Life-cycle investment cost (EUR)
94,000
94,000
7,000
5,000
Table 4: Compilation of information on EV charging station cost.
(Source: Comparison of diverse sources, i.e. Morrow et al., 2008; Slater et al., 2009;
Wietschel et al., 2009; Wiederer and Philip, 2010)
All in all, the cost difference between public level 1 and 2 versus public level 3 chargers
seems flagrant at first glance. Aggregating over all users, though, fast charging infrastructure
is equally expensive with ca. 1,250 EUR per EV. Note, that a single fast charging station can
serve up to 75 users per day, while a level 1 charger is designed for a maximum of 4 users per
day. Hence, almost 20 slow chargers would be needed to equal one fast charging station.
Furthermore, all EV need to be equipped with costly and weightily AC/DC converters, which
are not necessary if batteries are replenished solely through DC fast charging. Hence, if the
entire battery charging system for EV would rely on DC fast charging only, EV owners could
save the cost and weight of additional converters.
The cost of installed recharging posts in Table 4 does not count the expenses required to plan
the deployment and to acquire planning permission. Nor is rental cost for parking spaces
included. This decision is mainly driven by the largely varying cost per space we expect to
see across regions and cities. Furthermore, parking availability is to be a primary concern for
fast charging stations as opposed to level 1 on-street chargers.
Regarding on-site storage adjoined to the charging station, it is assumed that the storage
device has 30 kWh capacity and 30 kW power limit, 85% conversion efficiency rate at total
cost of 6,000 EUR (200 EUR/kW). This can be considered as relatively low-cost device with
standard conversion efficiency.
For the calculations of contribution margins, one must distinguish life-cycle cost and
levelized investment cost. While life-cycle cost refers to total CAPEX, yearly levelized
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
42
investment cost distributes total cost over all years and is calculated as follows, with i being
the interest rate and n the lifetime of the project.
(3.1)
(3.2)
With interest fixed at 4% and a life length of 10 years, we obtain an annuity factor of 0.1233,
which implies a yearly CAPEX of 12.33 % of total CAPEX. A fast charging post with total
CAPEX of 94,000 EUR would thus require a levelized yearly CAPEX of 11,589 EUR. If a
storage device of 30 kWh capacity is added at cost of 200 EUR/kWh, the total CAPEX
amounts to 100,000 EUR which translates into levelized CAPEX of 12,233 EUR/year. To that
figure, one needs to add annual OPEX to obtain total cost.
3.2.2 General demand for fast charging
Since the average vehicle is parked 95% of the time and most of its trips are short (Kempton
& Tomić 2005), it is likely that EV owners will mostly rely on home charging solutions. On
the other hand it can be argued that EV will only spread widely if a critical number of public
charging facilities exist, including fast charging infrastructure.
When it comes to comparing the cost of fast charging infrastructure versus home charging
solutions, there is a clear advantage for home charging. Boxes in garages cost less than 500
EUR, are easy to be installed, little vulnerable to vandalism and no grid reinforcement is
needed. Furthermore, home charging promises to be a good option for controlled charging
operation with RES integration as a primary target. However, national statistics from
household travel surveys in Germany and the United Kingdom indicate that ca. 70% of car
owners do own of-street parking facilities in suburban areas. This percentage drops to below
30% in metropolitan centers, hence areas where EV are set to spread at the outset. In the
United States, Coloumb Technologies estimates there are 54 million garages for ca. 250
million registered cars meaning that a vast majority of cars would need to rely on open
charging facilities. Taking into account hybrid EV and expressed in terms of trips, Kang and
Recker (2009) estimate that 70–80% of all Hybrid EV trips (with 97 km range) can be
powered by home charging. Consequently, a widespread and comprehensive spread of EV
requires public charging options. While a system relying on home charging can serve up to
70-80% of household transportation demand, a comprehensive fast charging system would be
able to cover almost 100% of that demand segment.
In this line, estimations given in Wietschel et al. (2009) imply that roughly 20% of all EV car
owners would require fast charging solutions if all cars were EV; cf. Figure 14. Hence, if 1%
of the whole car fleet in a specific region consists of EV, it should be reasonable to assume
that at least 0.2% of all cars at a gas station with EV charging post are EV. Knowing that a
high-volume highway gas station serves approximately 500-1,500 cars in average per day
(Barnes & Liss 2008), 0.2% translates to an absolute number of one to two cars per day. The
rough estimate is based on the assumption that driving patterns and fuelling customs will
remain unmodified for EV owners when compared to conventional drivers. However, EV
must re-fuel more frequently than conventional cars. We believe the factor of EV charging
frequency versus conventional car fueling to be at two, since the range of conventional cars is
about double the size of EV. Therefore, a general EV adoption rate of 1% could also lead to
an average demand of 2-6 EV/day. All in all, these considerations show how uncertain
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
43
demand estimations are. For this reason, we revert to a scenario analysis with different
demand volumes.
A single CHAdeMO charging spot of 62.5 kW power limit can serve a maximum of 75 EV
slots per day, cf. Table 4. As we consider ca. 50% to be a reasonable maximum tolerable
occupation rate of a station we limit the scenario analysis to between zero and 40 cars per day
[0-800 kWh/day]. When EV adoption rates are higher, a filling station should ideally be
equipped with more than one single fast charging spot in order to avoid unnecessary queuing
of EV users.
Naturally, the degree of competition and the geographical location of a station matters for
demand. However, such particulars are left aside in this analysis, but the situation of a stylized
typical station type is assessed. Note that we exclude hybrid EV, rollers and other non-car EV
as we believe these segments to be marginally relevant for the economics of public fast
charging solutions.
Figure 14: How many EV can be fed through which charging infrastructure?
(Source: Wietschel et al., 2008)
3.2.3 Use pattern
The shape and amplitude of the demand profile strongly influences the profitability of an EV
charging station. Therefore, total demand and the pattern of daily electricity dispatch is a
critical consideration in estimating the business case. Refueling patterns can vary
considerably across geographical sites and across the type of customers served. As discussed
in Barnes and Liss (2008), there are three common fueling patterns which can be cited as (i)
random – vehicles come to refuel as needed; (ii) regular – vehicles refuel according to a
predictable pattern; and (iii) constant – vehicles pool together at a set time and refuel one after
another. We believe the random fueling type to be the most likely pattern for public EV fast
chargers. However, demand is likely to have a predictable (though unplanned) pattern. To
assist in formulating a demand profile, data were gathered and analyzed from key information
sources, including Kang and Recker (2009) and Barnes and Liss (2008).
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
44
Barnes and Liss (2008) shows that normalized profiles are relatively stable irrespective of the
fuel station location and type (Hydrogen, Natural gas, gasoline). The main difference between
different types of stations is not the profile but the amount of fuel demand that can be
observed with demand at residential stations being roughly double the size of demand at
interstate stations, according to data presented in Barnes and Liss (2008). Bearing this in
mind, we proceed with the calculation of a stylized charging pattern that could possibly be
observed at an EV fast charging station independent of its exact geographical location.
The hourly demand data from Conoco Phillips gasoline fuel stations stipulated in Barnes and
Liss (2008) were used to develop electricity demand values for a 62.5 kW EV charging
station over a period of one average week. Such derivation can be made under the assumption
that demand for fast charging will have similar characteristics as conventional gasoline
demand in terms of its temporal profile. As the defined aim of fast charging solutions is to
make electricity charging as much as possible like conventional fuel dispensing, the
assumption should be reasonable. EV recharging ought to replicate the convenience of
refuelling with gasoline.
A rounded estimate of the number of vehicles filled per hour over the course of a week is
outlined in Figure 15, where the dashed line illustrates deterministic values. With the
stipulated assumptions, the average demand per day is 20 EV per day and the average demand
per EV is a 20 kWh charge. The input values were subsequently varied, as presented in the
results section. We assume 20 kWh as an average charge because fast charging stations are
likely to attract users inclined to long-distance travel. It is indicated in the beginning of this
chapter that fast chargers have a key function as range extender for long-distance travel. It
would therefore not be sufficient to take the average charging of all EV and hybrid EV per
day (10-20 kWh) as a function of distance driven in average per day (32 miles (51 km) in the
United States, according to Kempton and Tomić (2005). The demand per charging cycle is
probably much higher for public EV fast charging stations than for conventional level 1 and 2
chargers. We believe that an average charge of 20 kWh would be more likely to occur in
reality. With a 20 kWh charge and a consumption of 10-15 kWh/100km, an EV driver can
travel a distance of roughly 125-200 km. 20 Minutes is needed to replenish batteries at a
CHAdeMO-standard 62.5 kW post. That would represent a ca. 80% charge of a Nissan Leaf
battery (24 kWh) and little more than MiEV battery capacity (16 kWh). 20 kWh would
correspond to a ca. 40% charge of a Tesla Roadster battery (53 kWh) or a ca. 20% charge of a
BYDe6 battery (72 kWh). These two EV are specifically designed to make long-range EV
trips possible.
Figure 15: Two synthetic weekly EV demand profiles at 62.5 kW station with 30 EV/day
(600 kWh).
(Source: Own illustration)
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
45
Figure 15 clearly sketches how randomly sampled profiles add to the volatility of mean
demand profiles. In real life, charging station operators are likely to be confronted with a
highly volatile load demand, which turns out to be much less at their convenience than
`smooth` mean values. Simulated charging demand follows a normal probability distribution
with time-varying mean Barnes and Liss (2008) and an arbitrarily chosen standard deviation
of one third of the mean. Since no real world charging data from fast charging stations is
publicly available, it is necessary to approximate a standard deviation that yields realistic
samples. All in all, the charging profile is moderately sensitive to the choice of a standard
deviation. Details of the calculation of electricity demand can be found in Appendix.
The randomly sampled profile excludes negative demand values and demand values
exceeding the capacity of a single charging station of 62.5kW. All realizations outside the
interval [0; 62.5] were cut out. In a transferred meaning, if demand is beyond 62.5 kWh some
EV either wait or find alternative charging spots. Eventually, demand is varied as exogenous
factor in a scenario analysis. Figure 15 plots the remaining values of a weekly demand profile
with average demand of 20 EV/day. These represent two randomly sampled charging profiles
in the course of a week. All profiles follow an obvious pattern of peak demand during day-
time and low demand during the night. Mean values feature a consistent pattern for mid-week
fueling, with a slight peak early in the morning followed by the highest level of demand
around 5 pm. Peak demand occurs on Fridays.
3.2.4 Electricity prices and tariffs
The charging operator is assumed to have perfect foresight of electricity purchase prices from
the energy exchange. This assumption is reasonable in a setting with hourly time resolution.
The price spreads and hours with lowest and highest prices are, in general, fairly predictable
while other factors, such as charging profiles, are a greater source of volatility than electricity
prices in the course of a day, cf. Figure 15. The simplification can potentially imply an
overestimation of the true arbitrage value of a storage device. However, Sioshansi et al.
(2008) prove how operation strategies with perfect foresight of hourly spot prices can capture
85-90% of the potential arbitrage value of a storage device. Although literature finds that
storage devices are in general too expensive to pay off simply by their arbitrage value, the
setting of an EV charging station may reveal to be slightly different since tariff mark-ups
allow for a greater arbitrage range.
Figure 16 plots the tariffs used in the calculations. Two different types of tariffs are
investigated: (a) a flat rate; and (b) a time-of-use rate (TOU). The willingness of the customer
to pay a markup or a subscription fee is untested so far. Accordingly, we retrieve to sensitivity
analysis regarding the allowed markup rate as exogenous model input factor. Naturally, the
markup is considered as margin over total electricity cost, including taxes and fees. Hence,
the electricity cost profile plotted in Figure 16 includes not only sport market prices from
German EEX (2010) but also other cost components such as fees and taxes representative for
Germany. Expressed in ct/kW, these comprise electricity tax (2.1), grid fees (0.5), grid
concession (0.3), measuring cost (6.0), distribution (1.99), RES and combined heat and power
allocation (0.8) and a variable purchase tax (19% of EEX price). Values were gathered from
the German Wind Energy Association.
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
46
Figure 16: Exemplary retail tariffs and electricity cost profile used in the calculations.
(Source: Based on EEX (2010))
3.3 Method
In this section, we present the procedure for a valuation of a CHAdeMO-conform 62.5 kW
charging station operation by an independent agent who purchases electricity at wholesale
prices. The economic valuation proceeds in three steps: First, a finite number of charging
stations is defined a priori. We set this number to one. Second, a random sample of 50
different demand profiles (Figure 15) is created and operational arbitrage profits are identified
under various tariffs (Figure 16). In Figure 16, an average markup of 25% is assumed and
electricity cost includes average EEX spot market prices for 2010 plus taxes, fees and all
other costs. Subsequently, an ex-post optimal hourly strategy of an on-storage device is
optimized to check how storage improves profits (equations below). In a third step, the annual
net profit of the charging station is compared to its levelized investment cost so as to obtain a
Return on Investment (ROI) figure as indicator of profitability. ROI is expressed as a
percentage value.
(3.3)
ROI represents a short-term assessment that indicates what operating contribution margin a
charging station can achieve under various conditions. The advantage of the ROI concept over
long-term evaluations such as NPV and real option evaluation is that it does not require any
assumptions on the uncertain dynamics of costs and prices in the far future.
The operation of an on-site storage device of 30kWh capacity is simulated with the linear
optimization program outlined below. The operator’s objective (equ.3.2) is to maximize the
yearly profit from charging station operations through appropriate on-site storage
management under a given tariff. He must serve demand, there is no curtailment of demand.
SOUT and SIN are positive decision variables. Qref is load demanded, pref is the electricity
wholesale price and prob is the probability of any scenario s. While the set s designates the
scenarios (50 in total), t refers to the time period (168 hours in total). The parameter η is the
storage conversion efficiency. Paramters sinmax, soutmax and scapmax are exogenous
characteristics of the storage device, i.e. inflow and outflow limit as well as storage capacity
limit. Since the storage is emptied at the last period (equ.3.9), there is no need to assign any
left-over value to remaining kWh.
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
47
(3.4)
∑∑ [ ( )
]
s.t.:
(3.5)
Power limit inflow
(3.6)
Power limit outflow
(3.7)
∑
∑
Storage outflow never
exceeds reserve
(3.8)
∑
∑
State of charge never
exceeds capacity
(3.9)
∑
Storage balance (zero
left-over)
(3.10)
Non-negativity
3.4 Results
Results of our calculations give an impression of yearly contribution margins under varying
markup and demand. Figure 17 indicates how these key parameters affect the profitability of a
level 3 charging station. It illustrates how the ROI evolves with the markup over electricity
prices. For reference, information was included on what tariff rate would correspond to the
variable cost level of a 3-liter consuming conventional car (ca. 3.50 EUR/100km). The graph
illustrates that a positive project benefit is fairly unlikely if life-cycle investment cost
(CAPEX+OPEX) amounts to 94,000. With a markup of 15-30% over marginal cost, as
common in the liberalized German electricity sector London Economics (2007), demand at a
single station would need to exceed 30 EV/day (600kWh) for the investment to prove
beneficial. According to our estimations this would correspond to a fairly unlikely EV
adoption rate of more than 3% of the car fleet. Naturally, this number can only be taken as a
vague estimate. But it indicates that a station costing 94,000 EUR is far from economic in
2011. On the right side of Figure 17, ROI is depicted at life-cycle investment cost of
54,000 EUR. In this case, a markup of 25% (average tariff 22.83 ct/kWh) yields positive
project benefits at demand rates beyond 20 EV/day. Still, this demand rate reflects optimistic
projections of approximately more than 2% EV adoption rate. A more likely demand
projection of 10 EV/day (> 1% EV adoption rate) requires at least 26.48 ct/kWh average
tariff. Concluding from these estimations one could state that fast charging stations at 54,000
EUR total cost require average tariffs above 27.4 ct/kWh (50% mark-up) at EV adoption rates
which lie within realistic bounds. The tariff would correspond to a variable cost of roughly 4
EUR per 100 km. When cost figures at 94,000 EUR, charging stations are barely beneficial at
usual markup rates. In that case, a charging operator would need to markup by roughly 80%
to cover investment cost. If recouping all costs through a charging fee the EV user would pay
in average 33 ct/kWh. That rate translates into ca. 4.70 EUR for 100km, hence a value close
to variable cost of a state-of-the-art gasoline car. All in all, the estimations suggest that fast
charging is unlikely to be economic at EV adoption rates below 1% of the car fleet. However,
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
48
if localized demand lies above 10 EV/day, electricity could be provided through fast charging
at rates which roughly correspond to specific gasoline cost.
Figure 17: Return on Investment under different investment cost levels.
(Source: Own illustration)
In general, a high local demand for level 3 charging can only be attained if EV users do not
exclusively rely on charging facilities at home or at work. It is important for level 3 station
operators to ensure there is little competition against alternative charging solutions. Level 3
chargers may be a losing deal even under high EV adoption rates if too few EV users revert to
fast charging facilities. The substitution effect between home charging solutions and level 3
charging can be one of the main risk factors determining investment choices. Level 3
charging is therefore likely to be located at spots where there is little competition to home
charging. These locations are likely to expose a high share of transit traffic as opposed to
commuter traffic, as the latter could mostly rely on inexpensive home charging. Interstate,
highway gasoline stations and other stopover locations such as supermarkets and coffee shops
could ideally fall into this category.
A crucial question is how to reach the EV penetration rate which renders fast charging
solutions financially viable. Some experts argue that the presence of DC charging
infrastructure is a prerequisite to a high adoption rate. Corollary to this thinking is that a
comprehensive EV charging public infrastructure should be built up if necessary with public
financial support. The example of Tokyo shows how DC fast charging technology can spread
in supportive political conditions. The findings of this chapter indicate that investment
incentives are hitherto too low for a market-driven roll-out. Conversely, there is reason to
believe that commitments taken at this premature stage are rather driven by non-financial
prospects. Besides, EV stations may be used as a perk to attract consumers while the main
revenue is generated from the sale of other products, for instance parking space or
commodities. It is pervasive practice for instance at gasoline stations to generate high
revenues from non-fuel services.
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
49
Figure 18: Operation of an on-site storage device of 30 kWh capacity and 30 kW power
limit.
(Source: Own illustration)
Figure 19: Return on Investment with and without storage.
(Source: Own illustration)
So far, ROI is considered without the use of on-site storage. A storage facility can potentially
affect the profitability of charging stations as it is filled at low cost during off-peak times and
it is emptied at peak time rates; cf. Figure 18. Arbitrage benefits from a high spread between
off-peak purchase at wholesale level and a peak retail tariff. In the case of a public fast
charging station, arbitrage can potentially become particularly interesting as retail tariffs can
be set much higher than with lower speed charging stations.
In general, the storage unit is not necessarily emptied at times where the tariff is highest but at
specific time slots where tariff is highest conditional on that demand is non-zero. This implies
that accounting for volatile usage patterns with partly zero demand can diminish the arbitrage
value of storage since it confines flexibility to a certain extent.
It is found that the storage unit of 30 kWh is not filled and emptied more than once per day. It
can be testified that the use of a different tariff type does not greatly affect the temporal
operation of the storage unit. The storage unit is found to improve the revenue stream in
average by 3-5%, depending on the tariff used. The revenue boost is countered by a 6.4% cost
increase (at 200 EUR/kWh). Figure 19 illustrates that storage hardly affects (in fact slightly
deteriorates) ROI of a charging station. The estimations clearly show that on-site storage is
unlikely to be a profitable option for charging infrastructure operators. Apparently, the
flexibility of storage facilities does not yield a sufficient arbitrage value to cover the high
investment cost of batteries, unless a feed-in tariff is provided. This finding echoes Sioshansi
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
50
et al. (2009) and Sioshansi and Denholm (2010). If at all, storage devices may gain positive
value when they are explicitly used for relaxing power flow congestion in low voltage grids.
In case fast charging stations are provided and operated through a vertically integrated grid
operator and utility, storage units may become an interesting option to sidestep possible grid
congestion arising due to extensive use of fast charging during peak times.
While the retail price markup and demand seem to be pivotal for valuing a charging station,
the used tariff is equally a big factor. All ROI calculations above were made with a TOU
tariff. TOU yields better performance than setting an equivalent flat rate in all scenarios. At
30 EV/day demand, choosing TOU rates instead of a flat rate of equivalent size increases
revenue by 4% in average. When an on-site storage system is installed, it is found that the
advantage of TOU accentuates to a little extent. Storage seems to yield the greatest
improvements if a TOU tariff is used. Clearly, this difference in profits between TOU and flat
rate pricing indicates that pricing with temporal price discrimination should be preferred over
flat tariffs by a charging system operator. However, simpler tariff structures are likely to be
better understood and hence more positively received by consumers than variable prices such
as TOU. A compromising option would be to offer tariffs with at least a two-part structure
and a sufficient spread. Night rates at below 20 ct/kWh and daytime rates at around 23
ct/kWh, as used at several charging stations in Germany in 2011, appear too low and not
sufficiently detailed for a profitable operation of a public charging station.
3.5 Conclusion
This chapter conveys a simple but clear message by means of a straightforward valuation
method applied to EV fast charging infrastructure. Besides the mere cost and benefit
estimations given in this chapter, four key insights emerge from the analysis.
1) Since less than 20% of all car trips would require fast charging opportunities in an all-
electric world, a market-driven roll-out of DC fast charging infrastructure is fairly unlikely to
happen at current EV penetration rates. If private investment takes place at this premature
stage, it appears to be driven by other than project prospects. Possibly, EV stations may be
used just as a perk to attract consumers with main revenue generated from (indirect) non-
electricity sales, such as commodity sales or to a certain extent parking fees.
2) While the investment incentive for public fast chargers may turn positive under optimistic
circumstances, investment remains fairly risky. One of the main risk factors, besides EV
adoption rates, is competition between public and private home charging facilities. Further
promotion of home charging boxes deteriorates incentives for investment in public fast
chargers.
3) The arbitrage value of an on-site storage facility at quick charging stations is unlikely to
cover its own investment cost even under highly marked-up tariffs. This result reflects a
general consensus that storage devices hardly pay off through arbitrage in power wholesale
markets in the absence of feed-in credits.
4) Tariffs with temporal price discrimination appear to be the most profitable option from an
operator’s pe rspective. However, EV users could possibly prefer simpler rates over erratic
TOU tariffs.
Chapter 3 – Fast Charging Infrastructure for Electric Vehicles
51
3.6 Appendix
Figure 20: Estimation of the load pattern of a single charging station over the course of
one week.
10
(Source: Calculations based on data given in Barnes and Liss (2008))
10
Assumptions: 20 EV/day in average with 20 kWh load demanded in average.
Chapter 4 – An Investment-Dispatch Equilibrium Model
with Long-Term Uncertainty
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
53
4.1 Introduction and literature review
This chapter investigates the power plant expansion planning of electric utilities under
uncertainty about long-term trends in fuel prices. General idea and hypothesis is that
expectations of carbon, coal, oil and gas price evolutions are one of the main drivers for
investment decisions into power plants (Weber & Swider 2004; Geiger 2010). By reflecting
the uncertain nature of the fuel price evolution, we expect to replicate and understand the
portfolio effect of investment choices and explain postponement of investment.
Power plant investment decisions are complex and risky given long amortization periods, the
volatility of market prices, uncertainty regarding competitors’ investment and generation
decisions as well as the high regulatory risks. Investments often involve substantial sunk
costs, rendering the investment decision almost irreversible. Numerous seminal studies deal
with power plant investment decisions without taking appropriate account of uncertainties
(dena 2008; EC 2011; EWI et al. 2010). Ninghong et al. (2008) demonstrate how ignoring
uncertainties significantly undervalues the operational flexibility and can even result in an
insufficient investment into power plants. The representation of uncertainty is thus a
prerequisite for a realistic depiction of investment choices.
In principle, two different streams of literature can be found which carry-out quantitative
investigations on uncertainties and their impact on investment. One line of literature deals
with a detailed treatment of uncertainties through scenario analysis, risk management,
decision theory and real options valuation. A second stream of literature deals with a decent
treatment of game theoretic aspects, including market analysis and the behavior of
competitors. Real options valuation serves as a stepwise solution procedure to investment
planning which is able to account for adaptive behavior and learning effects (Dixit & Pindyck
1994). In these real option models, the uncertain parameter evolves according to a random
process, firms decide (strategically) on the timing when to install further capacities. While the
insights provided are rich in terms of timing, there is a complete abstraction from spot
markets and operational inflexibilities. A further caveat of econometric real options valuation
is that it hardly takes into account feedback between investment and market interactions
(prices) and strategic aspects can be modeled only on a superficial basis. This is where
‘fundamental’ equilibrium models step in. Equilibrium models as presented in the present
chapter can incorporate long-term uncertainty and multi-stage decision-making, thus
accounting for the real option character of investment. They depict the relation between costs
and the market prices and the ability of firms to adjust their production after investment. At
the same time the models allow for a decent depiction of the so-called power dispatch
11
and
can include strategic action due to market power, which happened to be relevant for the
German electricity market in the recent past (Weigt et al. 2010; Traber & Kemfert 2011a;
BNetzA 2011c).
Strategic capacity choices have been extensively discussed in recent literature in a Cournot
spot market setting. The liberalization of power markets and the associated issues of
oligopolistic market structures and long-term uncertainty have given rise to increased interest
in models of strategic power plant investment, partly reflecting uncertainty (Grimm & Zoettl
2008; Murphy & Smeers 2005; Pineau et al. 2011b; Geiger 2010; Genc & Sen 2008), partly
deterministic (Ventosa et al. 2002; Pineau et al. 2011a). A more recent trend is the inclusion
of firm’s risk aversion attitudes into equilibrium models (Ehrenmann & Smeers 2011a; Fan et
al. 2010). Table 5 provides an overview of recent work in the field. The interested reader is
11
Power dispatch refers to the scheduling of power plant commitment.
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
54
also referred to Ehrenmann and Smeers (2011b) who include a more extensive review of the
use of equilibrium models to analyze power generation capacity expansion equilibria under
uncertainty.
All in all, the mentioned works are fairly theory-oriented but modest in their application.
There exist virtually only duopoly analysis with few constructive results according to Grimm
and Zoettl (2008). In view of the lack of decent applications, we intend to fill this void by
providing a case study analysis of the German electricity market with a combined investment
and dispatch model. The contribution of our work is to extend the existing electricity market
equilibrium model Esymmetry (Traber & Kemfert 2011a) with endogenous investment and
include long-term uncertainty. The main research question of this article is how fuel and
carbon price risk impact investment decisions. Fuel and carbon prices are one of the major
risk factors that utilities face in liberalized markets besides regulatory risk. Adding to the first
research question, the investment incentives for utilities are investigated under the current
market design and we attempt to answer what level of fuel and CO2 prices spur investment
into the various power plant technologies.
Authors
Title
Year
Model
Critique
Ehrenmann
Smeers
Generation Capacity Expansion
in a Risky Environment: A
Stochastic Equilibrium Analysis
2011
Stochastic, static, Conditional
Value at Risk minimization –
casted as MCP
Stylized application
with 3 technologies, 2
players, static.
Fan,
Hobbs,
Norman
Risk Aversion and CO2
Regulatory Uncertainty in Power
Generation Investment: Policy
and Modeling Implications
2010
Two-Stage stochastic MCP with
risk aversion
Simple gas vs. coal firm
comparison, static.
Geiger
Strategic Power Plant Investment
Planning under Fuel and Carbon
Price Uncertainty
2011
Stochastic dynamic
programming (LP/Mixed
Integer)
No electricity dispatch
model.
Genc, Sen
An Analysis of Capacity and
Price Trajectories for the Ontario
Electricity Market Using
Dynamic Nash Equilibrium
Under Uncertainty
2008
Stochastic dynamic, Cournot
Real-world application
but limited time horizon
of 6 consecutive years.
Grimm,
Zoettl
Strategic Capacity Choice under
Uncertainty: The Impact of
Market Structure on Investment
and Welfare
2008
Stochastic MCP with
oligopolistic structure.
Application to Germany
stylized.
Murphy,
Smeers
Generation Capacity Expansion
in Imperfectly Competitive
Restructured Electricity Markets
2005
Stochastic MPEC, Cournot/
Stackelberg, Open & Closed
Loop, 1 period
Only 2 players and
technologies (base and
peak)
Pineau et
al.
A Dynamic Oligopolistic
Electricity Market with
Interdependent Market Segments
2011
Deterministic NLP, 10 year
horizon
Only base load vs. peak
load and simplistic
dispatch model.
Pineau et
al.
Impact of Some Parameters on
Investments in Oligopolistic
Electricity Markets
2011
Stochastic dynamic MCP,
Cournot
2 Technologies (base
and peak)
Ventosa et
al.
Expansion Planning in
Electricity Markets. Two
Different Approaches
2002
Deterministic NLP/MPEC 11
year horizon
Stylized application.
Table 5: Literature overview in alphabetic order.
(Source: Own illustration)
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
55
4.2 Model
The electricity market model is a partial equilibrium model based on the power dispatch
model outlined in Traber and Kemfert (2011a). The original dispatch model is complemented
with endogenous capacity investment, stochastic elements and a multi-period perspective. The
investment planning constitutes an open-loop, multi-period stochastic equilibrium. In open-
loop equilibria, all decisions for all stages are set at the start of the game (Basar & Olsder
1999). Strategic decision variables are a sequence of investment and operations. The risk-
neutral investor has information on the likeliness of each scenario. Scenarios differ in their
assumptions on fuel and carbon prices.
The model is formulated as extensive-form stochastic equilibrium problem. It covers long-
term periods (a), short-term time steps for dispatch (t), generation technologies (n) and firms
(i). Firms maximize their individual expected and discounted profits π over the modeling
period, i.e. revenues net of production costs and fixed investment cost (Equation 4.1). The set
of variables comprises investment (Xi,n,a) as well as ramping (Li,t,n,a) and generation decisions
(Qi,t,n,a). Firms are constrained by a market balance and capacity restrictions for generation
and ramping up power generation up to a specific maximum load gradient (Equations 4.2 to
4.7). The market balance ensures that demand net of RES feed-in equals power supply at each
point in time. Generation (4.3) and ramping capacity limits (4.4, 4.5) make sure that
generation dispatch follows rules imposed by some technical constraints. Equation 4.6 puts an
upper limit to investment into specific technologies. The minimum reserve capacity condition
(4.7) makes sure that there is sufficient available capacity in the market at any point in time.
Equations 4.8 to 4.11 specify the linear demand function, generation cost and the cost of
ramping up power generation between two steps in time.
Several firms have the possibility of exerting market power while a competitive fringe is
regarded as price taker. This setting makes it necessary to solve the problem as MCP with
Karush-Kuhn-Tucker conditions (KKT). The Appendix entails the nomenclature and the KKT
conditions (Equations 4.12 - 4.21).
4.1 Profit
4.2 Market balance
4.3 Generation
capacity limit
4.4 Load gradient
upper limit
4.5 Load gradient
lower limit
4.6 Capacity
expansion limit
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
56
4.7 Reserve energy
minimum
4.8 Intercept
4.9 Slope
4.10 Generation cost
4.11 Ramping cost
4.3 Application to the German Power Market
The model is applied to the case of Germany with 4 major players exerting market power and
a competitive fringe. The model horizon goes from 2010 to 2035 at the investment stage and
includes an hourly time resolution at the dispatch stage with a horizon of at least 24h. 14
‘dispatchable’ generation technologies are considered and RES feed-in is represented as
exogenous feed-in. Data is collected to replicate 2010 market behavior and assumptions are
made regarding the long-term evolution of key input parameters, in line with Traber and
Kemfert (2011a). These key input parameters include investment cost, generation cost, fuel
cost, RES feed-in, reference demand, reference spot market prices, discount rate and salvage
values. Details can be found in Table 9. Most importantly, World Energy Outlook projections
(IEA 2011c) are used to build a scenario structure for fuel and carbon prices as detailed in
Figure 2. The IEA scenarios comprise the "current policies scenario", where no policies
beyond those adopted in 2011 will be enforced. This scenario translates into high oil and gas
prices while carbon prices are low. The "new policies scenario" is somewhat a middling
scenario, where more stringent than current policies are adopted notably in the vehicle sector.
This scenario is characterized by a moderate price path. On the other extreme, the IEA
describes the "450 ppm scenario" as a situation with 50% likelihood of meeting the 2 °C
climate policy target. This scenario naturally reflects high carbon prices but low oil and gas
prices due to reduced demand. Transition probabilities between scenarios are all set to equal
shares throughout all scenario nodes, except in cases where there is only one follower node.
As can be seen in Figure 22, we end up with 16 scenario nodes and 6 periods (3 stages) for
the time horizon 2015-2035.
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
57
Figure 21: Generation and investment cost.
(Source: Own illustration)
Figure 22: Scenario tree.
(Source: Own illustration)
4.4 Results
In what follows, the extensive-form stochastic problem is compared with its deterministic
expected-value counterpart and other forms of deterministic equivalents. The expected value
problem corresponds to the average of all scenarios at each stage of the stochastic model. The
deterministic perfect information model considers each of the four scenario series separately.
Investment cost
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
58
The comparison between stochastic and deterministic models allows for insights into the
value that agents would attribute to attaining more certainty and it shows how ignoring
uncertainty can lead to lower profits. The results section is sub-divided into an analysis of
profits, investments, prices, market structure and a subsequent discussion.
In analyzing the impact of investment risk on the objective value, some basic concepts of
stochastic programming are referred to and their outcome is compared. The concept of the
value of the stochastic solution (VSS) is commonly used in the stochastic programming
community as indicator for the added value of explicitly considering probabilities instead of
expected values. Another useful concept is the expected value of perfect information (EVPI).
It represents how much one would be willing to pay to receive information on the realization
of future events (Birge & Louveaux 1997).
The mixed complementarity program is solved with the PATH solver in GAMS.
4.4.1 Profits
Table 6 shows that profits are highest in the deterministic model under perfect information
(EPI). This outcome represents perfect foresight and it is hardly attainable in reality.
Naturally, the expected value (ExV) problem and the expectation of the expected value (EEV)
problem are both lower than the EPI. They are also lower than the expected stochastic
solution (ESS). This is because the stochastic model allows for adaptation to extreme scenario
realizations and agents can then perform well in each scenario path. In contrast, the
expectation of the EEV allows for no flexibility and the ExV problem entails no extreme
events which could raise profits.
(1000EUR)
ESS
ExV
EEV
EPI
VSS
EVPI
Eon
52,658
49,158
50,257
54,991
2,401
4.56%
2,333
4.24%
EnBW
28,661
26,849
29,102
32,007
-441
-1.54%
3,345
10.45%
RWE
42,161
39,470
40,725
45,425
1,436
3.41%
3,264
7.19%
Vattenfall
41,291
36,798
40,058
44,753
1,232
2.98%
3,462
7.74%
Dummy
43,106
30,954
28,730
34,844
14,376
33.35%
-8,262
-23.71%
Total
207,876
183,229
188,872
212,020
19,004
9.14%
4,144
1.95%
ESS
=
min E[f(x)]
Expected stochastic solution
ExV
=
min f[E(x)]
Deterministic expected value problem
EEV
=
E[min f(E(x))]
Expectation with ExV solution
EPI
=
E[min f(x)]
Expectation under perfect information
VSS
=
ESS - EEV
Value of the stochastic solution
EVPI
=
EPI – ESS
Expected value of perfect information
Table 6: Expected profits over the horizon 2010-2035.
(Source: Own illustration)
Results show how the solutions of the deterministic model perform differently in a “real”
stochastic world compared to the predictions of the stochastic model. The VSS is used as
indicator how much worse a deterministic model performs in real life and it figures at around
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
59
9% in this application, with huge variations across players. For some players, VSS and EVPI
are negative. Zhuang (2005) and Egging (2010) explain that such curiosity can occur in
equilibrium modeling as opposed to optimization.
4.4.2 Investment
As concerns the optimal decisions of investment sequences, taking into account fuel price risk
strengthens the overall level of investment into flexible plants in comparison to the
deterministic ExV model (Table 7). This is due to the occurrence of extreme scenarios where
agents gain from investing large amounts into one specific technology, once a particular
scenario materializes. Another result sound with theory is that investment choices become
more diverse in the stochastic model, owing to the portfolio effect. Agents flexibly adapt to
newly arising information on scenario realizations and thus choose fairly different technology
portfolios at each scenario node, making it overall a diverse mixture of investment choices. In
this application, agents invest in new hard coal plants as well as combined cycle gas-fired
plants (Table 7). We also see the timing of investment to alter by the presence of imperfect
knowledge in a multi-period setting. Agents tend to postpone irreversible investment
decisions when holding the option to invest in later periods. As imperfect information unfolds
and reduces over time (scenario tree in Figure 22), agents automatically reduce investment
risk exposure when postponing decisions.
Stochastic ESS
(mean
values)
2010
2015
2020
2025
2030
2035
CC-New
0
0
6,465
0
0
0
6,465
HC-New
0
4,500
6,279
50
0
0
10,829
0
4,500
12,744
50
0
0
17,294
Deterministic
ExV
2010
2015
2020
2025
2030
2035
CC-New
16,481
0
0
0
0
0
16,481
16,481
0
0
0
0
0
16,481
Table 7: Investment levels under perfect competition and with 9% discounting.
(Source: Own illustration)
12
It should be further pointed to the importance of the discounting rate in determining results.
Sensitivity analysis shows that discounting has a direct impact on the investment decisions of
all players in terms of time, level and also technology choice. In general, the higher the
discount rate, the lower is investment into capital-intensive technologies such as coal-fired
power. Overall investment levels decrease with increasing discounting rates. Higher discount
rates also tend to increase incentives to postpone investment. At later stages, the relation
between upfront investment and subsequent revenues becomes smaller due to exponential
discounting. All results reported here adopt a 9% real interest rate used for exponential
discounting.
12
‘CC-New’ is Gas Combined Cycle; ‘HC-New’ is a new hard coal-fired plant. Unit is MW.
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
60
4.4.3 Prices
Figure 23 shows how price profiles alter over the years in a run with 120 hours at the dispatch
stages. Several counteracting drivers affect prices. The increasing availability of low-cost
RES dampens prices. However this so-called merit-order effect can be offset when flexible
generation units with high variable cost are increasingly called upon. Note that fuel costs tend
to rise over time and thus make electricity generation from fossil resources more expensive
over time. Additionally, the shortage of power plant capacities can increase the market share
of oligopolistic players and thus the ability of exerting market power through capacity
withholding. We observe price spikes to be more pronounced in later years and prices are on
average higher in later years compared to 2010 reference prices. This finding can be explained
by rising fuel prices, the increased use of generation technologies with high variable cost and
the more intense ramping regime due to stronger fluctuations in RES feed-in.
Figure 23: Price profile.
(Source: Own illustration)
4.4.4 Market form
The strategic behavioral assumption of Cournot competition seems far more appropriate than
assuming perfect competition. By comparing with historic spot prices from the European
Energy Exchange (Figure 23) and historic generation levels, it is clear that Cournot
competition results are better in replicating observed prices. This is in line with Traber and
Kemfert (2011a) and Weigt and Hirschhausen (2008) which indicate how oligopolistic
structures historically affected electricity prices in the German market. For the future, though,
it is uncertain whether strategic power continues to be present in the power market since
market barriers to new entrants and existing small participants are low in the liberalized
market.
Note that accounting for market shares and market power in imperfect markets drives results
into a certain direction: It drastically reduces investment of strategic players to zero while
investment of the competitive fringe is enhanced to levels beyond the perfect competition
case. Overall new capacity rises to ca. 29 GW versus ca. 17 GW in perfect competition.
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
61
Although the overall investment level increases, strategic capacity choices of the four
dominant market players are consistently lower than in the presence of perfect competition.
As a matter of fact, no single investment is performed by oligopolistic players in the Nash-
Cournot setting, while we see investments being undertaken by all players in the perfect
competition scenario (Table 7). As noted earlier, large strategic firms have a smaller incentive
to invest since they expect a price that includes a mark-up in addition to full cost recovery, as
opposed to price-taking agents. Since it is questionable whether market power in the power
sector prevails in future, and since there are no significant market barriers to investment into
new power plants, the analysis here concentrates on the case of perfectly competitive markets
and only results from those model runs are reported.
4.5 Conclusions
In this chapter, long-term developments of fuel and carbon prices are analyzed as drivers of
investment decisions into thermal power plants. General theory on risk management suggests
that agents tend to invest in more (reserve) capacity in stochastic models, but delay
investment in a multi-stage setting as uncertainty unfolds over time. Overall, the investment
portfolio becomes more diverse with the stochastic model. A stylized application of the model
to the German case replicates theory. We show that agents do postpone investment decisions,
they increase overall levels of investment, they diversify technology choices and their profits
are lower when confronted with uncertainty.
We have provided a framework for the evaluation of investment decisions under long-term
uncertainty which helps integrating numerous scenarios in one single model and including
security criteria such as minimum system capacity constraints. It was shown that outcomes of
investment strategies differ by the type of model used – deterministic or stochastic. The
managerial implication is that private investors should take into account long-term uncertainty
in integrated stochastic models instead of using scenario analysis with deterministic models.
In doing so, investors account for the flexibility in second-stage decision-making after
investment. Optimal decisions paths thus differ by the type of model used.
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
62
4.6 Appendix
Indices
a
Year (deterministic) or scenario node (stochastic)
i
Player
n
Generation technology
NS
Subset of Nash players i
Pred
Predecessor node a
Succ
Successor node a
t
Hour
Variables
L(i,t,n,a)
Load gradient
MW
P(t,a)
Price
EUR
Q(i,t,n,a)
Production
MWh
TQ(n,t,a)
Total production of all firms
MWh
X(i,n,a)
Investment
MW
γ(t,a)
Shadow price of reserve capacity requirement
EUR/MW
δ (i,t,n,a)
Shadow price of load gradient definition
EUR/MW
κ(i,t,n,a)
Shadow price of capacity constraint
EUR/MW
λ(i,t,n,a)
Shadow price of ramp-up constraint
EUR/MW
ρ(i,n,a)
Shadow price of capacity expansion limit
EUR/MW
θ (i,t,a)
Market share
%
Parameters
av(n)
Availability
%
cd(n)
Marginal depreciation while ramping
EUR/MW
ce (n,a)
Marginal emission cost
t/MWh
cf(n,a)
Fuel cost
EUR/MWh
cL (n,a)
Marginal ramping cost
EUR/MW
co(n)
Operating cost
EUR/MWh
cQ (n,a)
Marginal cost of generation
EUR/MWh
cre (n,a)
Marginal ramping emission cost
t/MW
cX(n)
Investment cost
EUR/MW
d(a)
Discount rate
%
d0 (t)
Reference demand
EUR
emf(n)
Emission factor
t/MWh
Φ(a)
Emission price
EUR/t
int(t,a)
Intercept of demand curve
bar{l}(i,n,a)
Maximum load gradient
%/hour
η(n)
Efficiency
%
p0(t)
Reference price
EUR
pr(a)
Probability
%
bar{q}(i,n,a)
Installed capacity
MW
underline{q}(a)
Minimum reserve capacity requirement
MW
res(t,a)
RES and CHP feed-in
MW
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
63
s(n)
Ramp-up fuel requirement
MWh/MW
slp(t,a)
Slope of demand curve
sv(n,a)
Discounted salvage value
EUR
σ
Price elasticity of demand
w(a)
Number of weeks per period
bar{x}(i,n,a)
Maximum capacity expansion
MW
Table 8: Nomenclature
(Source: Own compilation)
KKT Conditions
(4.12)
(4.13)
(4.14)
(4.15)
(4.16)
(4.17)
(4.18)
(4.19)
(4.20)
(4.21)
Chapter 4 – An Investment-Dispatch Equilibrium Model with Long-Term Uncertainty
64
a) (IEA et al. 2010) – exchange rate EUR-USD 1.33
b) (EWI et al. 2010) – for 2020
c) (Konstantin 2007)
d) (Traber & Kemfert 2011a)
e) (Genc & Sen 2008)– exchange rate EUR-USD 1.33
f) (IEA 2011c)
g) (IEA 2011b)
Table 9: Technical and economic parameters
(Source: Own compilation)
Investment cost
Fuel emission (d)
Efficiency (d)
O & M costs (d)
Ramp-up fuel
(d)
Ramp-up
depreciation (d)
Maximum load
gradient (g)
Available (d)
Fuel price (f)
kEUR/MW
kg/kWh
%
ct/kWh
kWh/kW
ct/kW
%/hour
%
ct/kWh
Pumped hydro
HYD
-
0
1
0.26
0
0
100
75
0.00
Nuclear
NUC-L
-
0
0.34
0.1
16.7
0.17
15
86
0.76
Lignite
BC-Old
-
0.4
0.38
0.26
6.2
0.1
40
85
0.29
Lignite new
BC-New
1700 [1950 (b)]
0.4
0.43
0.1
6
0.3
50
100
0.29
Coal old
HC-Old
1300 (b) [800 (e)]
0.34
0.34
0.2
6.2
0.15
40
82
0.65
Coal retrofit
HC-Retro
1100
0.34
0.38
0.1
6
0.5
40
100
0.65
Coal new
HC-New
1300 [1950 (a), 2250 (b)]
0.34
0.43
0.1
5.5
0.5
50
100
0.65
Gas combi cycle old
NG-CC
650
0.2
0.58
0.13
3.5
1
50
86
1.66
Gas combi cycle new
NG-CC-New
700 [950(b), 530 (f)]
0.2
0.6
0.12
2.9
1
55
90
1.66
Gas steam turbine
NG-ST
600
0.2
0.4
0.15
4
1
36
86
1.66
Gas gas turbine old
NG-GT
400 (b)
0.2
0.35
0.15
1.1
1
100
86
1.66
Gas gas turbine new
NG-GT-New
500 [400(b)]
0.2
0.47
0.13
1.1
1
100
90
1.66
Oil steam turbine
O-ST
600
0.28
0.38
0.15
4
0.5
36
84
3.02
Oil gas turbine
O-GT
500
0.28
0.33
0.15
1.1
0.5
100
84
3.02
Chapter 5 – An Investment-Dispatch Equilibrium Model
Applied to Europe
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
66
5.1 Introduction
This chapter presents results gained from the model “EMELIE-ESY”, a partial equilibrium
model with focus on electricity markets where private investors optimize their generation
capacity investment and the hourly operation of power plants (‘dispatch’) over a long-term
horizon up to 2050. EMELIE stands for Electricity Market Liberalization in Europe - ESY
refers to energy symmetry in regard to supply and demand. The contribution forms part of the
Energy Modeling Forum 28 (EMF28) study which is based on a comparison of results from a
variety of well documented energy models. The study focuses on the impact of energy
technology availability on the costs of achieving European climate policy targets with
different stringencies of the emission trading system. The model EMELIE-ESY participates in
the EMF28 model comparison with a partial equilibrium model to gain detailed sector-
specific perspectives. A distinctive feature of EMELIE-ESY is that investments in power
capacities are driven by market clearing prices received by private investors on a basically
free electricity market with expansion restrictions and at the high expected private discount
rate of 8% in real values, common for long term private investments in the sector.
Furthermore, the model includes the effect of power plant ramp-up restrictions on the hourly
supply profile of an exemplary day and the consequent impact on price profiles in each
country.
In the model application presented here fundamental determinants of investment and dispatch
decisions are investigated. The EMF28 scenario set-up is used in assessing the implications of
climate policy targets and technology availability on technology choices for conventional
power plants. We study the impact of climate policies and technology availability on market
outcomes with regard to investment choices and the power mix. We find that the European
electricity sector will be able to meet stringent climate policy targets without relying on
contentious technologies such as nuclear power and Carbon Capture and Storage (CCS) if an
accelerated role out of renewable energy sources (RES) is realized. EMELIE-ESY
demonstrates how the conventional power sector develops under these targets relying on
forces induced by power and emissions markets.
After the introduction, key model features are outlined and the different scenarios are
explained. The results are presented, followed by a conclusion.
5.2 Model
The EMELIE-ESY model is a partial equilibrium model of the power sector. Aiming for
profit maximization, numerous agents make investment decisions for conventional
technologies and dispatch decisions. EMELIE-ESY combines the investment model EMELIE
(Traber & Kemfert 2011b) and the dispatch model ESYMMETRY (Traber & Kemfert
2011a). It hence constitutes an integrated multi-period investment-dispatch model, coded as
MCP in GAMS software. The algebra of the model formulation is presented in Traber and
Kemfert (2012) and resembles the one of the model used in the previous chapter. Input
parameters regarding economic and technical parameters are largely in line with a study
prepared by Schroeder et al. (2013).
5.2.1 Regional resolution
In terms of regional resolution, the model application includes all countries of the EU-27 plus
Norway and Switzerland. Figure 24 provides an overview of the regional disaggregation.
Spain and Portugal are grouped into IBERIA; Great Britain and Ireland are included as British
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
67
Isles; Denmark, Sweden, and Finland constitute the regional aggregate NORDIC; Lithuania,
Latvia, and Estonia are represented as BALTIC, while the group SOUTHEAST comprises
Slovakia, Slovenia, Hungary, Romania, Bulgaria, and Greece. Finally, Belgium and
Luxemburg are merged in one group.
Figure 24: Regional resolution of EMELIE-ESY
(Source: Own illustration)
5.2.2 Temporal resolution
The temporal coverage is five 10-year periods representing the range from 2010 to 2050. Each
10-year period encompasses a dispatch stage represented by 24 consecutive hours. Hence,
each 10-year period is represented by one representative day in hourly resolution. The set-up
of 10-year periods and hourly dispatch is chosen to combine long-term and short-term
elements of investment planning. We should note that a representative day at the dispatch
stage does not take into account less probable extreme events such as extremely low
production of wind power.
5.2.3 Transmission
The projections of the grid structure and corresponding Net Transfer Capacities (NTC)
between countries are taken from ENTSO-E (2012). Winter and Summer NTCs are taken to
build averages. The expansion of the grid is line with indications in the EC Roadmap (EC
2011). The EMELIE-ESY model represents import-export-transfers between countries in a
piping model with scarcity pricing as outlined in Traber and Kemfert (2012). Scarcity pricing
refers to the fact that transmission line congestion effects are priced into market prices. The
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
68
piping model considers that electricity trade patterns disregarding physical flow
characteristics such as loop flows.
5.3 Scenarios
The scenarios were predetermined within the EMF28 group. They are grouped along a
technology availability dimension (horizontal) and a policy dimension (vertical). Table 10
provides an overview of the 10 scenarios and their abbreviations used hereafter.
The policy dimension essentially prescribes a reduction of greenhouse gas emissions until
2050 by 40% in the reference case and by 80% in the mitigation scenario, respectively
compared to values of 1990. These policies are implemented in EMELIE-ESY by emission
caps for the electricity sector. The reduction path for the power sector is actually tighter than
the economy-wide path with targets of 40% or 80% by 2050. In line with the Energy
Roadmap of the European Commission (EC 2011), we use targets which gradually reduce the
carbon emission of the electricity sector by two thirds in the reference case and by 97.2% in
the mitigation scenario compared to sectoral carbon emissions in 2010 (1.265 GT CO2).
The specifications of technology scenarios are further detailed in the subsections hereafter.
Default w
CCS
Default w/o
CCS
Pessimistic
Optimistic
Green
CCS
on
off
off
on
off
Nuclear energy
reference
reference
low
reference
low
Energy efficiency
reference
reference
reference
high
high
Renewable energies
reference
reference
reference
reference
optimistic
Reference: including the
2020 targets and 40% CO2
reduction by 2050
40%DEF
40%noCCS
40%PESS
40%EFF
40%GREEN
Mitigation: 80% CO2
reduction by 2050 (with
Cap&Trade within the EU)
80%DEF
80%noCCS
80%PESS
80%EFF
80%GREEN
Table 10: Scenario overview
(Source: Own illustration)
5.3.1 Demand and energy efficiency
Electricity consumption is endogenous and represented with linear, country-specific demand
functions which are constructed around a reference point representing historic realizations of
consumption and prices. Price-elasticity of demand at the reference point is set to 0.3
throughout all time periods and regions. Regarding reference demand, average hourly demand
values of the year 2010 published by ENTSOE are used. Starting from reference prices and
consumption of the year 2010, reference consumption is set to increase by 10% per decade for
OECD countries and 20% per decade for non-OECD countries in all scenarios where energy
efficiency is set to “refe rence”. In the energy efficiency “high” scenario, reference demand
only grows by 5% and 10% per decade respectively.
Reference spot market (day ahead) prices are taken from several European energy exchanges.
We use Nordpool prices for the specification of the Norwegian, Nordic and Baltic markets.
Poland and the Czech Republic are assigned Polish Power Exchange prices (exchange rate 4.2
PLN/EUR). SWISSIX prices are used for Switzerland. The remaining regions are assigned
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
69
Phelix EEX power prices. Reference consumption is based on values published by ENTSO-E.
The values for the German market are adjusted for the consumption of railroads and industries
not connected to the public grid and therefore not accounted for by ENTSO-E.
5.3.2 Renewable energy
RES capacities, i.e. wind, solar, biomass, and hydro are treated as exogenous feed-in based on
the National Renewable Energy Action Plans (NREAPs) up to 2020, and a trend projection
until 2050 (EEA 2012). Their hourly supply profile is fixed in each scenario and based on the
average German profiles, scaled to the generation values of the NREAPs to represent different
regions. Beyond the NREAPs projections of 2020, we assume a linear trend expansion of the
RES capacities up to 2050 in the renewable energy reference (“reference”) case. In the
scenarios with “optimistic” RES development, the growth of production is double the growth
in the reference scenarios in absolute terms.
5.3.3 Conventional generation
On the supply side, the dispatch of conventional generation - including hydro power - is
modeled endogenously. Up to 14 ‘dispatchable’ generation technologies are reflected in the
model as indicated in Table 11. Coal-fired plants are sub-divided by boiler criticality, fuel
type and CCS availability. Gas- and oil-fired plants are divided by turbine type. Nuclear
power plants are distinguished by vintage, in order to reflect evolutions from ordinary
generation III reactors towards new-type reactors such as EPR and AP-1000.
The availability of generation technologies differs across scenarios as outlined in Table 10.
“Off” denotes the non-possibility of investment into CCS technology. “On” refers to the
availability of CCS in certain countries. For nuclear power, “low” means there is no
possibility of new-built nuclear power plants in any countr y. In the “reference” case, upper
limits for investment into nuclear power are set at either the level of currently planned
projects or the amount of power plants decommissioned after 50 years of operation –
depending on which number is greater. These limits are constructed so as to allow countries to
at least keep their current nuclear capacity levels and possibly expand their capacity, if current
plans of new built exist.
Investment cost ranges between 6000 EUR/kW for new EPR nuclear reactors to 400 EUR/kW
single cycle gas turbines (Gas GT) (Schroeder et al. 2013). Following the assumed potential
for technological development, investment costs of CCS-Technologies, nuclear reactors and
combined cycle gas turbines show a decreasing cost trend, whereas investment costs of
mature technologies have constant investment cost expressed in current monetary value.
We further distinguish generation technologies by technological characteristics such as
efficiency, operation and maintenance costs, start-up fuel requirements, ramping limits, fuel
emissions, start-up depreciation and availability. Values are fixed over the model time horizon
as laid out in Table 11. Note that O&M costs for nuclear power include a surcharge for
nuclear waste disposal, as detailed in Schroeder et al. (2013). Ramping restrictions are
reflected at the dispatch stage in order to represent inflexibilities in the scheduling of power
plant commitment.
Major drivers of the full costs of generation are fuel prices. In order to attain model
comparability, we follow fuel price assumption in line with IEA projections (IEA 2011d) and
closely in line with partner models as laid out in Table 11.
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
70
Group
Description
EMF28
Denomination
Investment cost in EUR2010/kW
2010
2020
2030
2040
2050
Nuclear
Generation 3 Old Nuclear
Nuclear
6000
5833
5671
5513
5360
Generation 3 EPR Nuclear
Nuclear
-
-
-
-
-
Coal
Lignite Subcritical
Coal|PC|w/o CCS
-
-
-
-
-
Lignite Supercritical
Coal|PC|w/o CCS
1700
1700
1700
1700
1700
Old Subcritical
Coal|PC|w/o CCS
-
-
-
-
-
Coal Supercritical
Coal|PC|w/o CCS
1300
1300
1300
1300
1300
Lignite Oxyfuel CCS
Coal|PC|w CCS
3881
3577
3296
3038
2800
Coal IGCC CCS
Coal|IGCC|w CCS
2988
2794
2613
2443
2285
Gas
Gas Precombustion CCS
Gas|CC|w CCS
1637
1528
1425
1330
1241
Gas Combined Cycle
Gas|CC|w/o CCS
800
764
729
696
664
Gas Combustion Turbine
Gas|CT
400
400
400
400
400
Gas Steam Turbine
Gas|CT
-
-
-
-
-
Oil
Oil Steam Turbine
Oil|w/o CCS
-
-
-
-
-
Oil Combustion Turbine
Oil|w/o CCS
-
-
-
-
-
Hydro
Hydroelectric
-
-
-
-
-
-
Efficiency
O&M costs
Start-up fuel
Maximum
load gradient
Fuel
emission
Start-up
depreciation
Availability
[%]
[cent/kWh]
[kWh/kW]
[%/hour]
[kg/kWh]
[cent/kW]
[%]
Nuclear
0.34
1.8
16.7
0.04
0.00
0.5
0.81
Coal CCS
0.40
3.6
8.0
0.30
0.04
0.5
0.84
Coal
0.46
0.6
6.2
0.30
0.35
0.5
0.82
Lignite
0.43
0.6
6.2
0.08
0.40
0.3
0.85
Lignite CCS
0.31
4.1
8.0
0.08
0.05
0.3
0.87
Gas CCS
0.48
1.9
2.0
0.30
0.02
1.0
0.92
Gas CC
0.60
0.2
2.0
0.50
0.20
1.0
0.92
Gas GT
0.45
0.2
1.1
1.00
0.20
0.5
0.92
EUR2010/ MWhfuel
2010
2020
2030
2040
2050
Lignite
0.3
0.4
0.4
0.5
0.5
Hard Coal
1.3
1.3
1.4
1.6
1.7
Natural Gas
2.3
3.0
3.4
3.7
4.1
Uranium
0.2
0.2
0.2
0.2
0.2
Table 11: Technological characteristics and fuel price assumptions
(Source: Own illustration)
The decommissioning of existing generation capacity is set exogenously in line with existing
and near-term planning up to 2020 as indicated in the Platts database (Platts 2011). For the
period from 2030 onwards, we use a heuristic to approximate limits for new investments
based on the replacement of retiring capacities. More precisely, natural gas and hard coal
investments are allowed to overcompensate the decommissioning according to lifetime
expectancy by 100%, while investments in lignite capacities may at most replace
decommissioning. In the scenarios denoted “reference” nuclear technology construction is
confined to currently planned projects until 2020 or to the amount of decommissioned
capacity in the corresponding decade if the latter number is greater. For the decades following
2020 current plans until 2020 are used as a proxy for planning. Only in Germany,
decommissioning of old capacities does not imply the option of new investments. Notably,
this scenario disregards policy decisions taken in countries like Belgium and Sweden and,
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
71
thus, indicates an optimistic potential for nuclear investments. By contrast, in the scenario
nuclear “low” nuclear production relies on existing capacities or plants currently under
construction which are decommissioned after 50 years of lifetime or according to the German
nuclear phase-out policy. Finally, CCS in scenario “reference” follows the ex pansion limits of
ordinary gas and coal plants as indicated above, whereas the scenario CC S “off” does not
allow for construction of CCS power plants.
5.4 Results
Results are compared most explicitly to the models PRIMES and POLES. PRIMES is the
reference model since it is frequently used by the European Commission, for instance for the
EU Energy Roadmap (EC 2011). POLES is used as reference because of its similar format as
partial equilibrium model with detailed treatment of power markets.
5.4.1 Wholesale spot price projections
EMELIE-ESY is designed to calculate plausible electricity wholesale prices in the long run.
The model therefore relies on long-run marginal cost pricing plus an additional price
component which reflects ramping costs of power plants. Therefore, modeled electricity
prices cover all costs for the operators and investors of the marginal power plant, i.e. the
investment which breaks even with a return of 8% per year.
The comparison of the average volume weighted wholesale electricity price projections in
Figure 25 essentially reveals three distinct pathways. They range from a pronounced increase
of 190% until 2050 compared to 2010 in the most pessimistic scenario 80%PESS to the
scenario 40%GREEN, in which prices increase 20% between 2010 and 2050. High energy
efficiency and an accelerated RES roll-out in 40%GREEN alleviate price increases. As
variable fuel cost of a gas-fired power station increase by about 110% until 2050 and given
the reduction of plant utilization induced by RES, it follows that the profitability of a gas
power station significantly reduces over time in 40%GREEN.
Between the two extreme cases we observe an intermediate price path in scenarios with high
energy efficiency and either a less ambitious climate policy (40%EFF) or a high RES roll out
(80%GREEN), which lead to price increases of 81% and 59%, respectively. Prices drift apart
from the high price scenarios 80%PESS/80%DEF/40%DEF as of 2020. The high price
scenarios either assume a less ambitious climate policy (40%DEF) or a combination of low
increases in energy efficiency with (80%DEF) or without (80%PESS) the option of nuclear
power plant construction. The difference of the latter scenarios is the wholesale price effect of
newly built nuclear power plants, which amounts to 27% of the price level in the first period.
Finally, the price projection of scenario 80%EFF (not shown) corresponds closely to the
development in 80%DEF. This indicates the potential of increased energy efficiency to
compensate price effects induced by more stringent climate policy under our assumptions.
Prices in other EMF 28 models differ in the way they are composed and in their type
(wholesale versus end-user prices, average versus maximum). A rough comparison of results
shows that electricity prices calculated by EMELIE-ESY are higher as compared to most
other models in a variety of scenarios. The prices reported by other models often seem to not
cover full cost of investment. Instead, investment seems to be triggered even at low producer
prices due to minimum capacity constraints and implicit additional revenue components.
However, a pronounced electricity consumption increase in POLES and PRIMES (Figure 28)
occurs despite significant increases in the fuel and investment costs of marginal power plants,
which opens up a question with regard to the demand elasticity used in those models.
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
72
Figure 25: Wholesale electricity prices EU-27 average
(Source: Own illustration)
5.4.2 Emission market prices
Our results on emission prices under the European Union Emission Trading System (EU ETS)
correlate closely with the wholesale power price developments. Notably in the scenario
40%GREEN with a more ambitious RES roll out and less ambitious climate policy we find a
decreasing price path after 2020 as laid out in Figure 26.
The comparison of our findings with POLES and PRIMES shows that the models compute
similar emission prices in the reference scenarios in both climate policy cases at least until
2040. Under reference climate policy and reference technology assumptions of scenario
40%DEF, the emission price projection of EMELIE-ESY shows only a slightly more
pronounced increase with an emission price of 65 EUR/t of CO2. To the contrary, the closely
related emission price pathways of POLES and PRIMES deviate significantly from our results
in the ambitious climate policy scenario 80%DEF. In scenarios 80%DEF, 80%PESS and
80%GREEN we find comparatively less accentuated emission prices with maximal values
ranging between 98 and 192 EUR/t by 2050. In the same scenario group POLES reports
emission prices of between 240 and 3629 EUR/t by 2050, whereas PRIMES respective results
are between 270 and 290 EUR/t.
The wide range of emission prices across scenarios highlights shows the sensitive nature of
emission prices in EMELIE-ESY. In particular, the difference in emission prices between
scenarios 80%DEF and 80%PESS (65 EUR/t by 2050) reveals a sensitivity of the model with
regard to the availability of a nuclear power option. The corresponding emission price
reduction induced by the availability of nuclear power and CCS technology is 12 EUR/t in the
PRIMES model. All comparative values have to be interpreted against the backdrop of much
higher nuclear power plant investments in POLES and PRIMES.
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
73
Figure 26: Carbon emission prices
(Source: Own illustration)
5.4.3 Market-driven capacity evolution
Investment pathes for conventional generation technologies differ significantly across
scenarios. Figure 28 gives details on the investment in new conventional power plants in the
EU-27. We observe identical outcomes for scenarios 40%DEF/NOCCS/PESS, and for
scenarios 80%DEF/NOCCS. As no investment into CCS technology materializes, identical
outcomes are computed in the scenario pairs 40%DEF/NOCCS and 80%DEF/NOCCS.
Furthermore, there are no investments in nuclear energy in scenario 40%DEF. It is therefore
not necessary to separately consider scenarios 40%NOCCS, 40%PESS and 80%NOCCS as
they can be represented by Scenarios 40%DEF, and 80%DEF. Furthermore, one can
categorize the scenarios into two groups by considering overall conventional capacity
investment levels until 2050. One group comprises scenarios 40%DEF to 80%DEF where
between 60 and 85 GW of new conventional capacities are constructed. In the second group
of remaining scenarios 80%PESS to 80%GREEN only 21 to 37 GW of conventional
technologies are incentivized by the markets. New nuclear power plants are only built in the
ambitious policy scenario with low energy efficiency and less ambitious RES roll-out in
80%DEF/NOCCS. In scenario 80%DEF the model suggests 49 GW of nuclear power plant
investment in 80%DEF. Coal fired power plant projects seem to be not impacted by the
availability of nuclear power technology. Consequently, total new built capacity reduces by
50% from 75 GW in scenario 80%DEF to about 38 GW in scenario 80%PESS.
Moreover, the scenarios of high energy efficiency suggest similar capacity developments, i.e.
within pair 40%EFF/GREEN and pair 80%EFF/GREEN. Differences within these pairs are
only due to the extent of power generation from RES and to the availability of nuclear power.
Since the latter plays no role in the non-ambitious emission policy scenario, differences
between scenario 40%EFF and 40%GREEN indicate the effect of a pronounced RES roll out
and lead to minor differences in timing and technology choice between gas and coal. In
scenario 40%GREEN slightly more coal fired power plants are constructed in the last model
period 2050, displacing some investment in gas fired power plants. Likewise, minor
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
74
differences are obtained for scenarios 80%EFF and 80%GREEN. In 80%EFF we find
investment in barely 2 GW of nuclear power. In 80%GREEN the non-availability of nuclear
investment options is partially compensated by about 1 GW higher natural gas investment.
Figure 27: Conventional capacity investments until 2050 [GWel net capacity].
(Source: Own illustration)
In total, future installed capacities in PRIMES and POLES are significantly higher than in
EMELIE-ESY although RES input is relatively similar across all models. Most notably,
PRIMES and POLES set themselves apart from EMELIE-ESY in that they are comparatively
optimistic on the deployment of CCS technology for both, gas and coal power plants.
PRIMES projects for both scenarios 40%DEF and 80%DEF around 50 to 60 GW of CCS-
equipped coal-fired power plants in the EU by 2050. Moreover, PRIMES calculates with
investment into Gas CCS power plants of around 142 GW in the stringent climate policy
scenario 80%DEF and 41 GW in the 40%DEF scenario by 2050, respectively. Emission
prices of the EU ETS as well as the development of electricity consumption can partly explain
these differences.
Similarly, installed nuclear power plant capacity by the year 2050 differs significantly across
the compared models. Whereas EMELIE-ESY calculates an installed capacity of 21 GW in
scenario 40%DEF, and 72 GW under stringent climate policy, the respective values range
between 102 and 156 GW in PRIMES and POLES. Two drivers of these differences can be
identified: First and foremost, the investment costs of nuclear power plants is up to 50% lower
in POLES, and up to 25% lower in PRIMES, notably in the early periods of the time horizon.
Adding to this, variable cost of 25 EUR/MWh for nuclear power are higher in EMELIE-ESY
than in any other model. Secondly, the demand development in EMELIE-ESY is dampened
by high prices, whereas other models, e.g. PRIMES and POLES, project an escalating
consumption of electricity.
We observe very low new built conventional capacity investments in our model in the
scenarios of ambitious climate policy without the option of nuclear energy
(80%PESS/80%EFF/80%GREEN). We shall stress at this point that our model does not per
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
75
se provide sufficient capacities to meet system reliability or adequacy but it represents an
‘energy-only’ market. Investors must recoup their investment cost by the pure sales of energy
without generating any additional revenues from any other service (i.e. no capacity payments,
no ancillary services). We presume that system requirements are likely to be fulfilled by
cheap single cycle gas turbines and stronger network integration in Europe.
Overall, the results of the EMELIE-ESY model indicate that even a low-carbon EU is likely
to see relatively little private investor engagement in CCS technology, nuclear, coal-fired and
new gas-fired plants in most European countries. This holds even though market prices
continue to rise steadily in most countries. Besides the effect of overall demand growth as key
driver of investment, we explain the low investment level by implicit assumptions regarding
investment incentives. Investment behavior in the EMELIE-ESY model is market-driven
assuming the current market design without capacity instruments and system stability
requirements for private investors. In comparable peer models, system stability requirements
are crucial regarding capacity investment.
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
76
EMELIE-ESY
PRIMES
POLES
Default 40% Climate Policy Target
Default 80% Climate Policy Target
Figure 28: Power generation in the EU-27
(Source: Own compilation)
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
77
5.4.4 Power consumption and generation mix
An important determinant of the market developments and a major explanation for the
observed deviations in the results of our model comparison from other peer models is the
development of electricity consumption. The evolution of net power generation, i.e. final
consumption including network losses, is shown in Figure 28 for the two climate policy
scenarios 40%DEF and 80%DEF. Clearly, the price increases in EMELIE-ESY induce only
modest increases or even a stagnant development in consumption, although reference demand
grows significantly over the time horizon. Taking into account price and demand effects, we
obtain a 10% increase until 2050 in scenario 40%DEF. In scenario 80%DEF we observe an
increase until 2030 and a modest decrease afterwards. Quite differently, the two models used
for comparison report consumption growth rates between 44 and 48% compared to the base
year 2010, largely unaffected by the stringency of climate policy and the corresponding high
carbon emission prices of 240-270 EUR/t in scenario 80%DEF.
Figure 28 also entails power generation by source. For the less ambitious policy scenario
40%DEF, a fading significance of nuclear power generation in the EU is demonstrated in
EMELIE-ESY. Starting with a share in power generation of 27% in 2010, nuclear energy
reaches 24% in 2020 and diminishes to a 4% share by 2050. The most important electricity
source by 2050 is wind power, followed by biomass and hydro power. Gas power production
reduces over time but replaces coal in its position as dominant fossil fuel. Whereas the 2010
reference power mix is similar in PRIMES and EMELIE-ESY, there is a significantly
different evolution until 2050. The PRIMES model projects a much larger generation of
conventional power plants in absolute terms. By 2050, PRIMES projects for the 40%DEF
scenario all conventional power sources to exceed 50% of the EU’s power production, with
nuclear power as dominant source (27%). PRIMES’ share of RES production of 45% by 2050
contrasts with 76% in EMELIE-ESY. This difference is mainly due to the 27% higher power
consumption in PRIMES (4545 TWh/year) compared to EMELIE-ESY (3592 TWh/year).
Under the more ambitious climate policy targets of scenario 80%DEF, the role of RES gains
dominant importance with a production share of 83% by 2050. The increase of RES
corresponds with a reduction of nuclear power to a share of 15%, and an almost complete
cutback of fossil fuel usage. Natural gas fired power production keeps merely a 2% share in
power generation, whereas coal-fired power production declines completely. The absence of
coal power production arises despite significant coal-fired production capacities not reaching
their full lifetime by 2050. Accordingly, gas-fuelled powered plants reach only a low rate of
utilization, and coal-fired power plants are not able to recover fuel and emission costs through
electricity prices in the last period. Reduced competitive utilization rates and increasing
emission and fuel prices are also a major obstacle for CCS technology investments as
modeled in EMELIE-ESY. Since emission rates of CCS are not irrelevant under CO2 prices of
over 100 EUR/t and as high capital costs of CCS gain importance under low utilization rates,
levelized costs of CCS are escalating. Under a moderate price elasticity of -0.3 the model
suggests that demand is reduced rather than new CCS power plants being built.
These findings contrast with the picture drawn by the models PRIMES and POLES, where
fossil fuels keep a significant share in power generation even in a world of ambitious climate
policy. POLES calculates a 36% share of fossil fuelled power plants in power generation by
2050 in 80%DEF, whereas PRIMES projects a corresponding 27% share. Finally, PRIMES
projects a share of nuclear energy of 20%, and POLES finds a quarter of European electricity
generation produced by nuclear power in the year 2050 for scenario 80%DEF. Given
increasing electricity generation, PRIMES finds a 10% decrease of nuclear power generation
Chapter 5 – An Investment-Dispatch Equilibrium Model Applied to Europe
78
compared to today’s production, whereas the model POLES computes an increase of about
10% with a generation of 985 TWh in 2050.
5.5 Conclusion
We have assessed the potential impacts of different climate policy regimes on electricity
prices, CO2 prices and generation capacity investment in this chapter. The results of EMELIE-
ESY suggest that climate targets can be met by the power sector with only few to no
investment into CCS and nuclear power plants. In fact, most scenarios propose no private
investment into CCS and nuclear technology at all. The lack of new investment gives rise to
high wholesale spot market prices. Price increases on the wholesale market exert downward
pressure on overall power demand. Our findings contrast with the models PRIMES and
POLES. Differences can be explained by significant variations of model assumptions
regarding investment and generation costs for nuclear and CCS power plants. Adding to this,
a key driver for differences in results is that consumption in EMELIE-ESY strongly reacts to
rising wholesale prices, which result from increasing fossil fuels and CO2 prices. PRIMES
and POLES report a comparatively stable increase of electricity consumption by 2050, despite
high emission prices. All in all, our findings suggest that the projected growth of RES supply
can sufficiently meet electricity consumption complemented by only few capacity
investments in conventional technology. This comes at the price of rising power prices which
contain demand growth.
Chapter 6 – Transmission Grid Congestion Analysis
Chapter 6 – Transmission Grid Congestion Analysis
80
6.1 Introduction
The geographic disconnect between power generation resources and demand hubs is an
important issue in the European electricity sector. Moreover, as the projected share of RES
generation in the European Union is likely to triple by 2030, a temporal misalignment of
demand and non-dispatchable fluctuating resources is set to become a challenge for electricity
grid planners. Amongst many solutions to tackle such challenges, grid capacity expansion is
often proposed to be relatively cheap but hard to implement due to problems with public
acceptance. Long lead times for the planning of transmission infrastructure create the need for
long planning horizons. The 3d energy package of the European Commission mandated
ENTSO-E to establish a ‘Ten-Year Network Development Plan’ since 2010. It is the first
policy effort to bring forward coordinated long-term planning processes for European power
transmission infrastructure. The German political situation is characterized by implementation
of the TYNDP through the National Grid Development Plan (‘Netzentwicklungsplan’). The
ongoing process defines the need for additional transmission capacity within Germany up to
2032.
In the light of recent policy proposals to expand electricity grids so as to better incorporate
RES into the system, different studies examine their suitability on an EU-wide scale (Troester
et al. 2011; Leuthold et al. 2012; Schaber et al. 2011) and national scale (dena 2010). The
project of Troester et al. (2011) makes use of a comprehensive AC load flow model to
investigate transmission needs on a European level and covers the years 2030 and 2050. A
peculiarity of their study is that RES generation projections are fairly optimistic with 68% and
97% of generation in 2030 and 2050, respectively. While the study is good in its geographic
coverage of whole Europe, it does not allow for detailed conclusions as regards Germany
since its grid representation is relatively coarse. The same holds true for Schaber et al. (2011)
which focuses on European transmission grid expansions with the aim of better integrating
fluctuating RES. Inner-German grid congestion and capacity expansion requirements are
scrutinized in the study of dena (2010), where infrastructure needs are determined for the time
range up to 2020. Although the study qualifies as the national reference study it is widely
criticized for a lack of transparency (Jarass 2010) and its short temporal horizon of 2020
(Hirschhausen et al. 2010). Neither does this study allow for reproduction and scrutiny nor
does it offer a place for visionary concepts of grid expansion over a long-term horizon. A
long-term perspective is necessary for electricity infrastructure where excessive lead times
make project planning a long-lasting endeavor. The present article is intended to address the
shortcomings of the mentioned studies by applying a European-wide model with high
resolution of Germany for the year 2030. Such model allows for conclusions in relation to
specific line expansion projects in Germany and it also accounts for fundamental system
changes likely to occur by 2030 on a European scale.
Hitherto, the research community has dealt little with applied analysis of transmission
infrastructure needs. Mills et al. (2011) perform an analysis of grid integration of RES for the
Western US grid. George & Banerjee (2011) do likewise for a specific Indian region. None of
these studies cover the European dimension addressed specifically here in this article. Schaber
et al. (2011) come close to the work performed here but focus on variability in RES provision
in whole Europe while not providing detailed needs of specific transmission line expansions.
In view of the need for advanced planning, paragraph 12 of the renewed German Energy
Industry Act (Federal Government 2011a) requires TSOs to establish a plan for infrastructure
needs by 2012. TSOs are requested to put up a power flow model of transmission
requirements for Germany based on scenarios that have been approved by the regulatory
authority, the Bundesnetzagentur (BNetzA). The latest scenario draft is published in a
Chapter 6 – Transmission Grid Congestion Analysis
81
preliminary (BNetzA 2011a) and a definitive version (TSO 2011). The article here picks up
BNetzA’s call for a transmission infrastructure plan and proposes solutions for the 2030
horizon with a focus on the German grid, embedded in the European context. Three scenarios
are designed that describe alternative approaches to accomplish the fundamental shift in
energy supply that Germany is striving for. For quantification, a variant of the state-of-the-art
DC load flow model ELMOD (Leuthold et al. 2012; Weigt et al. 2010) is applied to a
regionally disaggregated electricity grid under a welfare-maximizing regime. Further
methodological details can be found in section 6.2, following this introduction and literature
review. Section 6.3 describes input parameters. Section 6.4 presents the three scenarios of
interest. Results and their discussion are outlined in sections 6.5, with section 6.6 providing
the concluding remarks to the article. A more detailed analysis, including the mathematical
formulation, extensive data calculations and further scenario results can be found in Boldt et
al. (2012).
6.2 Methodology
The DC load flow model ELMOD is used as basis and complemented with several features as
detailed hereafter. The mathematical formulation is based on an optimization problem that
maximizes social welfare and it is solved in GAMS as a QCP using the CPLEX solver.
The model applies a welfare maximizing approach with a target function maximizing
consumer and producer surplus (Equation 6.1). The bi-linear program is constrained by a
nodal energy balance (Equation 6.5) which states that the difference between generation and
demand at a specific node, net of storage, demand shifting and load in- or outflow, must be
zero. A generation capacity constraint (Equation 6.6) incorporates technical generation limits
of each plant type at each node and time. Production cannot be higher than the maximum net
generation capacity. Net generation capacity equals gross capacity times the technology
specific availability factor. Linear ramp-up constraints (Equations 6.8 and 6.9) limit the
amount of capacity that can be ramped up in one time period for each technology. Ramping
costs equal the product of ramped capacity and a technology-specific cost parameter.
The model includes storage and DSM as measures to flexibilize load. Constraints 6.17 and
6.18 are included stating that at each point in time at each node, storage in- and outflow
cannot be greater than the corresponding storage power limit. It is assumed, over all periods,
that storage power in- and outflows, corrected by the conversion efficiency factor, need to be
balanced and thus their sum is equal to zero (Equation 6.21). It is further assumed that
consumers have the possibility to shift their electricity consumption for a limited time range
through DSM (Equations 6.22-6.24). When shedding load, consumers get compensated
depending on the amount of demand that is shifted. The compensation costs are included in
the objective function.
The flow on a specific line is determined by all net inputs into all adjacent nodes multiplied
by their respective PTDF (Equation 6.11). These PTDF describe the flow through any
individual line in dependence of the feed-in of one unit of electricity at some specified hub.
They take into account that power does not necessarily flow across the shortest distance, but
rather it finds its way through the grid via the path of the least resistance. This nature of power
flows gives rise to so-called loop-flows in meshed grids. Implicitly, the PTDF matrix respects
the Kirchhoff rules which define the relationship between electric tension and currents: At
each node the sum of in- and outgoing electricity flows needs to be zero and the directed sum
of the electrical potential differences (voltages) around every closed circuit (loop) equals zero.
Chapter 6 – Transmission Grid Congestion Analysis
82
Line flow constraints (Equations 6.11-6.16) state that the electricity flowing through a line
cannot be greater than the maximum capacity of that line, in absolute terms. Since electricity
can flow in both directions and the line flow can thus be positive or negative, two separate
constraints are included guaranteeing that the line flow does not exceed its capacity limit on
each line. By reducing the maximum line capacity below its technical potential by 20%, the n-
1 security criterion is accounted for and it functions as reliability margin. A similar reasoning
applies to the modeling of DC line flows. The net input into a DC line is determined by the
line flows of the DC lines multiplied by their factor in the incidence matrix (Equation 6.16).
As in the case of AC lines, DC lines have a certain technical power limit that cannot be
exceeded at any point in time. Therefore, two constraints are included thus guaranteeing that
the power flowing through a line does not exceed its technical power limit.
6.3 Application
In this section, basic input parameters and assumptions of the model are explained. The
analysis considers an hourly time resolution. It is applied to four distinct representative weeks
in the year 2030 and all input parameters are calibrated so as to match realistic projections for
that year. It comprises 21 European countries, and disaggregates Germany into 18 zones as
defined in dena (2010). Conclusions are only drawn on results for Germany although the
model covers whole Europe.
The aggregation of zones results in a 41-node base model with Denmark being composed of
two nodes. Note that while the model considers 234 AC lines and 35 DC lines, PTDF are used
to aggregate inter-zonal lines. The calculation of PTDF is based on the ELMOD database
including 3,449 European high-voltage lines at 220 and 380 kV level (Leuthold et al. 2012).
Some lines are added to the existing database to reflect grid expansion projects up to 2030 as
proposed in the TYNDP (details in Table 15 and Table 16). PTDF are derived from the
incidence matrix and an inversion of the admittance matrix ‘B’ as outlined in Duthaler et al.
(2007). Since the model application considers aggregated zones, PTDF are defined for all
inter-zonal lines while all lines within a zone are left out. For nodes within a zone, there are
different options for including weighting factors such as demand, gross or net generation
(Smeers 2008). Weighting based on demand and generation is the best choice in theory, but
not chosen here since demand and generation are endogenous. It is chosen to weigh nodes at
equal rates.
6.3.1 Electricity grid
In order to model the German power market for 2030, assumptions are made about the
evolution of the electricity grid, both for Germany and the rest of Europe. The section here
outlines the additions that are made to the grid in place in early 2012. A number of grid
expansion projects that are under consideration, in planning or in an early construction phase
as of 2012 are applied exogenously to the model. German legislature, European TSO
(ENTSO-E) and regional TSO indications are the basis for qualified projections of the 2030
European grid. The Energy Line Extension Act (Federal Government 2011b) prioritizes a
series of national projects that have reached either late planning or early construction phases.
For transmission projects at the international level the TYNDP (ENTSO-E 2010) identifies a
number of projects, of which only several are picked for the application here. The upgrade of
existing or construction of new lines between Germany and its neighbors provides additional
power exchange capacities and increases security of supply. Since most of the projects are
Chapter 6 – Transmission Grid Congestion Analysis
83
commissioned before 2017, they are assumed to be completed and operational by 2030. The
transmission network topology in Germany and its neighboring countries are further detailed
in graphs in the results section.
6.3.2 Electricity demand
According to the Federal Energy Concept on Environmentally Sound, Reliable and
Affordable Energy Supply (Federal Government 2010), the German government is aiming for
a demand reduction of 25% between 2008 and 2050. This amounts to approximately 16%
until 2030, when applying a compound annual growth rate. It is thus assumed that there is
yearly electricity demand of 463 TWh in 2030 in Germany as reference point. Note that actual
demand realizations may deviate from this figure since an elastic demand function is used in
the model application. On a European level, the application here uses hourly load values of
the year 2010 provided by the European Network of Transmission System Operators
(ENTSO-E 2011). Total German demand is allocated to the 18 model nodes inside Germany
based on population data.
6.3.3 Renewable energies
The “Renewable Energy Policy Country Profiles” study of EcoFys et al. (2011) is used as a
consistent basis for RES production data in Europe. The study predicts the potential of
electricity generation by 2030 per technology for EU-27 countries. These projections were
directly derived from the NREAP for each country in the year 2020, and reflect the official
renewable energy target of each country. The 2030 forecasts also take into account existing
national RES support policies as well as expert opinions, providing a higher level of detail
than other comparable studies. Electricity generation data for wind, solar, hydro, wave and
tidal, geothermal and biomass are converted into installed capacity using technology- and
country-specific full load hour assumptions taken from the NREAP and recent projections in
EcoFys et al. (2011). 2,906 TWh of RES generation are expected in the EU 27 in the year
2030. Both, on- and offshore wind, contribute a significant portion of total RES generation
with 19% and 17%, respectively. Another 16% of photovoltaic generation increases the total
portion of fluctuating RES to 52%.
Chapter 6 – Transmission Grid Congestion Analysis
84
Figure 29: Onshore wind generation: Reference vs. Strategic South Scenario.
(Source: Own calculation based on EcoFys et al. (2011); Map of zones in Figure 30)
For countries with a single node representation in the model, the generation capacity is
aggregated. For Germany, however, a greater level of detail is needed to guarantee accuracy.
Total capacity is broken down to 18 DENA zones in a way that is plausible given geographic
potential and local development plans. As there is no exact data on the regional distribution of
RES generation in Germany in the EcoFys et al. (2011) study, this information is adopted
from the TSO scenario pathway mentioned earlier (TSO 2011). After applying that
distribution to the capacities given in the EcoFys et al. (2011) study, a regional breakdown of
2030 RES capacity in Germany is obtained (see Table 12).
Since biomass and geothermal are dispatchable technologies, their generation is controllable
and does not need to be determined as time series. For the fluctuating RES, hourly feed-in-
series are elaborated to model the actual generation mix over the course of a year.
Wind power output is derived from a representative wind park as a function of wind
speed. 6-hourly wind speed data is retrieved from ECMWF-ERA Interim Re-Analysis
for 2005 (Dee et al. 2011) and interpolated values are derived. Data is available for a
coordinate grid of 1.5 to 1.5° density, with 18 area points available for Germany. The
advantage of using wind speed data over simple output time series is that offshore and
onshore wind output can be disentangled and derived separately, which is done for
Germany here. For other countries, their geographic center is chosen as single
reference point. Note that the Interim Re-Analysis consists in a mixture of forecast and
actual measures. Grid cells cover a large area and thus build average values for
specific grid cells. When validating the simulation model with actual feed-in data, an
R2 of 70% can be achieved in some grid regions.
Chapter 6 – Transmission Grid Congestion Analysis
85
Solar power output derivation is also based on meteorological data. Hourly irradiation
values for 2005 (SoDa 2005) are used and converted into power output taking into
account various losses and efficiency reductions (pre-conversion losses, inverter
losses, thermal losses and conduction losses) by aggregating them in a performance
ratio (Quaschning 2009). The same geographic reference points are used as for wind
power derivation;
As opposed to solar or wind power, hydro power features a fairly continuous
generation profile, so there is no need for an accurate hourly generation time series.
Still, seasonal variations in generation can be observed. For this reason, a generation
profile by month is adopted here. Generation data from the years 2008, 2009 and 2010
is extracted from Eurostat (2011) and used as a basis for the time series calculations of
hydro power.
6.3.4 Conventional electricity generation
Since the NREAP and the EcoFys et al. (2011) study do not provide any information on
electricity generation from conventional resources, we revert to a study by the European
Commission (EC 2010) for 2030 data on a European level. Regarding data on non EU-
members, public and private studies of the respective countries were examined. A higher
degree of resolution is applied to Germany for which data in the Platts (2011) database, a
BNetzA (2011b) list and the original ELMOD database (Leuthold et al. 2012) are
triangulated. This data is extended with projected new investments (VGB 2011) and we
remove those plants which are likely to be decommissioned by 2030. For the reference
scenario, it is implicitly assumed that the geographic spread of power plants does not alter
until 2030. Generation costs, particularly short-term variable costs, play a crucial part in the
model since they determine the sequence in which power plants are dispatched. Adding to
this, ramping costs further complicate the dispatch order of power plants. Table 13 presents
assumptions on marginal generation cost assuming a CO2 certificate price of 50 EUR/tCO2.
Fluctuating RES have no fuel costs at all, and are therefore always in merit. Deep geothermal
energy does not incur any fuel cost either, but its variable operation and maintenance costs of
around 1.5 EUR/MWh are reflected in the marginal generation costs. Biomass plants in
Europe are able to run on a variety of fuels, and their costs are aggregated at 50 EUR/MWh
(BMU 2010). More details about the costs, also including ramping costs and limits can be
found in the publication of Boldt et al. (2012).
Chapter 6 – Transmission Grid Congestion Analysis
86
DENA
Zone
Geo-
thermal
Hydro-
power
Photo-
voltaics
Wave
&Tidal
Onshore
Wind
Offshore
Wind
Biomass
Sum
21
0.61
0.00
2.74
1.74
5.47
10.97
0.25
21.76
22
0.00
0.05
2.04
1.74
2.47
5.48
0.54
12.32
23
0.00
0.06
2.51
0.00
2.60
0.00
0.59
5.76
24
0.24
0.00
4.08
0.00
1.11
0.00
0.20
5.63
25
0.15
1.85
10.58
0.00
0.50
0.00
0.92
14.01
26
0.10
1.23
7.40
0.00
0.34
0.00
0.61
9.69
41
0.10
0.49
3.04
0.00
0.63
0.00
0.33
4.59
42
0.20
0.98
5.83
0.00
1.26
0.00
0.65
8.93
71
0.00
0.03
1.37
0.00
1.41
0.00
0.32
3.13
72
0.00
0.05
2.97
0.00
1.73
0.00
0.39
5.14
73
0.00
0.04
2.23
0.00
1.30
0.00
0.29
3.86
74
0.06
0.02
2.31
0.00
1.02
0.00
0.25
3.65
75
0.30
0.00
4.45
0.00
0.97
0.00
0.25
5.97
76
0.05
0.62
3.70
0.00
0.17
0.00
0.31
4.84
81
0.00
0.00
2.92
1.74
4.48
5.48
2.89
17.51
82
0.00
0.12
0.00
0.00
0.04
0.00
0.12
0.29
83
0.00
0.00
2.46
0.00
2.23
0.00
0.43
5.12
84
0.00
0.12
2.06
0.00
1.65
0.00
1.35
5.19
Sum
1.82
5.66
62.69
5.22
29.39
21.93
10.68
137.38
Table 12: Breakdown of RES generation capacities on Dena zones in 2030 in GW.
(Source: Own calculations based on EcoFys et al. (2011); Map of zones in Figure 30)
CHP generation is included in the analysis. Some power plants show “must run”
characteristics, i.e. they generate electricity whenever they are required to produce heat. For
power plants for public supply this is especially the case in winter, when district heating
systems are online. In order to allocate CHP capacity to fuel type, a forecast on the share of
fuel types of CHP has been made. The forecast takes into account long-term trends of CHP
development and displays a significant growth of the gas and RES production share, a
considerable decline in coal and oil utilization and a sharp decline of the share of other fuels,
mainly due to the phase-out of nuclear energy. The share of must-run CHP and RES is not
modeled separately, as renewable energies are generally considered as must run facilities. In
the analysis a maximum installed capacity of 15 GW for must run non-renewable CHP plants
is estimated for 2030. This maximum is reached in winter, in autumn and spring it amounts to
10 GW while in the summer it is 5 GW. The assumption represents 42% of the overall
German CHP capacity if an installed capacity of 35.7 GW for the year 2030 is taken as basis
(BMU 2010).
MCoE + CO2
[EUR/MWhel]
Lignite
51.69
Hard Coal
63.69
Gas
74.91
Oil
142.84
Uranium
9.93
Table 13: Costs for fossil-based power generation including CO2 costs.
(Source: Own depiction based on BMU (2010) and EWI et al. (2010))
Chapter 6 – Transmission Grid Congestion Analysis
87
6.3.5 Infrastructure cost
Infrastructure cost needs to be taken into account into the overall analysis of transmission line
extensions. These costs comprise line extension cost on the one hand and generation capacity
cost on the other hand.
The cost of upgrading the transmission grid depends on the length, type, capacity and terrain
of the underlying transmission lines. High-voltage AC is the cheapest technology of power
transmission and well established in today’s power system. No large cost reductions are
expected throughout the modeling horizon. Based on already built or pending project cost
specifications (Troester et al. 2011), AC line extension cost is set at 400 EUR per MW and
km. For a long-distance power transmission, DC lines have many advantages compared to AC
lines with the same power rating. While DC lines are mainly limited by a maximum
conductor temperature, the capacity of AC lines is also limited by high reactive power
consumption. The DC line extension cost is set at 0.7-0.8 million EUR/km at a 3000 MW
power rating with 500-600 kV voltage capacity. An AC line with the same power rating
would cost 1.22 million EUR/km. It is obvious that DC lines have lower unit cost than AC
lines mainly as a result of a lower number of parallel lines needed. This cost advantage is
reduced by the cost for converter station costs which cost about 150,000 EUR per MW.
Hence, landside DC lines pay off over long distances. All costs are annualized in order to suit
to the model time horizon.
The 2030 projection of generation capacity capital cost is mainly based on values derived
from the World Energy Outlook 2011 (IEA 2011a) and can be found in Boldt et al. (2012).
For established generation technologies it is assumed that lower capital costs due to research
and development are offset with increasing costs for materials, labor and space by 2030. For
upcoming RES technologies, substantial reductions of investment costs are likely to
materialize due to economies of scale, learning curves and research & development.
6.4 Scenarios
A scenario analysis is conducted that revolves around a central reference case. The variations
on the Reference Scenario explore alternative possible states of the 2030 power market: while
the ‘Strategic South Scenario’ mainly differs from the Reference Scenario in its generation
structure, the ‘DC Hi ghways Scenario’ focuses on alternative transmission topology. The
scenarios encompass assumptions regarding demand, generation, fuel and certificate prices,
grid expansions and political motives.
The Reference Scenario depicts a state of the European electricity market that is probable
under the condition that additional policies support the development of RE and infrastructure
development in Germany and Europe. No significant changes to current climate and energy
policies are made over the course of the next 20 years. The phase-out of nuclear energy in
Germany, as appointed by a 2011 amendment to the Nuclear Energy Act, will see the last
nuclear power utility exit the grid in the year 2022. Newly constructed fossil-based power
plants are assumed to be built at the same locations where old ones have been closed.
The Strategic South Scenario investigates an alternative to the expansion of transmission
networks on a North-South axis. The research question behind the scenario is whether the
strategic placement of conventional power plants close to load centers, as well as an equal
distribution of RES between North and South can substitute the construction of transmission
Chapter 6 – Transmission Grid Congestion Analysis
88
to a certain extent. The Strategic South Scenario consists of two major changes compared to
the Reference Scenario: First, while in the Reference Scenario new conventional power plants
are built on the location of old power plants exiting the grid, they are now being placed
strategically along the metropolitan and industrialized areas of West and Southwest Germany.
Especially the flexibility of additional gas turbines allows them to serve as back-up capacity
for peak demand hours. Second, there is a reallocation of RES capacity from Northern
Germany to the centers of high demand. The reduction of offshore wind energy capacity in
the North goes with increasing RES technologies (such as PV and onshore wind) in the
Southwest without affecting the total ratio of renewable versus conventional generation.
Offshore wind is reduced in the Strategic South Scenario by nearly 19 GW and half of
onshore and PV capacities are shifted from the North to the South. See Figure 29 for a
comparison of wind capacity in the Reference and Strategic South Scenarios. It is apparent
that generation in the Strategic South Scenario is explicitly larger in the zones of high demand
(24, 25, 26, 41, 42, 72, 73, 74, 75 and 76) than in the Reference Scenario owing to the
reallocation of resources.
Figure 30: Proposal of DC lines. Dark circles indicate converter stations.
(Source: Own depiction based on the dena II report (2010))
The third scenario variation, the DC Highways Scenario, explores the possibilities of using
state-of-the-art DC transmission technology to alleviate congestion on the high-voltage AC
Chapter 6 – Transmission Grid Congestion Analysis
89
grid. Since projected and existing offshore wind capacity is located mainly in the North,
transmission capacities on the North-South-axis are considered as efficient to relieve
congestion. This discussion has gained some momentum in late 2011 when first insights into
a DC-Overlay master plan have emerged. First sketches of the three DC lines’ pathway were
shown, see Figure 30. The lines span over 2,100km, running north to south and east to west.
50 Hertz, the transmission operator in eastern Germany, has already entered the application
process for the line connecting rural Brandenburg to the densely populated Rhine-Main area.
Amprion and EnBW, operating in western and southwestern Germany, are planning a 600 km
line linking the Ruhrgebiet and Stuttgart, the state capital of Baden-Wuerttemberg. That
region will be facing a shortage of 5 GW of reliable generation once the last of the nuclear
power plants exit in 2022. TenneT, operating on a Northwest-Southeast-axis, is planning the
longest of all lines, reaching over 900 km from Schleswig-Holstein to Bavaria. Its purpose
will be to haul the generation of 28 GW of offshore wind across the country to a populous
region that will also face substantial nuclear phase-outs. The DC Highways Scenario assumes
that these projects will have reached completion and will be fully operational by 2030. The
lines will start at a capacity of 1 GW with the possibility to be upgraded to 3 GW. To account
for this degree of uncertainty, the three lines are modeled with 2 GW capacity. The aim of the
scenario is to investigate the effects of DC overlay lines on the existing AC grid. Will the DC
highways alleviate congestion on the AC grid and ease the transfer of power from north to
south? All assumptions from the Reference Scenario are left intact except for the addition of
the three DC lines. This methodology allows for filtering out a ceteris paribus effect of an
overlay grid on transmission constraints in the AC grid.
6.5 Results and discussion
6.5.1 Four representative weeks
Four representative weeks are chosen, one for each season of the year. The ratio between RES
generation from wind and solar (by far the largest contributors to RES generation in
Germany) against weekly demand is chosen as the main determinant for the selection of
representative weeks. The comparison of the four weeks and a more elaborate explanation of
the selection process can be found in Boldt et al. (2012) together with additional information
on the share of RES in total generation and on the import-export performance of Germany in
the different weeks and scenarios.
Chapter 6 – Transmission Grid Congestion Analysis
90
Figure 31: Congestion index for all scenarios in weeks 14, 28, 41 and 51.
(Source: Own depiction)
For an in-depth comparison of transmission grid congestion, we analyze line capacity shadow
prices. Shadow prices represent the total value that the operator is able to recover in form of
the so called congestion rent. Alternatively it can be interpreted as the contribution of line
expansion to welfare when releasing the lines capacity constraint by 1 MW. In a transferred
meaning, values indicate the urgency or priority of line expansion.
A general grid-wide weekly congestion index is used to compare congestion across scenarios.
It relates the sum of shadow values of all lines in each scenario in relation to the reference
scenario. This congestion index is visualized in Figure 31, the congestion index of the
Strategic South and DC Lines Scenario is compared to congestion index of the Reference
Scenario which is normalized to one. A value of the indicator above one represents
deterioration; a lower index implies an improvement compared to the reference scenario. A
drop in the congestion index may be due to the fact that lines are congested at fewer times or
that the value of the congestion – the price difference between the zones – may have fallen.
The chart clearly shows that the Strategic South Scenario reduces the sum of the shadow
variables throughout all weeks compared to the Reference case. Its congestion index is 0.25 in
average. The DC Scenario paints a different picture. It increases congestion in spring and
winter, and decreases congestion in summer and autumn. The mean congestion index of the
DC Scenario is 0.97, which means that on average, congestion is significantly decreased.
Since the spread between the Reference index and the Strategic South index is largest for
week 51, this particular week is chosen for a detailed analysis hereafter.
6.5.2 Detailed results for one exemplary week
In what follows, detailed results are outlined for week 51 of the model year. Figure 32 shows
the generation portfolio of week 51 in the Reference Scenario. It shows the generation mix of
the specific technologies in MW for the 168 hours of one week. While the dotted black line
represents demand, the cumulated areas stand for the generation share of the respective
technologies. The difference between total German demand and total German supply
Chapter 6 – Transmission Grid Congestion Analysis
91
represents imports or exports at each hour. One can distinguish the intermittent RES, wind
and PV, the controllable RES hydro, geothermal and biomass, as well as the conventional
energy sources oil, gas, combined heat and power, hard coal and lignite.
Figure 32: Generation portfolio of week 51 in the reference scenario.
(Source: Own depiction)
Concerning the generation mix, it is striking that throughout the whole week, the wind from
the north of Germany, originating mainly from the offshore wind parks in the North Sea,
contributes the main share of generation in Germany. There is no generation at all from oil-
fired and generation of hydro power, wind from the South of Germany, geothermal, solar
power and gas only represents a small fraction of total German energy supply. Electricity
generation from base load technologies (lignite, hard coal, biomass and combined heat and
power) accounts for an equal share of around 10 to 15%. One can observe the gas peaks
which even out the uncertainties of intermittent RES. During this exemplary winter week,
German production exceeds German consumption and import only occurs in a few peak
demand hours. Overall, Germany exports around 3% of its electricity generation.
The generation portfolio of week 51 in the DC Highways Scenario does not change compared
to the Reference Scenario owing to the similar assumptions on installed capacities. In the
Strategic South Scenario there is a higher share of installed wind capacity in the south of
Germany. Consequently the generation by wind power from southern Germany increases
from around 5% in the Reference Scenario to more than 27% in the Strategic South Scenario.
On the other hand, one can notice the decreased generation by northern wind power.
Generation by the remaining technologies in each case only differs slightly, the share of
fossils increases by around 5%. The RES share in the German generation portfolio remains
relatively stable across all three scenarios, deviating by not more than 1%.
Chapter 6 – Transmission Grid Congestion Analysis
92
Figure 33: Net Input: Median of hourly import/export in German zones.
(Source: Own depiction)
Figure 33 shows the import/export-balance of each node in Germany. It represents the median
of net electricity generation at each node over all 168 hours of week 51. The Reference
Scenario clearly shows a set of exporting nodes exclusively in the very north of Germany.
Sorted in descending order by their net export amount, these are: 21, 81, 84, 22, 71, 41 and
72. For the nodes 21, 22 and 81, the reason for the high amount of exported electricity lies in
the large amounts of offshore wind power in the North and Baltic Sea. As wind is under a
must-run condition (marginal cost of zero) and exceeds local demand, the zones become net
exporters in weeks with significant wind, such as week 51. The other four exporting nodes
have a high installed capacity of onshore wind and good wind conditions over the whole year.
The major importing zones of the Reference Scenario are 73, 42, 24 and 26, all located in
Germany’s west and south. This is caused by the loss of large shares of installed capacity
(nuclear phase-out) and a strong demand.
The DC Highways Scenario brings little structural change to the national export and import
patterns observed in the Reference Scenario, except in the Northern German zone 21. Here, a
major increase of electricity export to other zones is made possible through new DC
transmission capacity to the Southern load centers. A side effect is that nodal prices increase
in Northern exporting zones and they align with formerly high southern prices. All in all, the
nation-wide export to neighboring countries increases by 4%.
In the Strategic South Scenario, the national import-export pattern is fundamentally shifted.
First of all, the inner-German disequilibrium between northern exporters and southern
importers tends towards a balance. All nodes experiencing a major decrease in imported
electricity are located in the south and west of Germany and all former main exporters
experiencing a decline of net exports are located in the north of Germany. A second
observation is that there is a clear shift towards more export from Germany into neighboring
Chapter 6 – Transmission Grid Congestion Analysis
93
countries. As a matter of fact, Germany turns from a net moderate importing (around 3% of
production) in the Reference Scenario to a major net exporting country (around 17% of
production). We conclude that the strategic placement of installed capacity to demand regions
brings relief to the connection between exporting and importing zones and improves the
overall German export ratio.
Figure 34: Line congestion in three scenarios measured in terms of shadow value.
(Source: Own depiction)
In what follows, congestion patterns in week 51 are scrutinized in detail in order to point out
changes across the different scenarios. Subject of investigation is the congestion status of the
German AC Grid, which is evaluated by the individual shadow variables of the lines.
Figure 34 illustrates the congestions of each line in the three scenarios. Congestion is
categorized in three classes depending on its severity, as explained in the legend. As
anticipated there is strong congestion on the interconnectors to northern Europe and on the
inner-German line called “Rennsteig” (line from node 25 to node 83), which is an important
north-south connector in development. These results show that there will be a need for further
grid extension in the reference case to transport all the offshore and onshore wind energy from
northern Germany to southern Germany and to the rest of Europe.
Most of the congestion in the northwest is alleviated in the South Scenario as the congestion
index falls significantly for almost all inner-German lines and interconnectors. Especially the
north-south connectors and interconnectors to northern Europe, which were congested in the
Reference Scenario, show a strong improvement. We conclude that grid capacity planning
and generation capacity planning are intertwined problems which should ideally be
coordinated in conjunction so as to reduce cost from a societal perspective.
A key finding of the DC Highways Scenario is that inner-German congestion is not
necessarily relieved by building DC lines across the country. Even though a DC-grid
enforcement reduces the congestion of some interconnectors and parallel running north-south
lines, it goes along with higher congestion on other inner-German lines. The main reason for
the latter is that additional congestion occurs at the starting and ending points of the DC lines
Chapter 6 – Transmission Grid Congestion Analysis
94
as the existing AC infrastructure is not yet equipped for spreading the electricity through
those “spokes” to the different consumer centers. It can be concluded that the planning of DC
lines is not sufficient in itself, but needs to go hand in hand with a surrounding AC grid
planning in destination zones.
6.5.3 Welfare analysis
The analysis of the impact on welfare contains results calculated from the model as well as
specific costs incurred to build the infrastructure available in the scenarios. For the Reference
Scenario no additional costs are added since this scenario is business-as-usual. However, for
the DC Highways Scenario costs for the expansion of the DC grid are added based on cost
assumptions explained previously. Moreover, infrastructure costs occur in the Strategic South
Scenario due to shifts in the newly built capacity in southern Germany. It is obvious that these
infrastructure costs should be taken into account for a welfare analysis.
Reference [m€]
Strategic South [m€]
DC Highway [m€]
Welfare per month
13,422
13,545
13,537
Infrastructure cost per month
-
-9
54
Net welfare per month
13,422
13,553
13,483
Change in %
-
+ 0.98%
+ 0.45%
Table 14: Overview welfare effects summed over four representative weeks.
(Source: Own calculation based on EcoFys et al. (2011))
Based on the investment costs for renewable energy, these changes lead to lower costs in
total. The reason is that the investment costs for onshore wind power plants are notably lower
than the costs for offshore wind power plants. In total 834 million EUR can be saved through
the shift of capacity in the Strategic South scenario. This translates into 8.6 million EUR
monthly when considering different physical lifetimes for technologies (PV: 25 years; on- and
offshore wind and wave and tidal: 20 years).
For the DC Highways Scenario, expansion costs with a total amount of 9 billion EUR are
assumed. This value includes variable grid costs and fixed costs for converter stations at nine
nodes (both referring to a line capacity of 2 GW). Since these costs are the investment costs
for a grid with an operational life of 40 years, an annuity with an interest rate of 7% is used,
analogue to the interest rate determined by the federal network agency BNetzA. The
calculation yields to annual costs of 675 million EUR and to monthly costs of 54.5 million
EUR.
In conclusion, we observe overall positive welfare effects of DC lines and a strategic
placement of generation capacity close to demand centers, even after deduction of
infrastructure costs, as seen in Table 14. Consequently, the placement of additional generation
capacities into demand centers is found to be effective in reducing congestion. Likewise, DC
lines as proposed in this study are a sensible and cost-effective approach to alleviating
transmission grid congestion. The positive effect on welfare is higher in the Strategic South
Scenario, certainly due to the cost reductions evoked by the major changes in installed
capacity. However, also the DC Highways Scenario generates a higher welfare without any
changes in the capacity. Hence, congestion relief appears to be the key driver for the
improvement through new lines. However, both scenarios show that there still remains further
Chapter 6 – Transmission Grid Congestion Analysis
95
need for grid upgrades in the ordinary AC grid. Implementing DC lines and placing capacities
in the South are not sufficient measures to fully satisfy the grid requirements imposed by the
2030 energy system. The analysis points to the need for grid expansion beyond what is
currently planned in the TYNDP context.
6.6 Conclusions
The results presented above indicate that the German AC/DC grid as planned in the TYNDP
is likely to feature high line congestion and it is thus not capable of fully integrating the
amount of renewable energy to the extent that welfare maximization would suggest desirable.
Unless transmission lines are reinforced, a welfare-optimizing dispatch of generation for
Germany in a European context is thus unlikely to take place.
Throughout all three scenarios, we observe congestion centers in the northwest of Germany
which extend towards the south, as well as at the interconnectors between Germany and its
northern neighbors. The connections to Poland, the Czech Republic and the Netherlands are
also continuously operating at capacity limit but with a lower possible contribution to welfare
optimization. As a consequence, RES power originating from the northern offshore generation
centers (DENA zones 21 & 22, Great Britain) does not reach German and foreign load centers
in its entirety.
The modifications made in the DC Highway and Strategic South Scenario create an
alleviating effect on congestion. The Strategic South Scenario shows the best results,
indicating that an even distribution of generation across the country does provide an
alternative to massive transmission investments. However, given that national policy is
ultimately aiming for 100% of RES generation in 2050, the reinforcement of existing and the
construction of new lines seem inevitable at this point. Within the DC Highways Scenario, the
AC congestion actually worsens after the introduction of the DC lines. While the north-south
axis is relieved, congestion problems are transferred to starting and destination hubs and
prove that there is still a need for reinforcements of the AC lines.
Chapter 6 – Transmission Grid Congestion Analysis
96
6.7 Appendix
The objective function maximizes social welfare
[
∑
(
( )
∑
∑
)
]
(6.1)
where the demand function may be described as
∑
(6.2)
with the slope
(6.3)
and the intercept
(6.4)
When solving Eq. (7.1) several energy balance constraints have to be accounted for. The
nodal balance constraint has to be true for any node at any point in time
∑
∑( )
(6.5)
as well as the generation capacity constraint
( 6.6)
the cost function
∑
( 6.7)
the ramping constraints
Chapter 6 – Transmission Grid Congestion Analysis
97
(6.8)
(6.9)
and the definition of the ramping variable
(6.10)
As we model a power market with both AC and DC flows, we account for AC flow
constraints
∑
(6.11)
(6.12)
∑
(6.13)
as well as for DC load flow constraints
∑
(6.14)
(6.15)
∑
(6.16)
The n-1 security criterion is approximated by reducing the capacity of each AC line by a
transmission reliability margin (20%). Note that the model neglects transmission losses. This
is done to keep the model tractable and to omit non-linear elements where possible.
Regarding the implementation of storage technologies, the model considers storage power
limits
(6.17)
(6.18)
and storage capacity limits
( )
(6.19)
We use the formulation of a storage state variable which indicates the state-of-charge.
Chapter 6 – Transmission Grid Congestion Analysis
98
(6.20)
An overall balance guarantees that the storage device left at the same state-of-charge as in the
beginning.
∑
(6.21)
DSM constraints for different cost segments restrict the amount of shiftable load
(6.22)
(6.23)
A balance condition ensures that load is shifted only within a certain time frame t-1 and t+1
(6.24)
All parameters and variables are detailed in the Table of Appendix 7.8.
Chapter 6 – Transmission Grid Congestion Analysis
99
Domestic
International
From
To
Type
From
To
Type
Ganderkesee
St. Hülfe
380kV
Aldeadávila (ES)
Lagoaça (PT)
new 400 kV line
Vieselbach
Altenfeld
380kV
Guillena (ES)
Tavira (PT)
new 400 kV line
Altenfeld
Redwitz
380kV
Moulaine (FR)
Aubange (BE)
new 220 kV line
Diele
Niederrhein
380kV
Bressanone (IT)
Innsbruck (AT)
new 400 kV line
Wahle
Mecklar
380kV
Okroglo (SI)
Udine (IT)
new 400 kV line
Hamburg
Dollern
380kV
Lavorgo (CH)
Morbegno (IT)
new 400 kV line
Wehrendorf
Gütersloh
380kV
Cornier (FR)
Piossasco (IT)
new 400 kV line
Kruckel
Dauersberg
380kV
Hurva/Hallsberg (SE)
Barkeryd (NO)
new 400 kV line
St. Peter (AT)
Isar (DE)
new 380 kV
Krajnik (PL)
Neuenhagen (DE)
new 400 kV line
Plewiska (PL)
Eisenhüttenstadt (DE)
upgrade to 400 kV
Doetinchem (NL)
Niederrhein (DE)
new 400 kV line
Table 15: Additions to the AC grid of 2030 versus today.
(Source: Based on ENTSO-E (2010))
Table 16: Additions to the DC grid of 2030 versus today.
(Source: Own compilation based on Le Tene Maps (2011))
International
Name
From - To
Capacity [MW]
NORNED
Netherlands - Norway
700
Baltic Cable
21 - Sweden
600
Kontek
81 - Denmark East
600
Kontiskan 2
Denmark West - Sweden
300
Skagerrak 1+2
Denmark West - Norway
500
SwePol
Poland - Sweden
600
IFA
Great Britain - France
2000
BirtNed
Great Britain - Netherlands
1000
Norwegian Interconnector
Great Britain - Norway
1400
Storebaelt
Denmark West - Denmark East
600
Nord.Link
22 - Norway
1400
NORNED2
Netherlands - Norway
700
NordSüd1
21 - 25
2000
NordSüd2
25 - 26
2000
NordSüd3
21 - 22
2000
OstWest1
81 - 24
2000
OstWest2
24 - 75
2000
Südwest
72 - 42
2000
Skagerrak 3
Denmark West - Norway
440
Skagerrak 4
Denmark West - Norway
700
East-West-Energy Bridge (Siemens)
81 - Poland
500
COBRA
Denmark West - Netherlands
700
NEMO
Great Britain - Belgium
1000
IFA 2
Great Britain - France
1000
Gunfleet Sands1
Great Britain - Netherlands
1000
Gunfleet Sands2
Great Britain - Belgium
1000
Noth Sea Plattforms UK - Dollert (Emden)
Great Britain - 22
1000
Noth Sea Plattforms - Danmark
22 - Denmark West
2000
SwePol 2
Poland - Sweden
600
Balltic Cable 2
21 - Sweden
600
Baltic Sea Plattforms - Sweden
81 - Sweden
600
Baltic Sea Plattforms - Danmark
81 - Denmark East
600
TYNDP - Sta. Llogaia (ES) - Baixas (FR)
Spain - France
2000
TYNDP - Grande Ile (FR) Piossasco (IT)
France - Italy
1000
TYNDP - Candia (IT) - Konjsko (HR)
Croatia - Italy
1000
Chapter 7 – Interactions between Generation Capacity
Expansion and Grid Development
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
101
7.1 Introduction
While the expansion and coordination of power transmission capacities remains an important
focus of network planning, stakeholders are increasingly concerned with the future
composition of the power generation mix as a whole and its interdependence with
transmission grid planning. The optimal combination of different types of plants that accounts
for the specific characteristics of an energy system dominated by RES has yet to be
determined.
Most stakeholders agree that securing RES integration calls for the expansion of power plant
capacities as back-up reserves in addition to the expansion of transmission capacities
(ENTSO-E 2009). An important and unanswered question, though, is how this additional
capacity will be composed and its optimal geographical distribution. Numerous studies have –
at least in part – dealt with the optimal amount of generation capacity expansion but they have
shortcomings in terms of infrastructure representation. In particular, the available literature
gives no or only vague information concerning transmission grids, the supply of reserve
capacities and the geographical allocation of plants. In this analysis we therefore propose a
more detailed approach on interactions between network planning and power plant
investment. We apply a welfare maximizing model for Germany and Central Europe in order
to determine how many back-up power plants of which specific type will be needed in the
medium term, given the grid structure of 2030. Our model also provides details on the optimal
geographical distribution of the future generation system and its impact on grid congestion.
This information is of great importance when allocating new back-up plants within the energy
grid. As benchmarks for the future expansion of RES generation have already been set in
Europe, we take a special focus on the expansion of conventional capacities. Our aim is to
investigate which conventional energy resource best fits into the future grid dominated by
RES, how many additional plants of this type are needed to provide energy security at
reasonable costs and where they should be best placed. Furthermore, we investigate how the
different flexibility options (i.e. storage, DSM and back-up power plants) affect congestion
patterns in the electricity grid and what that means for the recently proposed grid expansion
projects in Germany (TSO 2012).
The rest of the chapter is organized as follows. Section 7.2 gives a short overview on the
current literature on energy network planning and capacity expansion in Germany and
Europe. Section 7.3 briefly outlines the model applied in this study while Section 7.4 provides
details on the data used. Scenarios are outlined in Section 7.5. Results are presented in Section
7.6 and some conclusions from our findings as well as a summary can be found in Section
7.7.
7.2 Literature review
Numerous studies deal with the future development of conventional generation capacity in the
German energy grid and – using various types of models – their conclusions and methodical
disadvantages differ significantly. The majority of studies suggest that even with a continuous
increase of RES generation capacity, there will still be a need for the installation of additional
conventional power plants.
In a detailed discussion on future capacity adequacy, Maurer et al. (2012) claim that there is a
need for at least 19 GW additional generation capacity for Germany. The analysis is based on
a model that adopts a national ‘autarky’ view of system adequacy and no indication is given
to the expansion need under an integrated European market regime. As many other studies,
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
102
Maurer et al. (2012) omit the importance and benefits of integration of spatially separated
electrical systems with different generation mixes, as pointed out by Scorah et al. (2012).
The Kurzanalyse Kraftwerksplanung (dena 2008) optimizes power plant expansion under
exogenous demand but it is not specific on their geographic allocation. The analysis considers
an increasing need for reserve energy (from 0.84 GW positive and 0.6 GW negative in 2003
to 3.2 GW positive and 2.1 GW negative in 2015) and predicts a need for additional
conventional plant capacity (coal and gas) of 10 to 14.2 GW in 2020. Another study by dena
(2010) delivers more differentiated conclusions. Using the DIME model - in which power
demand is again determined exogenously - it predicts that the capacity of all conventional
power plants will decrease except for lignite-fired plants which is supposed to increase from
20.4 GW in 2005 to 24.3 GW in 2020. According to the authors, even though gas-fired power
plants might provide necessary flexibility, they would be replaced by modern and more
efficient new coal-fired plants due to high gas prices. However, even though the study builds
on a strong data basis regarding infrastructure, it neither specifically optimizes the power
plant fleet nor does it go beyond a 2020 horizon.
The Potsdam Institute for Climate Impact Research (Knopf et al. 2011) uses the model
MICOES to determine a need for increased fossil fueled power generation capacity by 8 GW
in addition to already planned power plants. It does not model plant construction as
endogenous variable though. The Potsdam Institute also uses LIMES (Haller et al. 2012), a
simultaneous grid and generation expansion model which minimizes power system costs.
Here, power demand is exogenously determined through existing projections and capacity
expansion is endogenous. The grid representation in the model is aggregated showing nation-
by-nation NTC values as well as employing a piping model rather than a power flow model.
In a transmission expansion scenario the authors consider Germany to use large energy
imports from Northern Europe to balance demand fluctuations and thus become a net importer
of energy. Nevertheless, the LIMES model results project massive gas power plant expansion
for Germany in the order of 20 – 30 GW by 2030. These values take into account projected
transmission grid expansion and, thus, improved European market integration.
On the European level, the Energy Roadmap 2050 (EC 2011) offers a comprehensive impact
assessment of several policy scenarios. It uses PRIMES and a set of complementing models
defining macro-economic developments in order to determine the market equilibrium for
energy demand and supply. Due to intermittency of RES production, additional investment in
conventional capacity is predicted to be necessary with the amount depending on which of the
outlined policy pathways are chosen. Installed gas-fired power capacity is supposed to
increase across all policy scenarios while coal-fired energy capacity decreases in most
scenarios. Other studies point into the same direction. The World Energy Outlook (IEA
2011d) takes a global perspective using the World Energy Model and predicts additional
installation of conventional energy capacity in Europe from 2011 to 2035 mainly in the field
of gas-fired plants (139 GW) and coal-fired plants (67 GW). EWI (2012) uses the
DIMENSION simulation model for the European electricity market and find that gas-fueled
generation capacity will almost double to 55 GW in 2030 while investment in other
conventional resources declines. Unfortunately, neither of these studies gives information on
the preferred allocation of power plants within Europe or Germany.
Some studies specifically consider uncertainty in energy supply from fluctuating RES. Nagl et
al. (2012) develop a stochastic combined investment and dispatch model with uncertainty in
the feed-in of wind and solar energy sources and apply it to the European electricity system.
The objective of the piping model formulated as LP is to minimize total system costs. It thus
adopts a system perspective and takes into account correlations between solar and wind feed-
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
103
in. Capacities of conventional power plants are projected to decrease for coal and nuclear
power and increase for gas power plants.
Only few studies provide implications on the optimal geographic distribution of power plants
in Germany. One of these is presented by Dietrich et al. (2010) who analyze power plant
placing in Germany with ELMOD under nodal pricing and in a system cost minimization
approach with 12 time slots included at the dispatch stage. In a welfare case where a
benevolent planner is assumed to minimize costs, power plants are mostly placed in the south-
western part of the country and on the northern coast line when taking a national perspective.
However, when allowing for multinational planning, the study sees much more capacity
investment in Lower Saxony and North Rhine-Westphalia, especially close to the Benelux
border in order to relieve cross-border congestion.
In the models currently used to predict developments in composition and distribution of the
power plant fleet in Germany, three general disadvantages arise from the preceding overview.
First, most applications minimize costs rather than maximizing welfare which could give
detailed insight into preferable energy policies by setting a benchmark. Second, none of these
models considers demand as price-sensitive and partly controllable input factor, although
DSM tools gain importance in electricity markets. In a market economy, the correct depiction
of demand should be given more consideration. Third, no study gives very detailed
implications on the desirable allocation of conventional power plants in Germany. Bearing in
mind the significant problems of transmission, this is a crucial question to be answered. All
three gaps could be filled by a model proposed in this chapter. An additional value of this
work stems from our novel consideration of German electricity grid expansion plans outlined
in the TSO proposal of June 2012 (TSO 2012). Most previously mentioned studies omit the
interaction between transmission grid planning and power plant placing. We explicitly model
the interaction between transmission projects flexible alternatives (i.e. Storage, DSM, back-up
power plants).
7.3 Model formulation
Our electricity market model is formulated as QCP. It maximizes a social welfare function
which is subject to several constraints and facing a price elastic demand function. The model
is an evolution derived from Boldt et al. (2012) which in turn uses the ELMOD model
developed by Leuthold et al. (2012). This DC load flow approach is superior to simple piping
models (EC 2011; Haller 2012) because it accounts for loop flows, a peculiar characteristic of
electricity flows. The lossless DC load flow model here is formulated on the basis of PTDF,
which indicate the amount of power flow at each line in dependence of power injection at
some specified hub. DC lines are treated separately from AC lines as they are assumed to be
point-to-point connections not causing loop flows.
The model also includes various storage technologies. It implements a stepwise cost function
for load management (DSM) in order to realistically represent this feature of a flexible energy
market. A restriction is imposed so that load can be shifted only within a certain time frame.
A detailed description of the model used is given in Boldt et al. (2012) so we will only briefly
recapitulate it here. In order to maximize social welfare we solve the following problem
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
104
∑( )
∑
∑
∑
(7.1)
where the demand function may be described as
∑
(7.2)
with the slope
(7.3)
and the intercept
(7.4)
When solving Eq. (7.1) several energy balance constraints have to be accounted for. The
nodal balance constraint has to be true for any node at any point in time
∑
∑( )
(7.5)
as well as the generation capacity constraint
( )
(7.6)
the cost function
∑
(7.7)
the ramping constraints
(7.8)
( )
(7.9)
and the definition of the ramping variable
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
105
(7.10)
As we model a power market with both AC and DC flows, we account for AC flow
constraints
∑
(7.11)
(7.12)
∑
(7.13)
as well as for DC load flow constraints
∑
(7.14)
(7.15)
∑
(7.16)
The “n-1” security criterion is approximated by reducing the capacity of each AC line by a
transmission reliability margin (20%). Note that the model neglects transmission losses. This
is done to keep the model tractable and to omit non-linear elements where possible.
Regarding the implementation of storage technologies, the model considers storage power
limits
(7.17)
(7.18)
and storage capacity limits
( )
(7.19)
We use the formulation of a storage state variable which indicates the state-of-charge.
(7.20)
An overall balance guarantees that the storage device left at the same state-of-charge as in the
beginning.
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
106
∑
(7.21)
DSM constraints for different cost segments restrict the amount of shiftable load
(7.22)
(7.23)
A balance condition ensures that load is shifted only within a certain time frame t-1 and t+1
(7.24)
Finally, an additional constraint ensures that total yearly demand equals the predetermined
level x (TWh).
∑
(7.25)
The QCP is coded in the GAMS modeling environment. The size of the application here
(10.1 GB) makes it necessary to use advanced computers. Computation times with facilities
available at DIW Berlin (64-bit Linux, 32 kernels, 3 GHz CPU, 512 GB Ram) range in the
order of 11-33 hours, including data compilation and export.
7.4 Data
In general it was taken care to align assumptions to the National Grid Development Plan
(TSO 2012) so as to allow for a comparison of results. As the Grid Development Plan does
not provide a lot of detailed information on assumptions and used data, some input
assumptions of the model used here deviate from the TSO Plan.
7.4.1 Geographic coverage
The model application covers Central Europe with 41 nodes. 18 thereof lie in Germany, in
line with the dena-Zones established based on congestion patterns in the seminal dena-II-
study (dena 2010). All countries other than Germany and Denmark are represented with one
node only.
7.4.2 Temporal coverage
The model is applied to the European electricity system as we expect it to be in 2030. Within
the fictive year 2030, an hourly dispatch of the whole year (8760 h) is optimized.
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
107
7.4.3 Generation
The model application includes six dispatchable generation technologies plus must-run feed-
in of wind, solar and hydro plants. Inflexibilities in the dispatch of fossil-fired and nuclear
power plants are reflected by constraints on load gradients and ramping cost. Variable costs
are in line with assumptions in the TSO report and produce a merit order curve plotted in
Figure 35. Since the model is applied to the year 2030, assumptions are made on the
generation capacity available by 2030. The Platts European power plant database (Platts
2011) is used as basis to exogenously determine the retiring dates for all power plants in
Europe and thereby attain remaining generation capacities. We expect over 60 GW of
installed conventional capacity to retire within Germany by 2030 (compared to 104 GW base
level in 2010) which is almost double the 33 GW expected in Maurer et al. (2012).
Information on energy plants found in Platts (2011) is combined with geographical
information of pre-defined congestion zones to allocate power plants to zones. Capacities
deviate between the National Grid Development Plan (TSO 2012) and our assumptions.
Scenario B 2032 of the Grid Development Plan is characterized by a high amount of new gas
power plant capacities in Southern Germany. The report does not specify how it determines
the amount of new capacity and where exactly it is placed. We therefore opt to base or own
assumptions on Platts (2011) and optimize the distribution and technology choice of new
capacities endogenously. Table 17 provides further details on the base assumptions.
in GW
NEP Scenario B
2032 (TSO 2012)
Own estimations
on the basis of
Platts (2011)
Lignite
13.9
9.0
Coal
21.2
20.6
Gas
40.1
8.4
Oil
0.5
0.8
Nuclear
0
0
Biomass
9.4
9.4
Table 17: Generation capacities in Germany in the reference scenario.
(Source: Own compilation)
Wind Index
(IWR 2012)
Solar Index
(SFV 2012)
2005
- 12.8%
+ 1%
2006
- 3.9%
+ 3%
2007
+ 2.7%
+ 3%
2008
+ 1.7%
+ 2%
2009
- 9.2%
+ 2%
2010
- 25.1%
- 4%
2011
+ 2.3
+ 9%
Deviation from
rolling 10-year
average
Deviation from
2005-2012
average
Table 18: Wind and solar production 2005-2011 in Germany.
(Source: Own compilation)
The growth of renewable energies in all countries else than Germany is based on projections
of productions outlined in EcoFys et al. (2011) which are based on NREAP. Construction of
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
108
feed-in time series for fluctuating RES is based on meteorological information (Dee et al.
2011; Eurostat 2011) and actual production data of Germany from 2011. Calculations are
based on the reference year 2011 as this year represents a relatively good average year in
terms of wind production in Germany, see Table 18. Further details on the derivation of
power output from solar radiation and wind speed data can be found in Boldt et al. (2012).
The time series expose a German peak demand of 84 GW just as in the TSO grid plan.
Maximal residual load of reference demand is 76.2 GW on a November day, peak
simultaneous feed-in of solar and wind power amounts to 106.7 GW (with 157 GW installed
capacity), the minimum lies at 1.4 GW. Peak excess supply of solar and wind feed-in amounts
to 33.1 GW. Note that these figures refer to reference demand. As demand is endogenous and
price-sensitive in the model, deviations can occur in the resulting actual demand.
Figure 35: Variable generation cost.
(Source: Own illustration)
7.4.4 Demand
For all scenarios, German net power demand equals 535 TWh per year, including industry
demand. This is equal to the 2010 realization of net demand (TSO 2012). While total yearly
demand is fixed in the model, its actual repartition over time is endogenous. Demand is
determined through a price-sensitive linear demand function with elasticity -0.1. Growth of
the reference demand outside Germany is set at 9.3% absolute growth between 2011 and
2030.
7.4.5 Storage & DSM
Three storage technologies are included as measures to flexibilize supply: Adiabatic
Compressed Air Storage (aCAES; 4 GW and 16 GWh in Germany), Pump Storage (9 GW
and 60 GWh in Germany) and Battery storage (5 GW and 40 GWh in Germany). The aCAES
figure is half of the potential identified for Germany in Gillhaus et al. (2006). Three categories
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
109
of DSM possibilities are included as measures to flexibilize demand. The cost for shifting
consumer load is described with a step-wise increasing cost function in order to account for
consumer heterogeneity: Low-cost household DSM (3 EUR/MWh), medium-cost commercial
DSM (5 €/MW h) and high-cost industrial DSM (10 EUR/MWh). Up to 20% of the reference
demand level can be shifted within a range of 2 hours.
7.4.6 Grid
Regarding the grid structure for 2030 (topology and capacities) we refer to the work
performed in Boldt et al. (2012) and the recently published plans of the German Transmission
System Operators (TSO 2012). Their projections take into account the Ten-Year Network
Development Plan of the European Transmission System Operators and further planned
projects. The application includes 41 nodes, 263 lines in the AC grid and 50 DC lines.
7.5 Scenarios
8 scenarios are established which allow for a detailed insight into the effect of storage, DC
lines and power plant investment on grid congestion. The reference scenario (1) is
characterized by the assumptions of the TSO Grid Development Plan scenario B 2032
regarding new transmission line projects and the existence of storage facilities. Alternatively,
we propose a storage scenario (2a) in which we add two types of storage facilities in Germany
as well as the possibility of DSM, while holding the grid structure unmodified. A No-HVDC-
scenario (2b) describes the same situation as in 2a but without HVDC lines. A Few-HVDC-
scenario (2c) includes just a subset of the HVDC lines proposed by the TSOs. A power-plant-
placing scenario with the proposed HVDC lines (3) runs scenario 1 with endogenous
generation capacities. The same holds for the power-plant-placing scenarios with storage and
HVDCs (3a), without HVDC (3b) and with few HVDC (3c). Table 19 summarizes the main
scenario characteristics.
Scenario
DSM
Storage
German
HVDC
Power
plant
1 – Reference
-
-
28 GW
-
2a – Storage
28 GW
-
2b - No HVDC
-
-
2c - Few HVDC
14.6 GW
-
3 – 1 with investment
-
-
28 GW
3a – 2a with investment
28 GW
3b – 2b with investment
-
3c – 2c with investment
14.6 GW
Table 19: Scenario overview.
(Source: Own production)
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
110
7.6 Results
7.6.1 Generation
Figure 36 shows the generation pattern over the whole year in hourly resolution. Lignite and
coal power plants are used as base load technologies unless RES feed-in is too strong. Note
that at the assumed carbon price of 43 EUR/t, gas power plants are still called after coal-fired
plants in the merit order (not taking into account cycling cost). Gas power plants are only
called upon at few occasions, in times where RES feed-in is weak. Additionally, gas power
plants are used during short intervals in periods of high fluctuations of renewable energies due
to their low ramping costs. This pattern pertains to all scenarios and is exemplarily pictured
for the reference scenario in Figure 36. Details on the usage of different several generation
technologies can also be found in Table 20 where different scenarios are compared. The table
demonstrates that all fossil-fired plants are increasingly used as HVDC transmission
capacities are eliminated or reduced (3b, 3c). The scenarios with endogenous investment shift
the power mix towards increased usage of new gas-fired power plants, to the detriment of all
other fossil-fired plants. Oil power plants are not used at any instance anymore for they are
too expensive with the assumed 43 EUR/t CO2 prices in 2030. The system-wide share of RES
production lingers around the 52% mark with slight deviations. Storage and DSM improve the
share of RES in Germany slightly from 76.3% to 76.5% in the presence of HVDC lines.
Scenarios 2b and 2c with no to few HVDC lines produce a lower system-wide RES share than
other scenarios. This suggests that HVDC is indeed used to promote the RES share in the
system. We find a systematic negative effect of endogenous power plant investment on the
RES share which is a pretty obvious result.
The net power consumption is in line with the TSO assumptions of 535 TWh in Germany
(TSO 2012). A constraint in the model ensures this amount of yearly demand. Power
production levels in Germany are lower than the demand level in most scenarios. As power
generation is short of demand, Germany is a net importer of electricity by 2030 in most
scenarios, contrasting the situation of 2012. We owe this effect to the increased price
differences between countries with fossil-based production versus those with constant hydro
production (Scandinavia) and nuclear energy (i.e. France). As German prices increase more
than proportionately to some neighbors’ power prices, there is increased import. The import
rate increases with the use of storage and DSM in scenario 3a. HVDC lines seem to have an
aggravating effect on electricity import of Germany. The more HVDC lines in Germany, the
higher is the import rate of Germany. As HVDC disappear (scenario 2b), cheap northern
German energy cannot be transported to southern demand zones and thus needs to be
exported to neighbors.
We observe no systematic effect of HVDC lines, power plant investment and storage on
demand levels by nature of the model constraints. The effect of storage and HVDC lines on
the average German price level is somewhat counter-intuitive. The presence of HVDC lines
puts upward pressure on German average prices. This could be due to the fact, that average
prices are not weighed by importance of nodes.
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
111
Table 20: Key results of scenarios.
(Source: Own compilation)
Figure 36: Generation dispatch pattern in the reference scenario.
(Source: Own compilation)
NO INVESTMENT
WITH INVESTMENT
NEP 2012
Scenario
1
2a
2b
2c
3
3a
3b
3c
B 2032
Reference
Storage
No HVDC
Few HVDC
Reference
Storage
No HVDC
Few HVDC
B 2032
Investment GW Europe
-
NEP Capacity
NEP Capacity
NEP Capacity
23,327
23,255
32,154
23,303
-
Investment GW Germany
-
NEP Capacity
NEP Capacity
NEP Capacity
0
0
5,348
0
-
RES share system-wide
52.30%
52.38%
51.72%
52.20%
52.05 %
52.15%
51.45%
51.96%
RES Share of production in Germany
76.31%
76.46%
76.53%
76.36%
76.33%
76.50%
76.53%
76.39%
Yearly demand in D in TWh
535
535
535
535
535
535
535
535
562
Yearly production in D in TWh
482
488
549.2
495
480.5
480.3
510.2
488
550
Export rate
-9,96%
-8.84%
2.65%
-7.48%
-10.19%
-10.23%
-4.64%
-8.82%
-2.06%
Use rate all AC lines
24.7%
24.7%
24.4%
23.9%
24.6%
24.6%
24.8%
23.9%
-
Use rate all DC lines
90.3%
90.2%
95.8%
79.4%
90.2%
90.4%
95.9%
79.6%
-
Use rate of proposed HVDC line projects
78.97%
78.88%
-
89.51%
79.38%
79.74%
-
90.48%
German average price EUR/MWh
57.26
56.75
54.35
56.76
57.08
57.29
54.06
57.39
-
Welfare in billion EUR
9.73068E+11
9.733E+11
9.69411E+11
9.73873E+11
9.74321+11
9.74500E+11
9.70739+11
9.74057+E11
-
Full Load Hours Lignite
4933
4437
4931
4422
4598
4625
4562
4617
-
Full Load Hours Coal (Old)
1799
1685
2126
1760
1560
1575
1747
1638
-
Full Load Hours Coal (New)
-
-
-
-
-
-
-
-
-
Full Load Hours Gas (Old)
2089
1580
1757
1604
805
764
768
795
-
Full Load Hours Gas (New)
-
-
-
7377
7388
7136
7415
-
Full Load Hours Oil
176
175
173
175
1
1
0
1
-
Full Load Hours Nuclear (abroad)
7863
7869
7327
7839
7870
7876
7333
7847
-
Extremely dry February 2011 (Omega high anticyclone), warm April 2011, rainy summer 2011, warm October 2011, dry November 2011, windy December 2011
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
112
7.6.2 Investment
Results show that optimal capacity expansion levels for most technologies are much lower
than previous “reference” studies propose for Germany (EWI et al. (2010); dena (2008); EC
(2011)). This holds across all technologies. A possible explanation is that investment cost and
carbon prices are set too low in the reference studies. Furthermore, many studies disregard
dispatch inflexibilities of coal and lignite technologies and omit the possibilities of flexible
demand and storage. However, we must admit that the model used here may undervalue the
necessity of power plants because not accounting for uncertainty in RES feed-in and demand.
Table 20 shows the level of overall EU capacity expansion by 2030 for all scenarios. Capacity
expansion in Germany is zero except in the absence of national HVDC lines in scenario 3b.
Figure 37 shows that capacities are foremost planted in the southern to central zones, and
Hamburg.
The model application suggests that investment into roughly 23-32 GW of gas-fired power
plants be undertaken in south and Central Eastern Europe (Italy and Slovenia). We explain the
(comparatively) low level of overall investment by the fact that other studies omit or
underestimate the value of storage and DSM. According to Maurer et al. (2012), DSM and
storage can only contribute little to reducing capacity needs. They argue that DSM and
storage are designed to shift loads for few hours whereas supply shortages can occur with
longer durations. The results here show that hydro pump storage and other facilities are also
used for seasonal storage, thus showing great value in the short term as well as in the long
term.
Figure 37: New generation capacity by 2030 in the absence of national HVDC lines.
(Source: Own illustration)
Regarding the technology choice, gas-fired power remains dominant in all scenarios, although
it lies behind coal in the merit order. Concentration on gas-fired plants is also due to increased
need for flexible resources with low ramping cost. 5,348 MW of gas-fired power plants are
placed in Central and Southern German zones in scenario 3b, in the absence of HVDC lines
(Figure 37). In all other scenarios, no power plant investment takes place in Germany. We
conclude that even under strong decommissioning - as assumed in this study here – the model
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
113
predicts hardly any need for new power plants in Germany with storage, demand-side-
management and HVDC line extensions providing for sufficient alternatives. As indicated by
the volatile generation profiles in Figure 36, new power plants – if built - will require good
cycling capabilities. Such importance of cycling flexibility in the investment decision has also
been pointed out in a related analysis carried-out by Fleten and Nasakkala (2010). The role of
cycling cannot be accounted for in full detail in this study, since a more detailed analysis
would require a stochastic model.
7.6.3 Congestion AC Grid
Regarding the congestion patterns inside Germany, Figure 38 provides details for the standard
grid (without German HVDC lines). Connections whose capacity limit is exhausted in less
than 20% of the time are shown in yellow color. Connections with more than 40% of
congested time and more than 60% are orange and red, respectively. Connections highlighted
in dark red are overloaded more than 80% of the hours observed.
The comparison between the reference scenario (1) and the storage scenario with HVDC (2a)
shows little changes. However scenario 3c demonstrates that the there is less congestion on a
few south-northern routes in absence of HVDC lines. This is true especially for the links 41-
42, 24-25 and 83-25 in central southern Germany. The relatively strong bottlenecks in
scenario 3b can be relieved by the placement of 14.6 GW of HVDC lines in scenario 3c.
Overall, we conclude that in scenario 3c, a reduced amount of HVDC capacity is a sufficient
measure to avoid severe shortages in the domestic AC grid. Scenario 3c shows that 14.6 GW
of HVDC lines are able to bringing congestion in the German power grid to a level relatively
close to the reference scenario with 28 GW HVDC capacity. The placement of additional
power plants (ca. 5.3 GW in Germany) in scenario 3b is not sufficient to relieve bottlenecks to
the level of the reference scenario.
1 – Reference
3b – Storage but no HVDC
3c – 14.6 GW HVDC
Figure 38: Congestion patterns in the standard grid.
(Source: Own illustration)
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
114
7.6.4 Congestion on HVDC lines proposed in the NEP 2012
While the HVDC lines proposed by TSOs contribute to less congestion in the AC grid, the
HVDC lines themselves are mostly used to a high extent, as plotted in Figure 39. The figure
only pictures the situation in the reference scenario. Its structure remains unchanged in other
scenarios, though. The average use rate is depicted on the right side of the graph and it is
consistently high for most lines, except for some lines on the north-south corridors B, C and
D. The left side shows the hours of congestion as percentage. We see that some HVDC lines
of the C Corridor between zones 21, 22 and the southern zones 42 and 25 are overloaded over
40% of the time. Most lines on the C Corridor are often overloaded. Given the large
dimensions of the range of 12 GW of transmission capacity of corridor C, this is an
interesting result. The large capacity of this connection appears to be fully justifiable. The
right part of the same chart shows that some lines in the Northwest part of the Republic have
high average usage rates, although congestion is not as frequent as in the corridor C. This
holds particularly for the HVDC transmission line 1 from Emden to Osterath (22-72), which
has a high average utilization rate over 85% - yet it is used to full capacity less than 40% of
the time. The situation is quite different for HVDC lines in the southwest and northeast. The
average utilization of the HVDC links 10 from Gustrow to Meitingen (81-76) and 9 from
Lauchstaedt to Meitingen (83-76) are relatively low. The same is true for the HVDC
transmission line 2 from the Rhenanian lignite mining area in Osterath to Philipsburg (72-41)
and Elsfleth-Philipsburg (22-41). One might r aise the question of the lines’ usefulness. Due to
the relatively low utilization of some HVDC lines, we investigate scenarios which deviate
from the configuration of an HVDC network as proposed by the TSOs. Due to the non-
existence of HVDC transmission capacity in scenarios 2b and 3b, congestion is transferred
from the DC to the AC grid where new bottlenecks occur. In scenarios 2c and 3c, we propose
the construction of only 14.6 GW of HVDC lines instead of 28 GW. It can be seen that the
remaining HVDC lines are in good utilization of around 90% with a positive impact on the
overall network. A value of 90% comes close to the use rates of traditional HVDC
interconnectors between countries.
Figure 39: Congestion on HVDC lines proposed in the NEP 2012 (reference scenario).
(Source: Own illustration)
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
115
A further detailed analysis of congestion patterns on the different corridors is illustrated in
Figure 40. All in all, corridors B & C are seldomly used to capacity (less than 10% of the
time). Corridor A and B are used to full capacity at less than 20% of the time. The use rate of
corridor D is lowest of all corridors, followed by corridor B. Note that use rates and congested
times within corridor C vary greatly, as indicated in Figure 39. In scenario 3a, storage seems
to be complementary to better usage of HVDC lines in times where lines are not congested. In
scenario 3c, the two corridors are almost always used to full capacity. We may conclude from
the analysis above, that the necessity of the HVDC lines proposed in the TSO plan varies
greatly case by case. While all corridors do show some positive impact on relieving
congestion in the AC grid, there seem to be some individual links which have little to no
positive impact. A prioritization of HVDC projects may thus be a good step to reduce costs of
grid expansion while equally ensuring the advantages that HVDC lines provide for the grid
system.
Scenario 1 - Reference Scenario 3a Storage & Investment
Scenario 3c – Only 2x2GW HVDC lines Indications in Grid Development Plan B 2022
Figure 40: Comparison of congestion patterns on HVDC lines proposed in NEP 2012.
(Source: Own illustration and TSO (2012, p.169))
7.6.5 Price differences
A basic assumption of the model application is that German producers and consumers face
nodal prices. While such market design is not in force today, we assume that it is going to be
implemented by 2030. As shown in Figure 41, nodal prices within Germany align around 54-
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
116
61 EUR/MWh in the reference scenario. Regional differentiation is low. This result can easily
explained by the balancing effect of massive HVDC capacity. As soon as this is left out,
prices between regions drift apart quite heavily, as shown in the middle section of Figure 41.
A huge price differential between exporting northern zones and importing southern zones
emerges. The right side of the graphs demonstrates that DSM, storage management and power
plant placing manage to bring the price structure closer to its reference case even in the
presence of only 14.6 GW of HVDC lines. However, effects are only local, and Germany
remains affected by price developments in neighboring states.
1 Reference
2b Storage but no HVDC
3c Investment & 14.6 GW
HVDC
Figure 41: Prices in different scenarios.
(Source: Own illustration)
7.7 Conclusions
This chapter presents a model for the analysis of power plant placing and grid congestion. An
application is done for Central Europe in 2030 and congestion patterns are compared to the
Grid Development Plan of the German TSOs (TSO 2012). We find that HVDC lines as
proposed in the German Grid Development plan are useful in relieving overall congestion.
However, some lines have less impact on overall congestion than others and could be marked
as second priority. A prioritization of HVDC projects would be an appropriate measure to
ensure that the positive effects of HVDC lines prevail.
The analysis shows that a mix of few HVDC lines, storage, DSM and the placement of power
plants can contribute to alleviating the need in expanding power transmission capacity.
Overall investment levels into generation capacity are way lower in our results compared to
related studies (e.g. dena (2008); EC (2011); EWI et al. (2010); Maurer et al. (2012), TSO
(2012)). We conclude that many comparable models over-estimate the necessity of power
plants by omitting the flexibilities offered by storage, DSM and increased grid capacities. We
suggest it would be beneficial to coordinate the planning of power plant investment along
with grid system planning.
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
117
The need for transmission capacity expansion and generation capacity investments are the
focus of the application presented here. It should be subject of another line of research
(Sauma & Oren 2009; Milstein & Tishler 2012) whether sufficient investment incentives are
present in today’s liberalized energy-only markets. Similarly, subjects such as security of
supply and risk aversion of planners deserve more attention (van der Weijde & Hobbs 2012)
and should possibly be modeled with tools that include uncertainty in demand and RES feed-
in.
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
118
7.8 Appendix
Sets
Set of all plant types
Set of all nodes
Set of all line
Set of all DC lines
Set of all times/hours
Set of all storage types
Parameters
Demand elasticity at reference point
Factor defining load levels
Maximum capacity of line
Maximum capacity of line
Maximum capacity of demand-side management at high cost
Maximum capacity of demand-side management at low cost
Maximum capacity of demand-side management at medium cost
Maximum storage inflow
Maximum storage outflow
Storage capacity limit
Maximum of energy generation by hydro powered plants
Cost for DSM
Investment Costs for plant type in node
Marginal ramping costs
Incidence matrix
Maximum of generation capacity at node of plant
Limit of ramped up generation capacity
Load Gradient as percentage of nominal capacity
Conversion efficiency storage
Reference price of demand function at
Maximum of energy generation by photovoltaic power
Chapter 7 – Interactions between Generation Capacity Expansion and Grid Development
119
Reference demand at
Maximum of energy generation by wind power
Cost for plant type
Slope of demand function
Power transfer distribution factor concerning node and line
Factor defining the availability of plant type
Predetermined level of yearly demand
Variables
Line flow on
Net input on node
Total generation cost
Line flow on
Net input at node
Area under demand function
Welfare
Positive
Variables
DSM shifting load at high cost
DSM shifting load at low cost
DSM shifting load at medium cost
DSM adding load at high cost
DSM adding load at low cost
DSM adding load at medium cost
Investment into generation capacity
Storage inflow
Storage level
Storage outflow
Generation change from one period to the next
Demand at node
Generation of plant type of firm at node
References
120
References
Aalami, H.A., Moghaddam, M.P. & Yousefi, G.R., 2010. Demand Response Modeling
Considering Interruptible/Curtailable Loads and Capacity Market Programs. Applied
Energy, 87(1), pp.243–250.
Abrell, J., Kunz, F. & Weigt, H., 2008. Start Me Up: Modeling of of Power Plants Start-Up
Conditions and their Impact on Prices. TU Dresden Electricity Markets Working
Paper, WP-EM-26.
Agora, 2012. 12 Thesen zur Energiewende, Berlin: Agora Energiewende. Available at:
http://www.agora-
energiewende.de/fileadmin/downloads/Agora_Impulse_12_Thesen_zur_Energiewend
e_Kurzfassung_web.pdf [Accessed December 10, 2012].
Ahman, M., 2006. Government Policy and the Development of Electric Vehicles in Japan.
Energy Policy, 34(4), pp.433–443.
Anegawa, T., 2009. Desirable Characteristics of Public Quick Charger. Available at:
http://www.emc-mec.ca/phev/Presentations_en/S12/PHEV09-S12-
3_TakafumiAnegawa.pdf [Accessed November 14, 2012].
Anegawa, T., 2010. Safety Designof CHADEMO Quick Charger and its impact on Power
Grid. Available at: http://www.ev-charging-
infrastructure.com/media/downloads/inline/takafumi-anegawa-tepco-11-
20.1290790915.pdf [Accessed November 14, 2012].
Arun, P., Banerjee, R. & Bandyopadhyay, S., 2008. Optimum Sizing of Battery-Integrated
Diesel Generator for Remote Electrification through Design-Space Approach. Energy,
33(7), pp.1155–1168.
Baker, J., 2008. New Technology and Possible Advances in Energy Storage. Energy Policy,
36(12), pp.4368–4373.
Baldick, R., 2002. Variation of Distribution Factors with Loading, Available at:
http://www.hks.harvard.edu/hepg/flowgate/Baldick_variation.distribution.factors_8-
03.pdf [Accessed December 6, 2012].
Barnes, T. & Liss, W., 2008. Analysis of Cost-Effective Off-Board Hydrogen Storage and
Refueling Stations, Available at: http://www.osti.gov/servlets/purl/947992-D6UWby/
[Accessed October 5, 2012].
Basar, T. & Olsder, G.J., 1999. Dynamic Noncooperative Game Theory 2nd ed., Society for
Industrial and Applied Mathematics. Available at:
http://www.books24x7.com/marc.asp?bookid=23050 [Accessed May 10, 2012].
BDEW, 2011. BDEW Kraftwerksliste April 2012, Berlin: Bundesverband der Energie- und
Wasserwirtschaft e.V. - BDEW. Available at: http://www.solarify.eu/wp-
content/uploads/2012/05/12-05-02-BDEW_KW-Liste-kommentiert.pdf [Accessed
December 6, 2012].
References
121
BDEW, 2010. Lastprofile unterbrechbare Verbrauchsprofile, German Association for Energy
Economics. Available at: http://www.bdew.de/bdew.nsf/id/
DE_Lastprofile_unterbrechbare _Verbrauchseinrichtungen? [Accessed August 8,
2010].
Benders, J., 1962. Partitioning Procedures for Solving Mixed Integer Variables Programming
Problems. Numerische Mathematik, 4, pp.238–252.
Birge, J. & Louveaux, F., 1997. Introduction to Stochastic Programming 1st edition., Berlin:
Springer Series in Operations Research.
BMU, 2010. Langfristszenarien und Strategien fuer den Ausbau der erneuerbaren Energien
in Deutschland bei Beruecksichtigung der Entwicklung in Europa und global, Berlin:
Federal Ministry for the Environment. Available at:
http://www.bmu.de/files/pdfs/allgemein/application/pdf/leitstudie2010_bf.pdf
[Accessed June 6, 2011].
BNetzA, 2012. Bundesnetzagentur legt Entwurf fuer Bundesbedarfsplan vor,
Bundesnetzagentur fuer Elektrizitaet, Gas, Telekommunikation, Post und
Eisenbahnen. Available at:
http://www.bundesnetzagentur.de/cln_1932/SharedDocs/Pressemitteilungen/DE/2012/
121126_NEPStrom2012Bestaetigung.html;jsessionid=91452E0021F37D3BF8163F63
A18DFF2B?nn=65116 [Accessed November 27, 2012].
BNetzA, 2011a. Genehmigung des Szenariorahmens zur energiewirtschaftlichen
Entwicklung nach § 12a EnWG., 7 December 2011: Bundesnetzagentur fuer
Elektrizitaet, Gas, Telekommunikation, Post und Eisenbahnen. Available at:
http://www.bundesnetzagentur.de/SharedDocs/Downloads/DE/BNetzA/Presse/Hinterg
rundinfosPressekonferenzen/111207Szenariorahmen/111207PKSzenariorahmenFolien
.pdf [Accessed August 12, 2011].
BNetzA, 2011b. Kraftwerksliste der Bundesnetzagentur - Stand: 14.11.2011, Bonn:
Bundesnetzagentur fuer Elektrizitaet, Gas, Telekommunikation, Post und
Eisenbahnen. Available at:
http://www.bundesnetzagentur.de/SharedDocs/Downloads/DE/BNetzA/Sachgebiete/E
nergie/Sonderthemen/VeroeffKraftwerksliste/VeroeffKraftwerksliste_xls.xls?__blob=
publicationFile [Accessed November 14, 2011].
BNetzA, 2011c. Monitoringsbericht 2011, Bundesnetzagentur fuer Elektrizitaet, Gas,
Telekommunikation, Post und Eisenbahnen. Available at:
http://www.bundesnetzagentur.de/SharedDocs/Downloads/DE/BNetzA/Presse/Bericht
e/2011/MonitoringBericht2011.pdf?__blob=publicationFile [Accessed December 10,
2012].
Boldt, J., Hankel, L., Laurisch, L., Lutterbeck, F., Oei, P.-Y., Sander, A., Schröder, A.,
Schweter, H., Sommer, P., Sulerz, J., 2012. Renewables in the Grid - Modeling the
German Power Market of the Year 2030. TU Dresden Electricity Markets Working
Paper, WP-EM-48, p.91.
Brown, S., Pyke, D. & Steenhof, P., 2010. Electric Vehicles: The Role and Importance of
Standards in an Emerging Market. Energy Policy, 38(7), pp.3797–3806.
References
122
Burstedde, B., 2012. Essays on the Economics of Congestion Management – Theory and
Model-based Analysis for Central Western Europe. PhD Thesis. Cologne: University
of Cologne.
Capros, P., 2011. PRIMES Energy System Model, Athens: National Technical University of
Athens. Available at:
http://www.e3mlab.ntua.gr/e3mlab/PRIMES%20Manual/PRIMES_ENERGY_SYST
EM_MODEL.pdf [Accessed April 20, 2012].
Conejo, A.J., Carrión, M. & Morales, J.M., 2010. Decision Making under Uncertainty in
Electricity Markets, New York: Springer. Available at:
http://public.eblib.com/EBLPublic/PublicView.do?ptiID=645540 [Accessed
December 6, 2012].
Cramton, P. & Ockenfels, A., 2011. Economics and Design of Capacity Markets for the
Power Sector. Zeitschrift fuer Energiewirtschaft, 36(2), pp.113–134.
Cramton, P. & Stoft, S., 2005. A Capacity Market that Makes Sense. The Electricity Journal,
18(7), pp.43–54.
Dee, D., Uppala, S., Simmons, A., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U.,
Balmaseda, M., Balsamo, G., Bauer, P., others, 2011. The ERA-Interim Reanalysis:
Configuration and Performance of the Data Assimilation System. Quarterly Journal of
the Royal Meteorological Society, 137(656), pp.553–597.
dena, 2010. dena Grid Study II. Integration of Renewable Energy Sources in the German
Power Supply System from 2015 – 2020 with an Outlook to 2025, Berlin: Deutsche
Energie-Agentur GmbH - dena.
dena, 2012. Energiesystem der Zukunft, Berlin: Deutsche Energie-Agentur GmbH. Available
at: http://www.powertogas.info/power-to-gas/gas-speichern.html [Accessed November
14, 2012].
dena, 2008. Kurzanalyse der Kraftwerks und Netzplanung in Deutschland bis 2020 (mit
Ausblick auf 2030), Berlin: Deutsche Energie-Agentur GmbH. Available at:
http://www.erfurt.ihk.de/files/11928E85D21/2008_dena_studie.pdf [Accessed January
15, 2012].
Diaf, S., Diaf, D., Belhamel, M., Haddadi, M., Louche, A., 2007. A Methodology for Optimal
Sizing of Autonomous Hybrid PV/Wind System. Energy Policy, 35(11), pp.5708–
5718.
Dietrich, K., Leuthold, F. & Weigt, H., 2010. Will the Market Get it Right? The Placing of
New Power Plants in Germany. Zeitschrift fuer Energiewirtschaft, 34(4), pp.255–265.
Dixit, A.K. & Pindyck, R.S., 1994. Investment under Uncertainty, Princeton, N.J.: Princeton
University Press.
Doughty, A., Butler, P., Akhil, A., Clark, N., Boyes, J., 2010. Batteries for Large-Scale
Stationary Electrical Energy Storage, Available at:
http://www.electrochem.org/dl/interface/fal/fal10/fal10_p049-053.pdf.
References
123
Duthaler, C.L., Kurzidem, D.I.M. & Andersson, G., 2007. Power Transfer Distribution
Factors: Analyse der Anwendung im UCTE-Netz. Master Thesis. Zurich: ETH Zurich.
Dye, J., Hobbs, B. & Pang, J., 2002. Oligopolistic Competition in Power Networks: A
Conjectured Supply Function Approach. IEEE Transactions on Power Systems, 17(3),
pp.597–607.
EC, 2011. Energy Roadmap 2050, Brussels: European Commission.
EC, 2010. EU Energy Trends to 2030 : Update 2009, Luxembourg: European Commission,
Publ. Office of the European Union.
EcoFys, 2009. Oekonomische und technische Aspekte eines flaechendeckenden Rollouts
intelligenter Zaehler, Bonn: Bundesnetzagentur. Available at:
http://www.bundesnetzagentur.de/cae/servlet/contentblob/153300/publicationFile/648
2/EcofysFlaechendeckenderRollout19042010pdf.pdf.
EcoFys, Fraunhofer Institute for Systems and Innovation Research - ISI, Energy Economics
Group (EEG) at TU Vienna, University of Cambridge, Lithuanian Energy Institute,
Utrecht University, EnergoBanking Advisory Ltd, Bocconi University, KEMA, 2011.
Renewable Energy Policy Country Profiles - 2011 version, Available at:
http://www.reshaping-res-policy.eu [Accessed January 15, 2012].
EEA, 2012. Annual European Union Greenhouse Gas Inventory 1990–2010 and Inventory
Report 2012. Available at: http://www.eea.europa.eu/publications/european-union-
greenhouse-gas-inventory-2012 [Accessed June 1, 2013].
EEX, 2012. Prices Dayahead Market, Leipzig, Germany: European Energy Exchange.
Available at: http://www.eex.com/en/Market Data/Trading Data/Power [Accessed
November 10, 2012].
EEX, 2010. Prices Dayahead Market, Leipzig, Germany: European Energy Exchange.
Available at: http://www.eex.com/en/Market Data/Trading Data/Power [Accessed
October 5, 2012].
Egging, R., 2010. Multi-Period Natural Gas Market Modeling Applications, Stochastic
Extensions and Solution Approaches. PhD Thesis. Maryland: University of Maryland.
Ehrenmann, A. & Smeers, Y., 2011a. Generation Capacity Expansion in a Risky
Environment: A Stochastic Equilibrium Analysis. Operations Research, 59(6),
pp.1332–1346.
Ehrenmann, A. & Smeers, Y., 2004. Inefficiencies in European Congestion Management
Proposals, Université Catholique De Louvain. Available at:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=746506 [Accessed January 25,
2013].
Ehrenmann, A. & Smeers, Y., 2011b. Stochastic Equilibrium Models for Generation Capacity
Expansion. Stochastic Optimization Methods in Finance and Energy - International
Series in Operations Research & Management Science, 163, pp.273–310.
References
124
Ekren, B.Y. & Ekren, O., 2009. Simulation Based Size Optimization of a PV/Wind Hybrid
Energy Conversion System with Battery Storage under Various Load and Auxiliary
Energy Conditions. Applied Energy, 86(9), pp.1387–1394.
Ekren, O. & Ekren, B.Y., 2010. Size Optimization of a PV/Wind Hybrid Energy Conversion
System with Battery Storage using Simulated Annealing. Applied Energy, 87(2),
pp.592–598.
Ekren, O., Ekren, B.Y. & Ozerdem, B., 2009. Break-Even Analysis and Size Optimization of
a PV/Wind Hybrid Energy Conversion System with Battery Storage – A Case Study.
Applied Energy, 86(7-8), pp.1043–1054.
Electricity Journal, 2008. Why Installing Smart Meters Might Not Be All That Smart.
Electricity Journal, 21(1), pp.6–7.
Electricity Storage Association, 2011. Technologies, Washington, USA: Electricity Stroage
Association. Available at: http://www.electricitystorage.org/ESA/technologies/.
ENTSO-E, 2011. Hourly Consumption Data for 2010. European Network of Transmission
System Operators for Electricity. Available at: https://www.entsoe.eu/resources/data-
portal/consumption [Accessed October 16, 2011].
ENTSO-E, 2012. NTC Values - Intro to the NTC Matrix and BCE Maps, Brussels: European
Network of Transmission System Operators for Electricity. Available at:
https://www.entsoe.eu/resources/ntc-values/ [Accessed October 15, 2012].
ENTSO-E, 2009. System Adequacy Forecast 2009-2020, Brussels: UCTE Union for the
Coordination of Transmission of Electricity.
ENTSO-E, 2010. Ten-Year Network Development Plan 2010-2020 (TYNDP). FInal Release.,
Brussels: ENTSO-E, , European Network of Transmission System Operators for
Electricity. Available at:
https://www.entsoe.eu/fileadmin/user_upload/_library/SDC/TYNDP/TYNDP-
final_document.pdf.
Erdmann, G. & Zweifel, P., 2008. Energieoekonomik : Theorie und Anwendungen, Berlin
[u.a.]: Springer.
Eurelectric, 2011. Regulation for Smart Grids, Available at: http://congreso-smartgrids.es/wp-
content/uploads/2012/03/Eurelectric-Report-on-Regutaion-for-Smart-Grids.pdf
[Accessed December 6, 2012].
Eurostat, 2011. Energy, Transport and Environment Indicators, Belgium: Office for Official
Publications of the European Communities.
EWI, 2012. Untersuchungen zu einem zukunftsfaehigen Strommarktdesign, Cologne: EWI,
University of Cologne. Available at:
http://www.bmwi.de/BMWi/Redaktion/PDF/Publikationen/endbericht-
untersuchungen-zu-einem-zukunftsfaehigen-
strommarktdesign,property=pdf,bereich=bmwi,sprache=de,rwb=true.pdf [Accessed
April 23, 2012].
References
125
EWI, PROGNOS & GWS, 2010. Energieszenarien fuer ein Energiekonzept der
Bundesregierung, Basel/Cologne/Osnabruck: Commissioned by the Federal Ministry
for Economics and Technology. Available at:
http://www.bmu.de/energiewende/downloads/doc/46367.php [Accessed August 8,
2011].
Fan, L., Hobbs, B. & Norman, C., 2010. Risk Aversion and CO2 Regulatory Uncertainty in
Power Generation Investment: Policy and Modeling Implications. Journal of
Environmental Economics and Management, 60(3), pp.193–208.
Federal Government, 2010. Energiekonzept fuer eine umweltschonende, zuverlaessige und
bezahlbare Energieversorgung, Berlin: Federal Ministry for Economics and
Technology, Federal Ministry for the Environment.
Federal Government, 2011a. Energy Industry Act - Energiewirtschaftsgesetz.
Federal Government, 2011b. Energy Line Extension Act - Energieleitungsausbaugesetz.
Feng, W. & Figliozzi, M.A., 2012. Conventional vs Electric Commercial Vehicle Fleets: A
Case Study of Economic and Technological Factors Affecting the Competitiveness of
Electric Commercial Vehicles in the USA. Procedia - Social and Behavioral Sciences,
39, pp.702–711.
Fletcher, R.H. & Strunz, K., 2007. Optimal Distribution System Horizon Planning - Part II:
Application. IEEE Transactions on Power Systems, 22(2), pp.862–870.
Fleten, S. & Nasakkala, E., 2010. Gas-Fired Power Plants: Investment Timing, Operating
Flexibility and CO2 Capture. Energy Economics, 32(4), pp.805–816.
Frontier & Consentec, 2008. Notwendigkeit und Ausgestaltung geeigneter Anreize fuer eine
verbrauchsnahe und bedarfsgerechte Errichtung neuer Kraftwerke, London: Frontier
Economics, Consentec. Commissioned by the Federal Ministry for Economics and
Technology. Available at: http://www.consentec.de/wp-
content/uploads/2011/12/anreize-errichtung-neuer-kraftwerke-abschlussbericht.pdf
[Accessed April 24, 2012].
Funk, K. & Rabl, A., 1999. Electric versus Conventional Vehicles: Social Costs and Benefits
in France. Transportation Research Part D: Transport and Environment, 4(6),
pp.397–411.
Gabriel, S., Conejo, A., Fuller, J.D., Hobbs, B., Ruiz, C., 2013. Complementarity Modeling in
Energy Markets, New York: Springer.
GAMS, 2011. GAMS. CPLEX 12. Solver manual, Available at:
http://www.gams.com/dd/docs/solvers/cplex.pdf.
Gatzen, C., 2008. The Economics of Power Storage : Theory and Empirical Analysis for
Central Europe, Munich: Oldenbourg Industrieverlag.
Geiger, A., 2010. Strategic Power Plant Investment Planning under Fuel and Carbon Price
Uncertainty. Available at: http://digbib.ubka.uni-
karlsruhe.de/volltexte/documents/1678193 [Accessed September 8, 2011].
References
126
Genc, T.S. & Sen, S., 2008. An Analysis of Capacity and Price Trajectories for the Ontario
Electricity Market Using Dynamic Nash Equilibrium under Uncertainty. Energy
Economics, 30(1), pp.173–191.
George, M. & Banerjee, R., 2011. A methodology for analysis of impacts of grid integration
of renewable energy. Energy Policy, 39(3), pp.1265–1276.
Giannoulis, E.D. & Haralambopoulos, D.A., 2011. Distributed Generation in an Isolated Grid:
Methodology of Case Study for Lesvos – Greece. Applied Energy, 88(7), pp.2530–
2540.
Gillhaus, A., Crotogino, F. & Huebner, S., 2006. Verbesserte Integration großer
Windstrommengen durch Zwischenspeicherung mittels CAES, Aachen: IEAE RWTH
Aachen, ALSTOM Power, EcoFys, EOn Energie, KBB, IAEW, REPower, Vattenfall
Europe Transmission. Available at:
http://www.bine.info/fileadmin/content/Publikationen/Projekt-Infos/Zusatzinfos/2007-
05_Abschlussbericht.pdf [Accessed October 11, 2012].
Goerner, M. & Abrell, J., 2011. Expansion Planning for the German Electricity Grid Using
Benders Decomposition. In ENERDAY - 6th Conference on Energy Economics and
Technology. Dresden.
Green, R., 2007. Nodal Pricing of Electricity: How Much Does it Cost to Get it Wrong?
Journal of Regulatory Economics, 31(2), pp.125–149.
Grein, A., Pehnt, M., Duscha, M., Aalami, H., 2009. Modellstadt Mannheim in der
Metropolregion Rhein-Neckar, Mannheim, Mannheim: E-Energy. Available at:
http://www.ifeu.de/energie/pdf/AP1_AS1_06_Studie_ThermischeSpeicher_20090731
a.pdf.
Grimm, V. & Zoettl, G., 2008. Strategic Capacity Choice under Uncertainty: The Impact of
Market Structure on Investment and Welfare, Friedrich-Alexander-Universitaet
Erlangen-Nuernberg. Available at: http://ockenfels.uni-
koeln.de/fileadmin/wiso_fak/stawi-
ockenfels/pdf/ForschungPublikationen/GrimmZoettl_2007_EER_01.pdf [Accessed
May 10, 2012].
Groschke, M., Eßer, A., Moest, D., Fichtner, W., 2009. Neue Anforderungen an optimierende
Energiesystemmodelle fuer die Kraftwerkseinsatz- und Zubauplanung bei begrenzten
Netzkapazitaeten. Zeitschrift fuer Energiewirtschaft, 33(1), pp.14–22.
Gunkel, D. & Kunz, F., 2012. Power Transmission Grid Expansion using Benders
Decomposition. In EURO - 25th European Conference on Operational Research.
Vilnius.
Hall, P.J. & Bain, E.J., 2008. Energy-Storage Technologies and Electricity Generation.
Energy Policy, 36(12), pp.4352–4355.
Haller, M., 2012. CO2 Mitigation and Power System Integration of Fluctuating Renewable
Energy Sources: A Multi-Scale Modeling Approach. PhD Thesis. Berlin: Technical
University Berlin.
References
127
Haller, M., Ludig, S. & Bauer, N., 2012. Decarbonization Scenarios for the EU and MENA
Power System: Considering Spatial Distribution and Short Term Dynamics of
Renewable Generation. Energy Policy, 47, pp.282–290.
Von Hirschhausen, C., Wand, R. & Beestermoeller, C., 2010. Bewertung der dena-Netzstudie
II und des europaeischen Infrastrukturprogramms.
Hogan, W., 2005. On an Energy-Only Electricity Market Design for Ressource Adequacy,
Cambridge, Massachusetts: Harvard University.
Ibrahim, H., Ilinca, A. & Perron, J., 2008. Energy Storage Systems—Characteristics and
Comparisons. Renewable and Sustainable Energy Reviews, 12(5), pp.1221–1250.
IEA, 2010. Modelling Load Shifting Using Electric Vehicles in a Smart Grid Environment,
Paris: IEA. Available at:
http://www.iea.org/publications/freepublications/publication/load_shifting.pdf.
IEA, 2011a. Assumed Investment Costs, Operation and Maintenance Costs and Efficiencies
for Power Generation in the New Policies, Current Policies and 450 Scenarios, WEO
2011, International Energy Agency. Available at:
http://www.iea.org/weo/investments.asp [Accessed September 7, 2011].
IEA, 2011b. Harnessing Variable Renewables : A Guide to the Balancing Challenge, Paris:
International Energy Agency, Organisation for Economic Co-operation and
Development.
IEA, 2011c. World Energy Model – Methodology and Assumptions, Paris: International
Energy Agency. Available at:
http://www.iea.org/weo/docs/weo2011/other/WEO_methodology/WEM_Methodolog
y_WEO2011.pdf [Accessed April 15, 2012].
IEA, 2011d. World Energy Outlook 2011, Paris: OECD Publishing.
IEA, NEA & OECD, 2010. Projected Costs of Generating Electricity, Paris: International
Energy Agency, Nuclear Energy Agency, Organisation for Economic Cooperation and
Development.
IWR, 2012. Der IWR-Windertragsindex® fuer Regionen, IWR. Available at:
http://www.iwr.de/wind/wind/windindex/index.html.
Jahnke, D., 2012. Mittlere monatliche Tagesgaenge der Globalstrahlung fuer Photovoltaik-
Standorte in Deutschland und Spanien, Gundelfingen: Solar-Wetter.com. Available at:
http://www.tagesgang-globalstrahlung.solar-wetter.com [Accessed October 4, 2012].
Jarass, L., 2010. Dena Netzstudie II: Annahmen rechtswidrig, Ergebnis sachwidrig,
Wiesbaden: Hochschule RheinMain Wiesbaden.
Jarass, L. & Obermair, G., 2012. Stellungnahme zum Entwurf des Netzentwicklungsplans
2012, Wiesbaden. Available at:
http://www.jarass.com/Energie/C/Netzentwicklungsplan,%20D&F.pdf [Accessed
December 10, 2012].
References
128
Joskow, P. & Tirole, J., 2007. Reliability and Competitive Electricity Markets. RAND Journal
of Economics, 33(1), pp.60–84.
Kall, P. & Wallace, S., 1994. Stochastic Programming, Chichester: Wiley.
Kang, J.E. & Recker, W.W., 2009. An Activity-Based Assessment of the Potential Impacts of
Plug-In Hybrid Electric Vehicles on Energy and Emissions Using 1-Day Travel Data.
Transportation Research Part D: Transport and Environment, 14(8), pp.541–556.
Kapsali, M. & Kaldellis, J.K., 2010. Combining Hydro and Variable Wind Power Generation
by Means of Pumped-Storage under Economically Viable Terms. Applied Energy,
87(11), pp.3475–3485.
Kempton, W. & Tomić, J., 2005. Vehicle-to-Grid Power Implementation: From Stabilizing
the Grid to Supporting Large-Scale Renewable Energy. Journal of Power Sources,
144(1), pp.280–294.
Kirschen, D.S. & Strbac, Goran, 2004. Fundamentals of Power System Economics,
Chichester: Wiley.
Knopf, B., Kondziella, H., Pahle, M., Goetz, M., Bruckner, T., Edenhofer, O., 2011. Der
Einstieg in den Ausstieg: Energiepolitische Szenarien fuer einen Atomausstieg in
Deutschland, Potsdam Institute for Climate Impact Research. Available at:
http://www.pik-potsdam.de/research/sustainable-
solutions/research/MitigationScenarios/energiewende/imagefolder/langfassung2.
Konstantin, P., 2007. Praxisbuch Energiewirtschaft : Energieumwandlung, -transport und -
beschaffung im liberalisierten Markt, Berlin: Springer.
Kumar, N., Besuner, P., Lefton, S., Agan, D., Hilleman, D., 2012. Power Plant Cycling Cost,
Sunnyvale: National Renewable Energy Laboratory (NREL), Western Electricity
Coordinating Council (WECC). Available at:
http://wind.nrel.gov/public/WWIS/APTECHfinalv2.pdf [Accessed September 25,
2012].
Lee, D.K., Park, S.Y. & Park, S.U., 2007. Development of Assessment Model for Demand-
Side Management Investment Programs in Korea. Energy Policy, 35(11), pp.5585–
5590.
Lefton, S. & Besuner, P., 2006. The Cost of Cycling Coal Fired Power Plants. Coal Power
Magazine, Winter 2006, pp.16–20.
Leuthold, F., Weigt, H. & von Hirschhausen, C., 2012. A Large-Scale Spatial Optimization
Model of the European Electricity Market. Networks and Spatial Economics, 12(1),
pp.75–107.
Leuthold, F., Weigt, H. & von Hirschhausen, C., 2008. ELMOD-A Model of the European
Electricity Market. Dresden University of Technology Electricity Market Working
Papers WPEM-00.
Linnemann, C., Echternacht, D., Breuer, C., Moser, A., 2011. Modeling Optimal Redispatch
for the European Transmission Grid. In PowerTech, 2011 Trondheim. Trondheim:
References
129
IEEE, pp. 1–8. Available at:
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6019442 [Accessed
December 7, 2012].
Lipman, T., 2011. An Overview of Hydrogen Production and Storage Systems with
Renewable Hydrogen Case Studies, Oakland, California: Clean Energy States
Alliance. Available at: http://www.cleanenergystates.org/assets/2011-Files/Hydrogen-
and-Fuel-Cells/CESA-Lipman-H2-prod-storage-050311.pdf [Accessed November 14,
2012].
Littlechild, S., 2006. Electricity Market Reform: An International Perspective. In Electricity
Market Reform: An International Perspective. Chapter Foreword: The Market versus
Regulation. Oxford: Elsevier, pp. xvii–xxix.
London Economics, 2007. Structure and Performance of Six European Wholesale Electricity
Markets in 2003, 2004 and 2005 Part II. Report to the European Commission DG
Competition, Available at:
http://ec.europa.eu/competition/sectors/energy/inquiry/electricity_final_part2.pdf
[Accessed October 5, 2012].
Lui, M. & Gross, G., 2002. Effectiveness of the Distribution Factor Approximations used in
Congestion Modeling. In Proceedings of the 14 th Power Systems Computation
Conference. Sevilla, Spain.
Markel, T., Smith, K. & Pesaran, A.A., 2009. Improving Petroleum Displacement Potential of
PHEVs Using Enhanced Charging Scenarios, Stavanger. Available at:
http://www.nrel.gov/docs/fy09osti/45730.pdf [Accessed October 5, 2012].
Martin, V., He, B. & Setterwall, F., 2010. Direct Contact PCM–Water Cold Storage. Applied
Energy, 87(8), pp.2652–2659.
Matthes, F.C., Schlemmermeier, B., Diekmann, C., Hermann, H., von Hammerstein, C., 2012.
Fokussierte Kapazitaetsmaerkte. Ein neues Marktdesign fuer den Uebergang zu einem
neuen Energiesystem, Berlin: Oeko-Institut, LBD Beratungsgesellschaft, Raue LLP.
Available at: http://www.lbd.de/cms/pdf-gutachten-und-studien/1210_Oeko-
Institut_LBD_Raue-Fokussierte_-Kapazitaetsmaerkte.pdf [Accessed December 10,
2012].
Maurer, C., Tersteegen, B. & Zimmer, C., 2012. Anforderungen an den konventionellen
Kraftwerkspark – wieviel und welche Kraftwerkskapazitaet wird benoetigt? Zeitschrift
fuer Energiewirtschaft.
Mills, A., Phadke, A. & Wiser, R., 2011. Exploration of resource and transmission expansion
decisions in the Western Renewable Energy Zone initiative. Energy Policy, 39(3),
pp.1732–1745.
Milstein, I. & Tishler, A., 2012. The Inevitability of Capacity Underinvestment in
Competitive Electricity Markets. Energy Economics, 34(1), pp.62–77.
References
130
Moghaddam, M.P., Abdollahi, A. & Rashidinejad, M., 2011. Flexible Demand Response
Programs Modeling in Competitive Electricity Markets. Applied Energy, 88(9),
pp.3257–3269.
Morrow, K., Karner, D. & Francfort, J., 2008. Plug-in Hybrid Electric Vehicle Charging
Infrastructure Review. U.S. Department of Energy Vehicle Technologies Program –
Advanced Vehicle Testing Activity, U.S. Department of Energy. Available at:
http://avt.inl.gov/pdf/phev/phevInfrastructureReport08.pdf [Accessed October 5,
2012].
Moura, P.S. & De Almeida, A.T., 2010. The Role of Demand-Side Management in the Grid
Integration of Wind Power. Applied Energy, 87(8), pp.2581–2588.
Muesgens, F. & Kuntz, L., 2007. Modelling Start-Up Costs of Multiple Technologies in
Electricity Markets. Mathematical Methods of Operations Research, 66(1), pp.21–32.
Muesgens, F. & Peek, M., 2011. Sind Kapazitaetsmaerkte in Deutschland erforderlich? Eine
kritische Analyse vor dem Hintergrund der Oekonomischen Theorie. Zeitschrift fuer
neues Energierecht, 15(6), pp.576–583.
Murphy, F. & Smeers, Y., 2005. Generation Capacity Expansion in Imperfectly Competitive
Restructured Electricity Markets. Operations Research, 53(4), pp.646–661.
Nagl, S., Fuersch, M. & Lindenberger, D., 2012. The Costs of Electricity Systems with a High
Share of Fluctuating Renewables - a Stochastic Investment and Dispatch Optimization
Model for Europe, Cologne: EWI. Available at: http://www.ewi.uni-
koeln.de/fileadmin/user_upload/Publikationen/Working_Paper/EWI_WP_12-
01_Costs_of_electricity_systems_with_a_high_share_of_fluctuating_ren.pdf
[Accessed April 18, 2012].
Nansai, K., Tohno, S., Kono, M., Kasahara, M., Moriguchi, Y., 2001. Life-Cycle Analysis of
Charging Infrastructure for Electric Vehicles. Applied Energy, 70(3), pp.251–265.
Neenan, B. & Hemphill, R.C., 2008. Societal Benefits of Smart Metering Investments. The
Electricity Journal, 21(8), pp.32–45.
NEW Netz, 2012. Veroeffentlichungspflichten der NEW Netz GmbH, NEW Netz GmbH.
Available at: http://www.new-netz-gmbh.de/1313.php [Accessed October 4, 2012].
Nicolosi, M., 2012. The Economics of Renewable Electricity Market Integration. PhD Thesis.
Cologne: Energiewirtschaftliches Institut an der Universitaet zu Koeln. Available at:
kups.ub.uni-koeln.de/4612/1/NicolosiDiss.pdf [Accessed December 6, 2012].
Niederrheinwerke, 2011. Veroeffentlichungspflichten Stromnetz Viersen und Toenisvorst,
Toenisvorst: NEW Netz GmbH. Available at: http://www.niederrheinwerke-
netz.de/index.php?id=209&lang=de [Accessed October 4, 2012].
Ninghong, S., Ellersdorfer, I. & Swider, D., 2008. Model-based long-term Electricity
Generation System Planning under Uncertainty. In The Third International Conference
on Deregulation and Restructuring and Power Technologies DRPT 2008. pp. 1298 –
1304. Available at:
References
131
http://www.ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=4511470 [Accessed
May 10, 2012].
NPE, 2012. Fortschrittsbericht der Nationalen Plattform Elektromobilitaet (Dritter Bericht),
Berlin: Nationale Plattform Elektromobilitaet. Available at: http://www.ika.rwth-
aachen.de/aktuell/elektromobilitaet-fortschrittsbericht-nationale-plattform.pdf
[Accessed December 6, 2012].
NPE, 2011. Zweiter Bericht der Nationalen Plattform Elektromobilitaet, Berlin: Nationale
Plattform Elektromobilitaet. Available at:
http://www.bmbf.de/pubRD/zweiter_bericht_nationale_plattform_elektromobilitaet.pd
f [Accessed December 6, 2012].
Nuessler, A., 2012. Congestion and Redispatch in Germany. A Model-based Analysis of the
Development of Redispatch. PhD Thesis. Cologne: Energiewirtschaftliches Institut an
der Universitaet zu Koeln. Available at: kups.ub.uni-koeln.de/4652/1/DisNuessler.pdf
[Accessed December 6, 2012].
Oei, P., Schroeder, A., Sander, A., Hankel, L., Laurisch, L., Lorenz, C., 2012.
Szenarienrechnungen zum Netzentwicklungsplan (NEP) 2012 - HGU-Leitungen
ueberdimensioniert. Energiewirtschaftliche Tagesfragen, 62(9), pp.80–82.
Overbye, T., Cheng, X. & Sun, Y., 2004. A Comparison of the AC and DC Power Flow
Models for LMP Calculations. In Proceedings of the 37th Hawaii International
Conference on System Sciences. Hawaii.
Papagiannis, G., Dagoumas, A., Lettas, N., Dokopoulos, P., 2008. Economic and
Environmental Impacts from the Implementation of an Intelligent Demand Side
Management System at the European Level. Energy Policy, 36(1), pp.163–180.
Paulus, M. & Borggrefe, F., 2011. The Potential of Demand-Side Management in Energy-
Intensive Industries for Electricity Markets in Germany. Applied Energy, 88(2),
pp.432–441.
Pineau, P.O., Rasata, H. & Zaccour, G., 2011a. Dynamic Oligopolistic Electricity Market
with Interdependent Market Segments. The Energy Journal, 32(4), pp.183–218.
Pineau, P.O., Rasata, H. & Zaccour, G., 2011b. Impact of some Parameters on Investments in
Oligopolistic Electricity Markets. European Journal of Operational Research, 213(1),
pp.180–195.
PlanNYC, 2010. Exploring Electric Vehicle Adoption in New York City, New York City,
USA. Available at: http://www.nyc.gov/html/
planyc2030/downloads/pdf/electric_vehicle_adoption_study_2010-01.pdf [Accessed
October 5, 2012].
Platts, 2011. World Electric Power Plants Database: Global Price Assessments and Indices.
Available at: http://www.platts.com/Products/worldelectricpowerplantsdatabase
[Accessed January 25, 2011].
References
132
Pudjianto, D., Cao, D.M., Grenard,, S., Strbac, G., 2006. Method for Monetarisation of Cost
and Benefits of DG Options, Energy Intelligent Europe. Available at:
http://www.ecn.nl/fileadmin/ecn/units/bs/DG-
GRID/Results/WP3/d7_pudjianto_method-for-monetarisation-of-cost-and-benefits-of-
dg-options.pdf [Accessed October 1, 2012].
Purchala, K., Meeus, L., Van Dommelen, D., Belmans, R., 2005. Usefulness of DC Power
Flow for Active Power Flow Analysis. In IEEE Power Engineering Society General
Meeting. IEEE, pp. 454 – 459. Available at:
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=1489581 [Accessed
December 7, 2012].
Quaschning, V., 2009. Regenerative Energiesysteme Technologie - Berechnung - Simulation
mit 113 Tabellen und einer DVD ., neu bearbeitete und erw. Aufl., M nchen Hanser.
Roy, A., Kedare, S.B. & Bandyopadhyay, S., 2010. Optimum Sizing of Wind-Battery
Systems Incorporating Resource Uncertainty. Applied Energy, 87(8), pp.2712–2727.
Sauma, E. & Oren, S., 2009. Do Generation Firms in Restructured Electricity Markets Have
Incentives to Support Social-Welfare-Improving Transmission Investments? Energy
Economics, 31(5), pp.676–689.
Schaber, K., Steinke, F., Mühlich, P., Hamacher, T., 2011. Parametric Study of Variable
Renewable Energy Integration in Europe: Advantages and Costs of Transmission Grid
Extensions. Energy Policy. Available at:
http://linkinghub.elsevier.com/retrieve/pii/S0301421511010081 [Accessed January 29,
2012].
Schill, W., 2011. Modeling Market Failures and Regulation in the Changing German Power
Market. PhD Thesis. Berlin: Technical University Berlin.
Schroeder, A., 2012. An Electricity Market Model with Generation Capacity Investment
under Uncertainty. Beitraege zur Jahrestagung des Vereins fuer Socialpolitik 2012,
Neue Wege und Herausforderungen fuer den Arbeitsmarkt des 21. Jahrhunderts -
Session: Energy Markets(No. F06-V1), p.17.
Schroeder, A., Kunz, F., Meiss, J., Mendelevitch, R., von Hirschhausen, C., 2013. Current
and Prospective Costs of Electricity Generation until 2050, DIW Data Documentation
68, p. 94.
Schroeder, A., Gerbaulet, C., Oei, P., von Hirschhausen, C., 2012. In Ruhe planen:
Netzausbau in Deutschland und Europa auf dem Pruefstand. DIW Wochenbericht,
(20), pp.3–12.
Schroeder, A., 2011. Modeling Storage and Demand Management in Power Distribution
Grids. Applied Energy, 88(12), pp.4700–4712.
Schroeder, A. & Bracke, M., 2012. Integrated Electricity Generation Expansion and
Transmission Capacity Planning: An Application to the Central European Region.
DIW Discussion Paper 1250, p.19.
References
133
Schroeder, A., Traber, T., Kemfert, C., 2013. An Investment-Dispatch Equilibrium Model
Applied to European Power Markets. Submitted to Climate Change Economics (EMF
28 Special Issue).
Schroeder, A. & Traber, T., 2012. The Economics of Fast Charging Infrastructure for Electric
Vehicles. Energy Policy, 43, pp.136–144.
Schweppe, F., Caramanis, T., Tabors, R., Bohn, R., 1988. Spot Pricing of Electricity,
Boston/Dordrecht/London: Kluwer Academic Publishers.
Scorah, H., Sopinka, A. & Van Kooten, G.C., 2012. The economics of storage, transmission
and drought: integrating variable wind power into spatially separated electricity grids.
Energy Economics, 34(2), pp.536–541.
SFV, 2012. Bundesweite Aufnahme der monatlichen Stromertragsdaten von PV-Anlagen,
Solarenergie-Foerderverein Deutschland e.V. Available at: http://www.pv-
ertraege.de/cgi-bin/pvdaten/src/region_uebersichten.pl/kl.
Sinden, G., 2007. Characteristics of the UK wind resource: Long-term patterns and
relationship to electricity demand. Energy Policy, 35(1), pp.112–127.
Sioshansi, R., Denholm, P., Jenkin, T., Weiss, J., 2009. Estimating the Value of Electricity
Storage in PJM: Arbitrage and Some Welfare Effects. Energy Economics, 31(2),
pp.269–277.
Sioshansi, R. & Denholm, P., 2010. The Value of Plug-In Hybrid Vehicles as Grid Resources.
The Energy Journal, 31(3), pp.1–22.
Skerlos, S.J. & Winebrake, J.J., 2010. Targeting Plug-In Hybrid Electric Vehicle Policies to
Increase Social Benefits. Energy Policy, 38(2), pp.705–708.
Slater, S., Dolman, M., Taylor, D.P., Trichakis, P., Shine, J., 2009. Strategies for the Uptake
of Electric Vehicles and Associated Infrastructure Implications, Cambridge, UK:
Element Energy. Available at: http://hmccc.s3.amazonaws.com/Element_Energy_-
_EV_infrastructure_report_for_CCC_2009_final.pdf [Accessed October 5, 2012].
Smeers, Y., 2008. Study on the General Design of Electricity Market Mechanisms close to
Real Time, Louvain, Belgium: Université Catholique De Louvain, School Of
Engineering. Commissioned by: the Commission for Electricity and Gas Regulation
(CREG). Available at: http://www.creg.info/pdf/Etudes/F810UK.pdf [Accessed June
1, 2011].
SoDa, 2005. Solar Radiation Data Project: Integration and Exploitation of Networked Solar
Radiation Databases for Environment Monitoring 2005. Available at:
http://www.soda-is.com/eng/services/services_radiation_free_eng.php [Accessed
August 21, 2011].
Stadler, I., 2008. Power Grid Balancing of Energy Systems with High Renewable Energy
Penetration by Demand Response. Utilities Policy, 16(2), pp.90–98.
Sterner, M., 2009. Bioenergy and Renewable Power Methane in Integrated 100% Renewable
Energy Systems: Limiting Global Warming by Transforming Energy Systems. Kassel,
References
134
Germany: University of Kassel, Faculty of Electrical Engineering and Computer
Science.
Stigler, H. & Todem, C., 2005. Optimization of the Austrian Electricity Sector (Control Zone
of Verbund APG) under the Constraints of Network Capacities by Nodal Pricing.
Central European Journal of Operations Research, 13(2), pp.105–125.
Stoft, S., 2002. Power System Economics - Designing Markets for Electricity, New Jersey:
IEE-Press and Wiley: Piscataway.
Strauss, K., 2009. Kraftwerkstechnik : Zur Nutzung fossiler, nuklearer und regenerativer
Energiequellen, Berlin; Heidelberg: Springer.
Strbac, G., 2008. Demand Side Management: Benefits and Challenges. Energy Policy, 36(12),
pp.4419–4426.
Sueddeutsche, 2012. BNetzA uebergibt Bundesbedarfsplan. Sueddeutsche Zeitung, Energie V
2(5 December 2012), p.2.
Tan, C.W., Green, T.C. & Hernandez-Aramburo, C.A., 2010. A Stochastic Method for
Battery Sizing with Uninterruptible-Power and Demand Shift Capabilities in PV
(Photovoltaic) Systems. Energy, 35(12), pp.5082–5092.
La Tene Maps, 2011. E WEA’s 20 Year Offshore Network Development Master Plan.
Available at:
http://www.ewea.org/fileadmin/ewea_documents/documents/publications/reports/Euro
pean_Offshore_Wind_Farm_Projects.pdf?utm_source=offshore&utm_medium=mapD
iagram&utm_campaign=OffshoreMap [Accessed October 17, 2011].
Torriti, J., Hassan, M.G. & Leach, M., 2010. Demand Response Experience in Europe:
Policies, Programmes and Implementation. Energy, 35(4), pp.1575–1583.
Traber, T. & Kemfert, C., 2011a. Gone with the Wind?–Electricity Market Prices and
Incentives to Invest in Thermal Power Plants under Increasing Wind Energy Supply.
Energy Economics, 33(2), pp.249–256.
Traber, T. & Kemfert, C., 2011b. Refunding ETS Proceeds to Spur the Diffusion of
Renewable Energies: An Analysis Based on the Dynamic Oligopolistic Electricity
Market Model EMELIE. Utilities Policy, 19(1), pp.33–41.
Traber, T. & Kemfert, C., 2012. German Nuclear Phase-out Policy - Effects on European
Electricity Wholesale Prices, Emission Prices, Conventional Power Plant Investments
and Electricity Trade. DIW Discussion Paper 1219, p.17.
Troester, E., Kuwahata, R. & Ackermann, T., 2011. European Grid Study 2030/2050,
Commissioned by Greenpeace International, Langen: energynautics GmbH.
Troncoso, E. & Newborough, M., 2010. Electrolysers as a Load Management Mechanism for
Power Systems with Wind Power and Zero-Carbon Thermal Power Plant. Applied
Energy, 87(1), pp.1–15.
References
135
TSO, 2012. Netzentwicklungsplan Strom 2012 - Entwurf der Uebertragungsnetzbetreiber,
Berlin: TenneT, 50 Hertz, Amprion and EnBW. Available at:
http://www.netzentwicklungsplan.de/content/netzentwicklungsplan-2012 [Accessed
May 30, 2012].
TSO, 2011. Szenariorahmen fuer den Netzentwicklungsplan 2012 Eingangsdaten fuer die
Konsultation, 50Hertz, Amprion, EnBW, Tennet. Available at:
http://www.bundesnetzagentur.de/SharedDocs/Downloads/DE/BNetzA/Sachgebiete/E
nergie/Energienetzausbau/SzenariorahmenNEP_2012pdf [Accessed July 19, 2011].
Ventosa, M., Ba llo, A., Ramos, A., Rivier, M., 2005. Electricity Market Modeling Trends.
Energy Policy, 33(7), pp.897–913.
Ventosa, M., Denis, R. & Redondo, C., 2002. Expansion Planning in Electricity Markets.
Two Different Approaches. In Proceedings of the 14th PSCC Conference - Session
43-4. 14th PSCC Conference.
VfS, 2012. Ethikkodex des Vereins fuer Socialpolitik, Verein fuer Socialpolitik. Available at:
http://www.mem-wirtschaftsethik.de/fileadmin/user_upload/mem-
denkfabrik/2012/VfS_Ethikkodex.pdf [Accessed September 24, 2012].
VGB PowerTech, 2011. Geplante Neubauprojekte in der EU. Available at:
http://www.vgb.org/neubauprojekte.html [Accessed January 9, 2012].
Wade, N., Taylor, P., Lang, P., Jones, P., 2010. Evaluating the Benefits of an Electrical
Energy Storage System in a Future Smart Grid. Energy Policy, 38(11), pp.7180–7188.
Waniek, D., 2010. Lastflussbasierte Bewertung von Engpaessen im elektrischen
Energieuebertragungsnetz. PhD Thesis. Dortmund: TU Dortmund Institute for Energy
Systems, Energy Efficiency and Energy Management.
Weber, C. & Swider, D., 2004. Power Plant Investment under Fuel and Carbon Price
Uncertainty. In Proceedings of the 6th IAEE EuropeanConference 2004. IAEE
European Conference. Zurich.
Weigt, H., Jeske, T., Leuthold, F., von Hirschhausen, C., 2010. “Take the long way down”
Integration of Large-scale North Sea Wind Using HVDC Transmission. Energy
Policy, 38(7), pp.3164–3173.
Weigt, H. & von Hirschhausen, C., 2008. Price Formation and Market Power in the German
Wholesale Electricity Market in 2006. Energy Policy, 36(11), pp.4227–4234.
Van der Weijde, A.H. & Hobbs, B.F., 2012. The Economics of Planning Electricity
Transmission to Accommodate Renewables: Using Two-Stage Optimisation to
Evaluate Flexibility and the Cost of Disregarding Uncertainty. Energy Economics,
34(6), pp.2089–2101.
Widen, J., Lundh, M., Vassileva, I., Dahlquist, E., Ellegard, K., Waeckelgard, E., 2009.
Constructing Load Profiles for Household Electricity and Hot Water from Time-Use
Data—Modelling Approach and Validation. Energy and Buildings, 41(7), pp.753–
768.
136
Widen, J. & Waeckelgard, E., 2010. A High-Resolution Stochastic Model of Domestic
Activity Patterns and Electricity Demand. Applied Energy, 87(6), pp.1880–1892.
Wiederer, A. & Philip, R., 2010. Policy Options for Electric Vehicle Charging Infrastructure
in C40 Cities, Transportation, Clinton Climate Initiative.
Wietschel, M., Kley, F. & Dallinger, D., 2009. Eine Bewertung der Ladeinfrastruktur fuer
Elektrofahrzeuge. ZfAW. Zeitschrift fuer die gesamte Wertschoepfungskette
Automobilwirtschaft, (3).
Wissner, M., 2011. The Smart Grid – A Saucerful of Secrets? Applied Energy, 88(7),
pp.2509–2518.
Zhuang, J., 2005. A Stochastic Equilibrium Model for the North American Natural Gas
Market. PhD Thesis. Maryland: University of Maryland.
Appendix – Source Codes
137
Appendix – Source Codes
Major parts of the codes of the developed models are collected here and further information
and data can be retrieved upon request at the author of this thesis. In making the use of data
and model code transparent, the Thesis abides by the “Ethical code for appropriate scientific
behavior for economists” set out by the Verein fuer Socialpolitik (VfS 2012), requiring,
amongst other things, that research be transparent and tractable, and that data, source code,
and results be made publicly available.
GAMS Code of the model in Chapter 2
*===============================================================================
* Andreas Schröder 23. October 2010
* Model on sizing of storage and DSM applicances.
* Version with Benders Decomposition per Scenario and Feasibility cut. Winter season.
* Stochastic wind feed-in and demand. DSM_max deterministic. 5-Node-Grid included.
* System Cost Minimization
* Model run requires access to the file: „input-smart-grid-umgebaut-fuer-stochastik-jahreswerte-9.xls“
*===============================================================================
* set key parameters
$set iter_max 40
$set dsm_cost 4.02
$set storage_cost 0.04
$set dsm_limit_per_node 360
*#####################################################################################
* DATA
*#####################################################################################
*------------------------------------------------------------*
* sets = Indices
*------------------------------------------------------------*
sets
t time / t1 * t24 /
sc scenario / 1*30 /
s type of plant / chp,pv,hydro,nuclear,lignite,hardcoal,gas,biomass /
l Line / l1*l4 /
n Node / 1*5 /
iter iteration /iter1*iter%iter_max%/
ocut(iter) optimality cut
fcut(iter) feasibility cut
Alias (t,tt), (s,ss), (l,ll), (n,nn);
ocut(iter) = no; fcut(iter) = 0;
scalar
alpha_low lower bound on recourse value /-50/
epsilon stopping criterium /1e-1/
converged one if converged /0/
feasible zero if subproblem infeasible /0/
;
parameter
* Needed for benders
lambda_dsm_inv_iter(iter,n) dual value of fixed first stage variables
lambda_scap_max_iter(iter,n) dual value of fixed first stage variables
gamma_dsm_inv_iter(iter,n) dual fixing constraint feasibility sub
gamma_scap_max_iter(iter,n) dual fixing constraint feasibility sub
beta_iter(iter) feasibility problem objective
alpha_iter(iter) subproblem objective by iteration
dsm_inv_iter(iter,n) first stage decision(DSM) by iteration
scap_max_iter(iter,n) first stage decision(storage) by iteration
dsm_inv_fix(n) first stage decision scap_max passed to subproblem
scap_max_fix(n) first stage decision dsm_inv passed to subproblem
lambda_dsm_inv_scen(sc,n) dual value dsm_inv by scenario
lambda_scap_max_scen(sc,n) dual value scap_max by scenario
alpha_scen(sc) subproblem objective by scenario
* Reports
iterlog iteration report of bounds
Appendix – Source Codes
138
report_iter1 iteration report first-stage variables
report_iter2_DSM iteration report second-stage variables DSM
report_iter2_SIN iteration report second-stage variables SIN
report_iter2_SOUT iteration report second-stage variables SOUT
report report parameter
report_scen report by scenario
prob(sc) probability of scenario
;
prob(sc) = 1/card(sc);
lambda_dsm_inv_iter(iter,n) = 0;
lambda_scap_max_iter(iter,n) = 0;
alpha_iter(iter) = 0;
scap_max_fix(n) = 0;
dsm_inv_fix(n) = 0;
dsm_inv_iter(iter,n) = 0;
scap_max_iter(iter,n) = 0;
lambda_dsm_inv_scen(sc,n) = 0;
lambda_scap_max_scen(sc,n) = 0;
alpha_scen(sc) = 0;
beta_iter(iter)=0;
gamma_dsm_inv_iter(iter,n)=0;
gamma_scap_max_iter(iter,n)=0;
*------------------------------------------------------------*
* Generation Parameters
*------------------------------------------------------------*
Parameter g_max(t,s,n) maximal plant capacities;
Parameter g_max_grid_supply_point(t,s) maximal plant capacities at Grid Supply Point in kW;
$LIBINCLUDE XLIMPORT G_max_grid_supply_point input-smart-grid-umgebaut-fuer-stochastik-jahreswerte-9.xls production1!ad5:al29
Parameter g_max_zero(t,s) maximal plant capacities at Grid Supply Point in kW;
$LIBINCLUDE XLIMPORT G_max_zero input-smart-grid-umgebaut-fuer-stochastik-jahreswerte-9.xls production1!ff5:fo29
Parameter g_max_distributed_generation(t,s) maximal plant capacities at Grid Supply Point in kW;
$LIBINCLUDE XLIMPORT G_max_distributed_generation input-smart-grid-umgebaut-fuer-stochastik-jahreswerte-9.xls production1!et5:fc29
g_max(t,s,'1') = g_max_grid_supply_point(t,s);
g_max(t,s,'2') = g_max_zero(t,s);
g_max(t,s,'3') = g_max_distributed_generation(t,s);
g_max(t,s,'4') = g_max_zero(t,s);
g_max(t,s,'5') = g_max_zero(t,s);
Parameter g_wind_max(t,sc,n) maximal wind power capacities at Grid Supply Point in kW;
Parameter g_wind_max_grid_supply_point(t,sc) maximal plant capacities at Grid Supply Point in kW;
$LIBINCLUDE XLIMPORT g_wind_max_grid_supply_point input-smart-grid-umgebaut-fuer-stochastik-jahreswerte-9.xls production1!at5:bx29
Parameter g_wind_max_zero(t,sc) maximal plant capacities at Grid Supply Point in kW;
$LIBINCLUDE XLIMPORT g_wind_max_zero input-smart-grid-umgebaut-fuer-stochastik-jahreswerte-9.xls production1!dm5:eq29
g_wind_max(t,sc,'1') = g_wind_max_grid_supply_point(t,sc);
g_wind_max(t,sc,'2') = g_wind_max_zero(t,sc);
g_wind_max(t,sc,'3') = g_wind_max_zero(t,sc);
g_wind_max(t,sc,'4') = g_wind_max_zero(t,sc);
g_wind_max(t,sc,'5') = g_wind_max_zero(t,sc);
Parameter g_wind_max_scen(t,n) maximal wind power capacities at Grid Supply Point in kW;
Parameter gen_per_node(t,s) generation per node for reporting;
display G_max;
parameter G_c(s) marginal generation costs in EUR per KWh
/
chp 0.0003
pv 0.0002
hydro 0.0004
nuclear 0.01
lignite 0.04
hardcoal 0.06
gas 0.07
biomass 0.0005
/
;
Scalar g_wind_c marginal generation cost in EUR per kWh for wind /0.002/;
*------------------------------------------------------------*
* Demand Parameters
*------------------------------------------------------------*
Parameter q_ref(t,sc,n) reference demand in kW;
Parameter dem_per_node(t,sc) for reporting;
Appendix – Source Codes
139
Table q_ref_demand_node(t,sc) reference demand in kW in summer
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
t1 112 120 129 113 129 119 118 115 124 117 118 132 129 120 114 128 117 118
119 125 123 121 127 124 116 112 123 117 123 120
t2 95 97 92 85 91 81 94 101 94 93 93 95 96 93 89 86 98 93 90
89 91 88 96 102 97 93 95 101 95 99
t3 77 78 76 80 82 80 76 80 83 80 74 84 81 79 77 82 82 81 78
80 79 82 86 81 71 77 82 81 74 77
t4 73 71 76 77 76 78 72 72 79 77 72 72 74 69 70 73 66 73 82
71 71 74 76 76 65 71 77 68 71 78
t5 74 71 69 74 75 70 74 72 66 75 77 68 69 69 64 71 79 71 72
69 68 69 72 73 74 70 68 70 69 70
t6 65 72 76 77 70 68 70 77 77 77 67 82 72 74 68 75 71 73 72
73 78 73 71 76 76 75 68 73 74 75
t7 85 81 83 78 74 81 78 77 71 76 76 77 78 80 82 80 74 81 76
81 74 78 73 78 76 80 92 78 85 74
t8 96 101 98 102 101 96 97 99 95 98 98 95 101 96 97 95 98 94 97
95 94 97 98 99 95 95 100 97 96 93
t9 107 129 114 112 117 119 122 127 112 105 122 115 133 119 119 120 126 110
116 121 115 120 132 120 111 121 123 119 117 122
t10 138 125 135 120 135 137 124 117 126 119 118 137 126 107 134 141 147 136
141 134 127 135 125 147 135 143 121 127 124 125
t11 123 128 137 131 150 117 139 127 138 129 140 147 141 133 150 142 144 135
107 128 152 111 127 139 128 127 121 134 123 127
t12 133 140 133 134 131 144 135 122 131 139 134 123 144 132 138 116 143 130
134 136 144 136 126 141 150 137 130 134 137 120
t13 142 129 114 130 131 135 136 133 132 144 128 153 146 137 134 148 157 129
143 137 132 147 146 137 137 149 141 137 138 153
t14 149 155 146 146 156 147 148 142 139 140 152 136 150 146 147 153 153 142
139 151 144 160 142 153 136 131 150 152 133 138
t15 127 126 142 124 138 142 132 151 137 134 136 149 140 140 144 129 135 140
136 143 148 145 148 121 142 150 147 128 143 140
t16 135 127 140 124 127 124 140 130 151 152 146 157 146 135 137 149 138 132
140 143 111 138 127 139 131 133 142 143 135 138
t17 139 145 137 148 133 122 145 136 140 147 147 131 135 132 138 141 140 143
142 128 142 145 125 134 134 130 138 150 139 149
t18 140 141 148 136 139 152 153 134 135 146 136 145 131 134 136 140 136 131
124 148 143 133 141 143 156 141 137 134 135 140
t19 155 149 150 149 143 145 142 157 139 138 149 133 143 144 139 144 141 149
144 139 156 145 147 158 146 155 139 151 154 154
t20 141 158 162 155 143 156 165 163 151 150 148 144 146 142 145 155 159 156
153 173 145 138 142 152 150 167 152 158 142 170
t21 154 149 159 139 163 156 160 155 152 156 156 156 153 157 149 160 165 157
149 167 147 165 154 170 158 165 162 162 152 153
t22 157 156 150 162 152 157 161 160 151 163 147 150 149 149 146 157 156 157
160 160 163 161 151 151 150 152 165 163 158 154
t23 170 162 142 153 146 151 158 150 162 163 163 157 141 170 145 156 154 163
157 161 159 153 156 162 158 151 169 161 150 153
t24 156 153 147 150 135 140 145 147 148 150 149 160 146 150 164 156 146 150
160 151 144 148 149 155 142 153 145 149 149 152
;
Parameter q_ref_zero(t,sc) reference demand in kW;
$LIBINCLUDE XLIMPORT q_ref_zero input-smart-grid-umgebaut-fuer-stochastik-jahreswerte-9.xls demand1!i5:am29
q_ref(t,sc,'1') = q_ref_zero(t,sc);
q_ref(t,sc,'2') = q_ref_demand_node(t,sc);
q_ref(t,sc,'3') = q_ref_demand_node(t,sc);
q_ref(t,sc,'4') = q_ref_demand_node(t,sc);
q_ref(t,sc,'5') = q_ref_demand_node(t,sc);
Parameter q_ref_scen(t,n) reference demand in kW ;
display q_ref;
*-------------------------------------------------------------------*
* Demand-side management parameters
*-------------------------------------------------------------------*
Parameter DSM_max_pos(t,n) Maximum capacity for demand-side management in kW;
$LIBINCLUDE XLIMPORT DSM_max_pos input-smart-grid-umgebaut-fuer-stochastik-jahreswerte-9.xls dsm1!b5:g29
Parameter DSM_max_neg(t,n) Maximum capacity for demand-side management in kW;
$LIBINCLUDE XLIMPORT DSM_max_neg input-smart-grid-umgebaut-fuer-stochastik-jahreswerte-9.xls dsm1!n5:s29
Scalar dsm_inv_cost investment cost in EUR per household / %dsm_cost% / ;
*-------------------------------------------------------------------*
* storage parameters
*-------------------------------------------------------------------*
Scalars
Sin_max input power limit of storage device in kW / 2600 /
Appendix – Source Codes
140
Sout_max output power limit of storage device in kW / 2600 /
S_c cost of energy from storage device in EUR per kW / 0.00004 /
S_eff conversion efficiency of storage device in per cent / 0.75 /
scap_inv_cost investment cost of storage in EUR per kWh capacity / %storage_cost% /
;
*-------------------------------------------------------------------*
* Line parameters
*-------------------------------------------------------------------*
parameter lf_max(l) Max Capacity of Line in KW in 10kV grid
/
l1 1850
l2 1850
l3 1850
l4 1850
/
;
* Source: DG Grid (2006) for grid level 11 kV and higher.
* Size (mm) Capacity(Amp) R (Ohm/km) X (Ohm/km) Installation and investment cost (GBP/km/year)
* 70 185 0.443 0.0705 3,062
* 300 420 0.1 0.0675 4,029
parameter Transformer(n) Maximum power capacity of transformer in kW
/
1 0
2 250
3 250
4 250
5 250
/
;
parameter X(l) Reactance of Line l
/
l1 0.4
l2 0.4
l3 0.5
l4 0.5
/
;
table Incidence(l,n) Connects Lines with Nodes (Start(1) -> End(-1))
1 2 3 4 5
l1 1 -1 0 0 0
l2 0 1 -1 0 0
l3 0 0 1 -1 0
l4 0 0 0 1 -1
;
Parameter H(l,n) Flow Sensitivity Matrix;
H(l,n) = 1/X(l) * Incidence(l,n);
Parameter B(n,nn) Network Susceptance Matrix;
B(n,nn) = SUM(l, Incidence(l,n) * H(l,nn) );
Parameter Slack(n) Slack Paramter (one node delta has to be zero);
slack('1') = 1;
*-------------------------------------------------------------------*
* auxilliary quantities - assigned after solving the model
*-------------------------------------------------------------------*
parameter q_tot(t,sc,n) energy demand incl. DSM and storage ;
Parameter lf(t,l) Line Flow ;
Parameter scap_max_total total storage investment;
Parameter dsm_inv_total total DSM investment;
*#####################################################################################
* MODEL FORMULATIONS
*#####################################################################################
*--------------------------------------- MASTER PROBLEM --------------------------------
variables
COST_M total cost Master Problem
ALPHA recourse value
;
positive variables
Scap_max(n) investment into storage capacity in kWh
DSM_inv(n) investment into DSM capacity absolute number of meters
;
Appendix – Source Codes
141
Equation
obj_m master objective function
res_ocut Benders optimality cuts
res_fcut Infeasibility cuts
res_alpha_low lower bound on recourse value
dsm_inv_fixed
;
obj_M..
COST_M =E= sum(n, scap_max(n) * scap_inv_cost + dsm_inv_cost * dsm_inv(n)) + ALPHA
;
res_ocut(ocut)..
alpha_iter(ocut) + sum(n, lambda_dsm_inv_iter(ocut,n)*(dsm_inv(n) - dsm_inv_iter(ocut,n))) + sum(n, lambda_scap_max_iter(ocut,n)*(Scap_max(n) -
scap_max_iter(ocut,n)) )
=L= ALPHA
;
res_fcut(fcut)..
beta_iter(fcut) + sum(n, gamma_dsm_inv_iter(fcut,n)*(dsm_inv(n) - dsm_inv_iter(fcut,n)) ) + sum(n, gamma_scap_max_iter(fcut,n)*(Scap_max(n) -
scap_max_iter(fcut,n)) )
=L= 0;
res_alpha_low..
alpha_low =L= ALPHA
;
dsm_inv_fixed(n).. dsm_inv(n) =l= %dsm_limit_per_node% ;
model master master problem
/
obj_M
res_ocut
res_fcut
res_alpha_low
dsm_inv_fixed
/
;
*------------------------------------ SUBPROBLEM -------------------------------
variables
COST_S total cost sub problem
DELTA(t,n) voltage angle difference
DSM(t,n) demand-side management
;
positive variables
SCAP_MAX(n) investment into storage capacity in kWh
DSM_INV(n) investment into DSM capacity absolute number of meters
GEN(t,s,n) generation of planttype s
GEN_WIND(t,n) generation of wind
SIN(t,n) storage input at time t and node n
SOUT(t,n) storage output at time t and node n
;
equations
obj_s objective function
G_limit Capacity limit of generation
G_wind_limit Capacity limit for wind generation
Energybalance Energy Balance
DSMlimit_upper Maximum of (positive) demand-side management
DSMlimit_lower Maximum of (negative) demand-side management
DSMbalance Demand-side management balance over time
Spowerlimit_in Storage input power limit
Spowerlimit_out Storage output power limit
Slimit_lower Maximum of (negative) storage management
Slimit_upper Maximum of (positive) storage management
Sbalance Storage in- and outflow balance over time
LF_limit_upper Upper capacity limit of lineflow
LF_limit_lower Lower capacity limit of lineflow
Slackbus Delta at reference bus equals zero
res_dsm_inv_fix restrition to keep dsm_inv fixed
res_scap_max_fix restrition to keep scap_max fixed
;
*** COST
obj_s.. COST_S =e= sum((t,n), sum(s, g_c(s) * GEN(t,s,n)) + g_wind_c * GEN_WIND(t,n) + S_c * SOUT(t,n) ) ;
*** GENERATION
G_limit(t,s,n).. 0 =g= GEN(t,s,n) - g_max(t,s,n);
G_wind_limit(t,n).. 0 =g= GEN_WIND(t,n) - g_wind_max_scen(t,n);
* DEMAND-SIDE-MANAGEMENT
Appendix – Source Codes
142
DSMlimit_upper(t,n).. 0 =g= DSM(t,n) - dsm_inv(n) * dsm_max_pos(t,n) ;
DSMlimit_lower(t,n).. 0 =g= DSM(t,n) - dsm_inv(n) * dsm_max_neg(t,n) ;
DSMbalance(n).. 0 =e= sum(t, DSM(t,n));
* STORAGE
Spowerlimit_in(t,n).. 0 =g= SIN(t,n) - scap_max(n);
Spowerlimit_out(t,n).. 0 =g= SOUT(t,n) - scap_max(n);
Slimit_lower(t,n).. 0 =g= sum(tt$(ord(tt)<=ord(t)), Sout(tt,n)) - sum(tt$(ord(tt)<=ord(t)-1), Sin(tt,n) ) ;
Slimit_upper(t,n).. 0 =g= sum(tt$(ord(tt)<=ord(t)), Sin(tt,n)) - sum(tt$(ord(tt)<=ord(t)-1), Sout(tt,n)) - Scap_max(n) ;
Sbalance(n).. 0 =e= sum(t, SIN(t,n) * S_eff - SOUT(t,n));
*** ENERGY BALANCE
Energybalance(t,n).. 0 =e= sum(s, GEN(t,s,n)) + GEN_WIND(t,n) + SOUT(t,n) - (q_ref_scen(t,n) + DSM(t,n) + SIN(t,n)) - sum(nn, b(n,nn) * DELTA(t,nn)) ;
*** GRID
*Transformerlimit(t,n).. Transformer(n) =g= q_ref(t,n)+DSM(t,n)+Sin(t,n)- sum(s,gen(n,t,s)) ;
LF_limit_upper(t,l).. 0 =g= sum(n, h(l,n) * DELTA(t,n)) - lf_max(l) ;
LF_limit_lower(t,l).. 0 =g= - sum(n, h(l,n) * DELTA(t,n)) - lf_max(l) ;
Slackbus(t,n).. 0 =e= slack(n) * DELTA(t,n) ;
res_dsm_inv_fix(n)..
dsm_inv(n) =E= dsm_inv_fix(n)
;
res_scap_max_fix(n)..
scap_max(n) =E= scap_max_fix(n)
;
model sub subproblem
/
obj_s,
*Transformerlimit,
G_limit,
G_wind_limit,
DSMlimit_upper,
DSMlimit_lower,
DSMbalance,
Spowerlimit_in,
Spowerlimit_out,
Slimit_lower,
Slimit_upper,
Sbalance,
Energybalance,
LF_limit_upper,
LF_limit_lower,
Slackbus,
res_dsm_inv_fix,
res_scap_max_fix
/
;
*--------------------------------- FEASIBILITY PROBLEM -------------------------------
Variable
COST_F feasibility objective
;
Positive Variable
V feasibility slack
;
equation
obj_f feasibility objective: min of slacks
fres_mkt(t,n) always feasible market clearing
;
obj_f..
COST_F =e= V
;
fres_mkt(t,n)..
0 =e= sum(s, GEN(t,s,n)) + GEN_WIND(t,n) + SOUT(t,n) - (q_ref_scen(t,n) + DSM(t,n) + SIN(t,n)) - sum(nn, b(n,nn) * DELTA(t,nn)) + V
;
model fsub feasible subproblem
/
obj_f
fres_mkt,
*Transformerlimit,
G_limit,
G_wind_limit,
DSMlimit_upper,
DSMlimit_lower,
DSMbalance,
Spowerlimit_in,
Appendix – Source Codes
143
Spowerlimit_out,
Slimit_lower,
Slimit_upper,
Sbalance,
LF_limit_upper,
LF_limit_lower,
Slackbus,
res_dsm_inv_fix,
res_scap_max_fix
/
;
*#####################################################################################
* DECOMPOSITION ALGORITHM
*#####################################################################################
option
*lp=cplex,
solprint=silent, limrow=0, limcol=0;
master.solvelink = 2;
sub.solvelink = 2;
option mip=bdmlp;
dsm_inv.fx('1')=0;
file out /output.txt/;
PUT out;
put "iter COST_M COST_S alpha_low dsm_inv scap_max dual_dsm dual_scap_max"/;
loop(iter$(not converged),
Scap_max.l('1') = 0;
Scap_max.l('2') = 0;
Scap_max.l('3') = 0;
Scap_max.l('4') = 0;
Scap_max.l('5') = 0;
DSM_inv.l('1') = 0;
DSM_inv.l('2') = 0;
DSM_inv.l('3') = 0;
DSM_inv.l('4') = 0;
DSM_inv.l('5') = 0;
SIN.fx('t24',n) = 0;
* ********************
* Solve master problem
* ********************
solve master using LP minimizing COST_M ;
* Fix decision variables
scap_max_fix(n) = scap_max.L(n);
dsm_inv_fix(n) = dsm_inv.L(n);
scap_max_iter(iter,n) = scap_max.L(n);
dsm_inv_iter(iter,n) = dsm_inv.L(n);
report_iter1(iter,"scap_max",n) = scap_max.L(n);
report_iter1(iter,"dsm_inv",n) = dsm_inv.L(n);
* Set lower bound
iterlog("lower bound",iter) = COST_M.L;
* ********************
* Fesibility Check
* ********************
feasible = 0;
loop(sc$(not feasible),
* Assign respective scenario parameters
q_ref_scen(t,n) = q_ref(t,sc,n);
* p_ref_scen(t) = p_ref(t,sc);
* DSM_max_pos_scen(t) = DSM_max_pos(t,sc);
* DSM_max_neg_scen(t) = DSM_max_neg(t,sc);
g_wind_max_scen(t,n) = g_wind_max(t,sc,n);
solve fsub using LP minimizing COST_F;
* ********************
* IF INFEASIBLE
* ********************
if(COST_F.L > 0,
* add feasibility cut
fcut(iter) = yes;
Appendix – Source Codes
144
beta_iter(iter) = COST_F.L;
gamma_dsm_inv_iter(iter,n) = res_dsm_inv_fix.M(n);
gamma_scap_max_iter(iter,n) = res_scap_max_fix.M(n);
* end the iteration and goto master programm
feasible = 1;
);
);
* ********************
* IF FEASIBLE
* ********************
if(feasible = 0,
* ********************
* Solve subproblem
* ********************
loop(sc,
* Assign respective scenario parameters
q_ref_scen(t,n) = q_ref(t,sc,n);
* p_ref_scen(t) = p_ref(t,sc);
* DSM_max_pos_scen(t) = DSM_max_pos(t,sc);
* DSM_max_neg_scen(t) = DSM_max_neg(t,sc);
g_wind_max_scen(t,n) = g_wind_max(t,sc,n);
solve sub using LP minimizing COST_S;
* Assign cut parameters
lambda_dsm_inv_scen(sc,n) = res_dsm_inv_fix.M(n);
lambda_scap_max_scen(sc,n) = res_scap_max_fix.M(n);
alpha_scen(sc) = COST_S.L;
* Write reports
report_iter2_DSM(iter,t,sc,n) = DSM.L(t,n);
report_iter2_SIN(iter,t,sc,n) = SIN.L(t,n);
report_iter2_SOUT(iter,t,sc,n) = SOUT.L(t,n);
);
* Add cut parameters
ocut(iter)=yes;
alpha_iter(iter) = sum(sc, prob(sc)* alpha_scen(sc));
lambda_scap_max_iter(iter,n) = sum(sc, prob(sc)*lambda_scap_max_scen(sc,n));
lambda_dsm_inv_iter(iter,n) = sum(sc, prob(sc)*lambda_dsm_inv_scen(sc,n));
* Set upper bound
iterlog("upper bound",iter) = alpha_iter(iter) + sum(n, scap_max.L(n) * scap_inv_cost + dsm_inv_cost * dsm_inv.L(n) ) ;
* report_iter(iter,"Sin",t,sc) = Sin.L(t,sc);
* report_iter(iter,"Sout",t,sc) = Sout.L(t,sc);
* report_iter(iter,"DSM",t,sc) = DSM.L(t,sc);
* ********************
* Check convergence
* ********************
iterlog("error",iter) = iterlog("upper bound",iter) - iterlog("lower bound",iter);
converged$(epsilon gt iterlog("error",iter)) = 1;
put iter.tl:10:0," ",COST_M.L:10:3," ",COST_S.L:10:3," ", alpha_low:10:0," ";
put / ;
* Add cut
* uiter(iter) = yes;
);
);
$ontext
* Report the final solution
report("stage1","Land",i) = X.L(i);
report(s,"Yield",i) = yield(i,s)*X.L(i);
report(s,"Purchases",i) = Y.L(i,s);
report(s,"Sold Normal",i) = W.L(i,s);
report(s,"Sold Quota",i) = Z.L(i,s);
report(s,"Sold Total",i) = Z.L(i,s) + W.L(i,s);
report("xxx","Profit","xxx") = -COST_M.L;
$offtext
lf(t,l) = sum(n, H(l,n) * delta.l(t,n) );
Q_tot(t,sc,n) = q_ref(t,sc,n) + DSM.l(t,n) + SIN.l(t,n) ;
Scap_max_total = sum(n, SCAP_MAX.l(n));
DSM_INV_total = sum(n, DSM_INV.l(n));
Appendix – Source Codes
145
Gen_per_node(t,s)= sum(n,gen.l(t,s,n));
dem_per_node(t,sc)= sum(n,q_ref(t,sc,n));
DISPLAY COST_M.l, COST_S.l, prob, GEN.l, g_wind_max, GEN_WIND.l, q_ref, B, H, slack, lf, DSM.l, SIN.l, SOUT.l, SCAP_MAX.l, SCAP_MAX_total,
DSM_INV.l, DSM_INV_total, Q_tot, delta.l, iterlog, alpha_iter, ALPHA.L, beta_iter, ocut, fcut, lambda_dsm_inv_iter, lambda_scap_max_iter, report_iter1,
report_iter2_DSM, report_iter2_SIN, report_iter2_SOUT ;
*** Write zeros in EXCEL file
SIN.l(t,n)$(not SIN.l(t,n)) = eps;
SOUT.l(t,n)$(not SOUT.l(t,n)) = eps;
DSM.l(t,n)$(not DSM.l(t,n)) = eps;
lf(t,l)$(not lf(t,l)) = eps;
SCAP_MAX.l(n)$(not SCAP_MAX.l(n)) = eps;
DSM_INV.l(n)$(not DSM_INV.l(n)) = eps;
GEN_WIND.l(t,n)$(not GEN_WIND.l(t,n)) = eps;
Gen_per_node(t,s)$(not Gen_per_node(t,s)) = eps;
Dem_per_node(t,sc)$(not Dem_per_node(t,sc)) = eps;
*** Write output in EXCEL file
$libinclude xldump Dem_per_node output-smart-grid-stochastic.xls Dem!b3
$libinclude xldump GEN_WIND.l output-smart-grid-stochastic.xls GEN_WIND!b3
$libinclude xldump Gen_per_node output-smart-grid-stochastic.xls gen!b3
$libinclude xldump Sin.l output-smart-grid-stochastic.xls Sin!b3
$libinclude xldump Sout.l output-smart-grid-stochastic.xls Sout!b3
$libinclude xldump lf output-smart-grid-stochastic.xls lf!b3
$libinclude xldump SCAP_MAX.l output-smart-grid-stochastic.xls INVEST!b3
$libinclude xldump DSM_INV.l output-smart-grid-stochastic.xls INVEST!b6
$libinclude xldump q_ref output-smart-grid-stochastic.xls demand!b3
$libinclude xldump DSM.l output-smart-grid-stochastic.xls DSM!b3
$libinclude xldump S_eff output-smart-grid-stochastic.xls INVEST!b9
GAMS Code of the model in Chapter 3
*===============================================================================
* Andreas Schröder 31 Juli 2011
* Model Esymmetry (Traber, Kemfert 2011) applied to E-Mobility
* Model run requires access to the file “Input_esymmetry2011.xls”
*===============================================================================
option mcp = path;
option iterlim = 100000;
set
f Firm /DE_Eon,DE_EnBW,DE_RWE,DE_Vattenfall,DE_Dummy/
t Period /1*168/
n Technology /HYD,NUC_L,NUC_S,BC_New,HC_New,BC_Old,HC_Old,NG_CC,NG_ST,NG_GT,O_ST,O_GT/
nash(f) Firmen die sich nach Nash verhalten;
nash(f):=no;
nash("DE_Dummy") = no ;
nash("DE_RWE") = yes ;
nash("DE_Eon") = yes ;
nash("DE_Vattenfall") = yes ;
nash("DE_Enbw") = yes ;
scalar nash1 Unterdrueckt Nash-Verhalten von Firmen /0/ ;
alias (f,ff);
parameter
q_max(f,n) Installed capacity of firm f and technology n
s(n) Start-up fuel requirement
dq_max(n) Maximum load gradient
MSD(n) marginal start up depreciation
p_f(n) fuel cost of tech n in cent pro kwh
emf(n) emissions factor
eta(n) degree of efficiency of tech n
oc(n) operating cost of tech n in t
a(n) availability of technology n
phi emission price in cent per kg CO2 /2.5/
maxGrad(f,n)
sigma(t) Periodic price elasticity of demand
;
Scalar EV_scaling scaling of EV vehicles profile to yield MW used - 1 corresponds to 1000 EV /50/;
Parameter EV_profile(t) kW demand profile of a fast charging station dispatching 35 kWh a week thus equivalent to the weekly use of one car. Source: Barnes
(2008)
/
1 0.032
2 0.027
3 0.038
4 0.065
5 0.113
Appendix – Source Codes
146
6 0.172
7 0.232
8 0.291
9 0.329
10 0.334
11 0.350
12 0.372
13 0.393
14 0.410
15 0.420
16 0.399
17 0.367
18 0.302
19 0.226
20 0.172
21 0.140
22 0.097
23 0.065
24 0.043
25 0.048
26 0.024
27 0.029
28 0.053
29 0.087
30 0.135
31 0.188
32 0.245
33 0.322
34 0.366
35 0.375
36 0.371
37 0.356
38 0.351
39 0.337
40 0.322
41 0.289
42 0.250
43 0.197
44 0.159
45 0.120
46 0.091
47 0.058
48 0.039
49 0.015
50 0.025
51 0.050
52 0.111
53 0.181
54 0.227
55 0.262
56 0.272
57 0.292
58 0.343
59 0.363
60 0.378
61 0.373
62 0.368
63 0.353
64 0.338
65 0.297
66 0.242
67 0.186
68 0.141
69 0.101
70 0.060
71 0.035
72 0.025
73 0.014
74 0.019
75 0.052
76 0.113
77 0.179
78 0.231
79 0.259
80 0.273
81 0.268
82 0.278
83 0.282
84 0.301
85 0.306
86 0.334
87 0.348
88 0.339
89 0.320
90 0.254
91 0.188
Appendix – Source Codes
147
92 0.132
93 0.099
94 0.056
95 0.038
96 0.024
97 0.019
98 0.024
99 0.053
100 0.120
101 0.192
102 0.235
103 0.269
104 0.283
105 0.273
106 0.278
107 0.283
108 0.297
109 0.307
110 0.331
111 0.345
112 0.340
113 0.326
114 0.264
115 0.192
116 0.144
117 0.101
118 0.058
119 0.038
120 0.024
121 0.020
122 0.025
123 0.055
124 0.125
125 0.200
126 0.245
127 0.280
128 0.295
129 0.285
130 0.290
131 0.295
132 0.310
133 0.320
134 0.345
135 0.360
136 0.355
137 0.340
138 0.275
139 0.200
140 0.150
141 0.105
142 0.060
143 0.040
144 0.025
145 0.021
146 0.026
147 0.058
148 0.131
149 0.210
150 0.257
151 0.294
152 0.310
153 0.299
154 0.305
155 0.310
156 0.326
157 0.336
158 0.362
159 0.378
160 0.373
161 0.357
162 0.289
163 0.210
164 0.158
165 0.110
166 0.063
167 0.042
168 0.026
/
;
Parameter EV(t) EV load aggregated;
EV(t) = EV_profile(t)*EV_scaling;
Parameter D0(t) Reference residual demand in MW
/
1 42040
Appendix – Source Codes
148
2 40797
3 40055
4 40149
5 41089
6 42876
7 48529
8 54265
9 56798
10 57116
11 57589
12 58344
13 57611
14 56863
15 55838
16 55131
17 54687
18 55604
19 56491
20 56305
21 54201
22 51621
23 49055
24 44879
25 41576
26 40271
27 39602
28 39637
29 40545
30 42325
31 47568
32 52972
33 55411
34 55913
35 56469
36 57303
37 56714
38 55879
39 54909
40 54292
41 53973
42 54902
43 55782
44 55799
45 53918
46 51516
47 48961
48 44761
49 42188
50 40790
51 40036
52 39849
53 40753
54 42565
55 47547
56 52831
57 55387
58 55944
59 56569
60 57253
61 56450
62 54788
63 53212
64 52378
65 52340
66 53541
67 54061
68 53471
69 51295
70 49039
71 47288
72 43767
73 40203
74 38377
75 37383
76 37349
77 37578
78 37417
79 37679
80 39818
81 42949
82 45450
83 46653
84 47296
85 46383
86 44591
87 42992
Appendix – Source Codes
149
88 42369
89 42728
90 44677
91 46103
92 46058
93 44023
94 42381
95 41574
96 38778
97 35938
98 34211
99 33580
100 33268
101 33419
102 33140
103 32804
104 33778
105 35942
106 38082
107 39927
108 42005
109 41688
110 39926
111 38455
112 37849
113 38422
114 40673
115 42897
116 43618
117 43129
118 42327
119 42172
120 39230
121 36704
122 35739
123 35528
124 35798
125 37001
126 39340
127 45795
128 52141
129 55311
130 56217
131 57107
132 58089
133 57548
134 56791
135 55639
136 54861
137 54255
138 55118
139 55746
140 55681
141 53891
142 51534
143 49022
144 44751
145 41570
146 40295
147 39792
148 39833
149 40874
150 42839
151 48636
152 54573
153 57367
154 57725
155 58093
156 58895
157 58254
158 57487
159 56499
160 55823
161 55300
162 56150
163 56823
164 56683
165 54710
166 52217
167 49608
168 45264
/
;
Parameter P0(t) Reference price in ct per kWh
/
Appendix – Source Codes
150
1 3.72
2 3.49
3 3.17
4 2.89
5 2.97
6 3.54
7 4.40
8 5.32
9 5.52
10 5.60
11 5.71
12 5.83
13 5.60
14 5.43
15 5.24
16 5.07
17 5.00
18 5.41
19 5.70
20 5.63
21 5.16
22 4.68
23 4.61
24 4.14
25 3.92
26 3.63
27 3.33
28 3.08
29 3.10
30 3.66
31 4.48
32 5.42
33 5.71
34 5.70
35 5.67
36 5.75
37 5.51
38 5.31
39 5.08
40 4.93
41 5.00
42 5.36
43 5.70
44 5.57
45 5.13
46 4.78
47 4.71
48 4.16
49 3.82
50 3.49
51 3.27
52 2.98
53 3.15
54 3.58
55 4.38
56 5.29
57 5.68
58 5.83
59 5.89
60 5.97
61 5.68
62 5.31
63 5.03
64 4.81
65 4.82
66 5.29
67 5.55
68 5.32
69 4.95
70 4.60
71 4.68
72 4.31
73 4.15
74 3.76
75 3.45
76 3.16
77 3.05
78 3.08
79 3.12
80 3.65
81 4.09
82 4.56
83 4.73
84 4.82
85 4.73
86 4.34
Appendix – Source Codes
151
87 4.08
88 3.98
89 4.07
90 4.57
91 5.08
92 5.01
93 4.47
94 4.24
95 4.46
96 3.98
97 3.51
98 3.08
99 2.72
100 2.27
101 2.16
102 2.00
103 1.63
104 2.02
105 2.85
106 3.41
107 3.71
108 4.08
109 4.07
110 3.44
111 3.13
112 2.93
113 3.03
114 3.81
115 4.58
116 4.81
117 4.70
118 4.47
119 4.65
120 3.96
121 3.59
122 3.10
123 2.80
124 2.37
125 2.43
126 3.04
127 4.62
128 5.44
129 5.66
130 5.76
131 5.83
132 6.04
133 5.74
134 5.58
135 5.36
136 5.14
137 5.04
138 5.53
139 5.75
140 5.59
141 5.12
142 4.67
143 4.62
144 4.12
145 3.85
146 3.54
147 3.29
148 3.02
149 3.17
150 3.74
151 4.50
152 5.42
153 5.81
154 5.84
155 5.87
156 6.05
157 5.74
158 5.60
159 5.40
160 5.19
161 5.18
162 5.61
163 5.85
164 5.65
165 5.12
166 4.72
167 4.65
168 4.16
/
;
Parameter
Appendix – Source Codes
152
TC_t(f,t) cost
TP_t(f,t) profit
;
$libinclude xlimport sigma .\Input_esymmetry2011.xls a15:fl16
$libinclude xlimport p_f .\Input_esymmetry2011.xls b23:m24
$libinclude xlimport eta .\Input_esymmetry2011.xls b27:m28
$libinclude xlimport oc .\Input_esymmetry2011.xls b31:m32
$libinclude xlimport q_max .\Input_esymmetry2011.xls a35:m40
$libinclude xlimport s .\Input_esymmetry2011.xls b43:m44
$libinclude xlimport dq_max .\Input_esymmetry2011.xls b47:m48
$libinclude xlimport emf .\Input_esymmetry2011.xls b51:m52
$libinclude xlimport MSD .\Input_esymmetry2011.xls b55:m56
$libinclude xlimport a .\Input_esymmetry2011.xls b58:m59
positive variables
P(t) Price in period t
TC Total Costs
TSC(f,n,t) Total Startupcosts
TP Total profit
MSC(f,n,t) Marginal start up costs
MSE(f,n,t) Marginal start up emissions
MC(n) Marginal Costs
ME(n) Marginal Emissions
q(f,n,t) Production
e Emissions
DIMq(f,n,t) stictly positive Production
dq(f,n,t) Load gradient
lambda(f,n,t) Shadow price of startup restriction
kappa(f,n,t) Shadow price of capacity restriction
theta(f,t) Market share
markup(f,t) Mark-up
;
scalar scaling_cost /1/;
equations
profit(f,n,t)
market(t)
market_share(f,t)
mark_up(f,t)
marginal_costs(n)
marginal_emissions(n)
marginal_startupcosts(f,n,t)
marginal_startupemissions(f,n,t)
startup_restriction(f,n,t)
load_gradient(f,n,t)
capacity_restriction(f,n,t)
total_costs(f)
startupcosts(f,n,t)
total_emissions
total_profit(f)
;
profit(f,n,t)..
MC(n)+phi*ME(n)+lambda(f,n,t)+kappa(f,n,t)
=e=
P(t)*(1-(theta(f,t)/sigma(t))$(nash1*nash(f)))+lambda(f,n,t+1)
;
market(t)..
sum(n,sum(f,q(f,n,t))) =e= EV(t) + D0(t)* (P(t)/P0(t))**(-sigma(t))
;
market_share(f,t)$(nash(f)*nash1)..
theta(f,t)*sum(ff,sum(n,q(ff,n,t)))=e= sum(n,q(f,n,t))
;
mark_up(f,t)$(nash(f)*nash1)..
markup(f,t)=e=P(t)*theta(f,t)/sigma(t)
;
marginal_costs(n)..
MC(n)=e= scaling_cost*( p_f(n)/(eta(n)+0.000001)+oc(n) )
;
marginal_emissions(n)..
ME(n)=e= scaling_cost*( emf(n)/(eta(n)+0.000001) )
;
marginal_startupcosts(f,n,t)..
MSC(f,n,t)=e= scaling_cost*( p_f(n)*s(n)+MSD(n))
;
marginal_startupemissions(f,n,t)..
MSE(f,n,t)=e= scaling_cost*( emf(n)*s(n) )
Appendix – Source Codes
153
;
capacity_restriction(f,n,t)..
q_max(f,n)*a(n)=g=q(f,n,t)
;
startup_restriction(f,n,t)$((ord(t) >= 2) or (ord(t)<card(t)))..
dq_max(n)*q_max(f,n)=g=dq(f,n,t)
;
load_gradient(f,n,t)..
dq(f,n,t)=e=q(f,n,t)-q(f,n,t-1)
;
total_costs(f)..
TC(f)=e=sum(t,sum(n,q(f,n,t)*(MC(n)+phi*ME(n))+dq(f,n,t)*(MSC(f,n,t)+phi*MSE(f,n,t))))
;
total_profit(f)..
TP(f)=e= sum(t,sum(n,P(t)*q(f,n,t)))-TC(f)
;
total_emissions..
e =e= sum(f,sum(n$(eta(n)),sum(t,q(f,n,t)*emf(n)/eta(n)+ s(n)*emf(n)*dq(f,n,t))))
;
startupcosts(f,n,t)..
TSC(f,n,t)=e= dq(f,n,t)*(MSC(f,n,t)+phi*MSE(f,n,t))
*sum(t,sum(n,dq(f,n,t)*(MSC(f,n,t)+phi*MSE(f,n,t))))
;
model esymmetry2011 /profit.q,market.p,market_share.theta,mark_up.markup
marginal_costs.MC,marginal_emissions.ME,capacity_restriction.kappa,
marginal_startupcosts.MSC,marginal_startupemissions.MSE,load_gradient.dq, startup_restriction.lambda,
total_costs.TC,startupcosts.TSC,total_profit.TP,total_emissions.e /;
P.l(t):=7;
*MSC.lo(f,n,t):=0.000000001;
kappa.lo(f,n,t):=0.00000001;
* Fixing ramping variables:
lambda.fx(f,n,t)$( (ORD(t)=1) or (ord(t) ne card(t)) ) = 0 ;
solve esymmetry2011 using mcp;
DIMq.l(f,n,t):=q.l(f,n,t)+0.000000001;
*$libinclude xldump e.l .\esymmetry2011Comp.xls Total_Emissions_e
*$libinclude xldump TC.l .\esymmetry2011Comp.xls Total_Costs_TC
*$libinclude xldump TP.l .\esymmetry2011Comp.xls Total_Profit_TP
*$libinclude xldump DIMq.l .\esymmetry2011Comp.xls Production_q
*$libinclude xldump lambda.l .\esymmetry2011Comp.xls shadow_price_startup_lamda
*$libinclude xldump TSC.l .\esymmetry2011Comp.xls Total_Startup_Costs_TSC
*$libinclude xldump MC.l .\esymmetry2011Comp.xls Marginal_Costs_MC
*$libinclude xldump markup.l .\esymmetry2011Comp.xls Share_Theta
*$libinclude xldump p.l .\esymmetry2011Comp.xls Price_P
*$libinclude xldump kappa.l .\esymmetry2011Comp.xls shadow_price_capacity_kappa
*$libinclude xldump EV .\esymmetry2011Comp.xls EV
****************
nash1:=0;
solve esymmetry2011 using mcp;
maxGrad(f,n):=dq_max(n)*q_max(f,n);
TC_t(f,t)=sum(n,Q.l(f,n,t)*(MC.l(n)+phi*ME.l(n))+dq.l(f,n,t)*(MSC.l(f,n,t)+phi*MSE.l(f,n,t))) ;
TP_t(f,t)= sum(n,P.l(t)*Q.l(f,n,t))-TC_t(f,t) ;
DIMq.l(f,n,t):=q.l(f,n,t)+0.000000001;
$libinclude xldump e.l .\esymmetry2011Nash.xls Total_Emissions_e
$libinclude xldump TC.l .\esymmetry2011Nash.xls Total_Costs_TC
$libinclude xldump TP.l .\esymmetry2011Nash.xls Total_Profit_TP
$libinclude xldump TC_t .\esymmetry2011Nash.xls Total_Costs_TC_t
$libinclude xldump TP_t .\esymmetry2011Nash.xls Total_Profit_TP_t
$libinclude xldump DIMq.l .\esymmetry2011Nash.xls Production_q
$libinclude xldump lambda.l .\esymmetry2011Nash.xls shadow_price_startup_lamda
$libinclude xldump TSC.l .\esymmetry2011Nash.xls Total_Startup_Costs_TSC
*$libinclude xldump MSC.l .\esymmetry2011Nash.xls Marginal_Startup_Costs_MSC
$libinclude xldump markup.l .\esymmetry2011Nash.xls Mark_up
$libinclude xldump p.l .\esymmetry2011Nash.xls Price_P
$libinclude xldump kappa.l .\esymmetry2011Nash.xls Shadow_price_capacity_Kappa
$libinclude xldump EV .\esymmetry2011Nash.xls EV
Appendix – Source Codes
154
GAMS Code of the model in Chapter 4
*===============================================================================
* Combined Power Plant Investment and Electricity Dispatch Model – November 2011 - Andreas Schroeder
*===============================================================================
option mcp = path;
option reslim = 12000;
*option iterlim = 100000;
$eolcom #
* this sets # as end-of-line comment (text after # will be ignored by GAMS)
set
f Firm /DE_Eon,DE_EnBW,DE_RWE,DE_Vattenfall,DE_Dummy/
t Period /1*12/
n Technology /HYD,NUCL,HC_New,BC_Old,HC_Old,NG_CC,NG_ST,NG_GT,O_ST,O_GT,CC_New,NG_GT_New,HC_Retro/
year period of years /2010,2015,2020,2025,2030,2035/
a scenario /s0*s15/
A_Matrix(a,a) Ancestor-successor node mapping in scenario tree / s0.s1, s1.(s2*s3), s2.(s4*s5),
s3.(s5*s7),s4.s8,s5.s9,s6.s10,s7.s11,s8.s12,s9.s13,s10.s14,s11.s15/
Ancestor_Matrix(a,a) Ancestor node mapping in scenario tree / s0.s1, s1.s2,
s1.s3,(s1,s2).s4,(s1,s2).s5,(s1,s3).s6,(s1,s3).s7,(s1,s2,s4).s8,(s1,s2,s5).s9,(s1,s3,s6).s10,(s1,s3,s7).s11,(s1,s2,s4,s8).s12,(s1,s2,s5,s9).s13,(s1,s3,s6,s10).s14,(s1,s3,s
7,s11).s15/
P_Matrix(year,a) Mapping of scenario node to time period / 2010.s0, 2015.s1, 2020.(s2*s3), 2025.(s4*s7), 2030.(s8*s11), 2030.(s12*s15)/
nash(f) Firmen die sich nach Nash verhalten;
nash(f):=no;
nash("DE_Dummy") = no ;
nash("DE_RWE") = yes ;
nash("DE_Eon") = yes ;
nash("DE_Vattenfall") = yes ;
nash("DE_Enbw") = yes ;
Alias (a,aa) ;
scalar nash1 Unterdrueckt Nash-Verhalten von Firmen wenn null /0/ ;
Parameter scaling_kw scaling from GW to kW /1/;
scalar scaling_cost /1/; #Scaling of prices and costs from kWh to GWh ct to EUR
Parameter weeks(a) weeks per period a;
weeks(a) = 8760/card(t)*5;
weeks('s12') = 8760/card(t)*15;
weeks('s13') = 8760/card(t)*15;
weeks('s14') = 8760/card(t)*15;
weeks('s15') = 8760/card(t)*15;
alias (f,ff), (a,aa);
parameter
q_max(f,n,a) Installed capacity of firm f and technology n
s(n) Start-up fuel requirement
dq_max(n) Maximum load gradient
MSD(n) Marginal start up depreciation
p_f(n,a) Fuel cost of tech n in cent pro kwh
emf(n) Emissions factor
eta(n) Degree of efficiency of tech n
oc(n) Operating cost of tech n in t
available(n) Availability of technology n
MC(n,a) Marginal cost of generation
MSC(n,a) Marginal start up costs
MSE(n) Marginal start up emissions
ME(n) Marginal Emissions
*TP(f,a) Total profit
*TC(f,a) Total Costs
TSC(f,n,t,a) Total Startupcosts
E(a) Emissions
TP(f,a) Revenue - Cost = Total Profit
Expected_profits(f) TP multiplied by their probabilities
TC(f,a) Total Costs
TRev(f,a) Total revenues
TQ_tech(t,a,n) Total non-renewable production over all firms
TQ_tech_s1(t,n) Total generation in scenario s1
TQ(t,a) Total non-renewable production over all firms and technologies
FullLoadHour(n,a) Full load hours per technology and year
AveragePrice(a) Average prices per year
Renewable_share(a) Share of renewable energy in overall production
Yearly_demand(a) Yearly demand in TWh
sigma(t) Periodic price elasticity of demand
;
Parameter yearnumber(a)
/
s0 2010
s1 2015
s2 2020
Appendix – Source Codes
155
s3 2020
s4 2025
s5 2025
s6 2025
s7 2025
s8 2030
s9 2030
s10 2030
s11 2030
s12 2035
s13 2035
s14 2035
s15 2035
/
;
Parameter discount(a) discount factor
$ontext
/
s1 0.85
s2 0.56
s3 0.56
s4 0.37
s5 0.37
s6 0.37
s7 0.37
s8 0.24
s9 0.24
s10 0.24
s11 0.24
s12 0.16
s13 0.16
s14 0.16
s15 0.16
/
$offtext
;
discount(a)=1;
Parameter q_min(a) Requirement of minimum reserve capacity in MW imposed by system operator
/
s0 0
s1 500
s2 1000
s3 1000
s4 1500
s5 1500
s6 1500
s7 1500
s8 2000
s9 2000
s10 2000
s11 2000
s12 3000
s13 3000
s14 3000
s15 3000
/
;
q_min(a)=0;
Table q_max_2010(f,n) Maximum capacity for generation in MW.
HYD NUCL HC_Old BC_Old NG_CC NG_ST NG_GT O_ST O_GT CC_New NG_GT_New HC_Retro
DE_Eon 1507 6999 8482 866 1212 2806 1244 815 24 0 0
DE_EnBW 427 4311 3171 872 552 317 409 1 227 0 0
DE_RWE 638 5465 4776 9463 2044 3457 808 33 232 0 0
DE_Vattenfall 1000 1461 1195 7451 734 423 922 259 557 0 0
DE_Dummy 893 1992 7458 531 4430 2746 3728 749 1200 0 0
;
Table q_max_2015(f,n) Maximum capacity for generation in MW.
HYD NUCL HC_Old BC_Old NG_GT NG_ST NG_CC O_ST O_GT CC_New NG_GT_New HC_Retro
DE_Eon 1507 4594 5052 866 803 723 1212 42 24
DE_EnBW 427 2636 3101 872 118 102 552 1 120
DE_RWE 638 3058 3330 1853 637 397 2044 32 2
DE_Vattenfall 1000 947 945 7451 605 0 734 80 277
DE_Dummy 893 1985 5875 531 3397 1920 4430 468 324
;
Table q_max_2020(f,n) Maximum capacity for generation in MW.
HYD NUCL HC_Old BC_Old NG_GT NG_ST NG_CC O_ST O_GT CC_New NG_GT_New HC_Retro
DE_Eon 1507 3319 2914 863 215 101 1212 42 5
DE_EnBW 427 1278 3078 872 78 13 552 0 0
DE_RWE 638 2095 3137 1232 570 37 2044 32 2
DE_Vattenfall 1000 947 945 7312 605 0 734 0 0
DE_Dummy 893 1664 4375 502 2883 1615 4430 273 244
Appendix – Source Codes
156
;
Table q_max_2025(f,n) Maximum capacity for generation in MW.
HYD NUCL HC_Old BC_Old NG_GT NG_ST NG_CC O_ST O_GT CC_New NG_GT_New HC_Retro
DE_Eon 1507 0 1957 533 211 77 1212 42 0
DE_EnBW 427 0 772 872 77 0 552 0 0
DE_RWE 638 0 764 1232 414 22 2044 32 0
DE_Vattenfall 1000 0 945 5488 270 0 734 0 0
DE_Dummy 893 0 2291 397 2299 1237 4430 273 233
;
Table q_max_2030(f,n) Maximum capacity for generation in MW.
HYD NUCL HC_Old BC_Old NG_GT NG_ST NG_CC O_ST O_GT CC_New NG_GT_New HC_Retro
DE_Eon 1507 0 638 533 211 74 1212 42 0
DE_EnBW 427 0 762 872 77 0 552 0 0
DE_RWE 638 0 394 1074 414 20 2044 32 0
DE_Vattenfall 0 0 289 4560 0 0 734 0 0
DE_Dummy 893 0 942 364 2023 566 4331 273 120
;
Table q_max_2035(f,n) Maximum capacity for generation in MW.
HYD NUCL HC_Old BC_Old NG_GT NG_ST NG_CC O_ST O_GT CC_New NG_GT_New HC_Retro
DE_Eon 1507 0 116 533 31 14 1114 0 0
DE_EnBW 427 0 355 865 72 0 384 0 0
DE_RWE 638 0 69 905 225 15 2044 0 0
DE_Vattenfall 0 0 0 3629 0 0 679 0 0
DE_Dummy 893 0 320 338 780 483 3869 218 21
;
Table q_max_2040(f,n) Maximum capacity for generation in MW.
HYD NUCL HC_Old BC_Old NG_GT NG_ST NG_CC O_ST O_GT CC_New NG_GT_New HC_Retro
DE_Eon 1507 0 0 0 28 14 827 0 0
DE_EnBW 427 0 0 0 0 0 0 0 0
DE_RWE 638 0 0 905 138 14 1160 0 0
DE_Vattenfall 0 0 0 0 0 0 299 0 0
DE_Dummy 893 0 0 0 85 350 2072 0 0
;
q_max(f,n,'s0') = scaling_kw*q_max_2010(f,n);
q_max(f,n,'s1') = scaling_kw*q_max_2015(f,n);
q_max(f,n,'s2') = scaling_kw*q_max_2020(f,n);
q_max(f,n,'s3') = scaling_kw*q_max_2020(f,n);
q_max(f,n,'s4') = scaling_kw*q_max_2025(f,n);
q_max(f,n,'s5') = scaling_kw*q_max_2025(f,n);
q_max(f,n,'s6') = scaling_kw*q_max_2025(f,n);
q_max(f,n,'s7') = scaling_kw*q_max_2025(f,n);
q_max(f,n,'s8') = scaling_kw*q_max_2030(f,n);
q_max(f,n,'s9') = scaling_kw*q_max_2030(f,n);
q_max(f,n,'s10') = scaling_kw*q_max_2030(f,n);
q_max(f,n,'s11') = scaling_kw*q_max_2030(f,n);
q_max(f,n,'s12') = scaling_kw*q_max_2035(f,n);
q_max(f,n,'s13') = scaling_kw*q_max_2035(f,n);
q_max(f,n,'s14') = scaling_kw*q_max_2035(f,n);
q_max(f,n,'s15') = scaling_kw*q_max_2035(f,n);
parameter investment_cost(n) Construction cost of a new plant in ct per kW
/
HYD 100000000
NUCL 330000
HC_New 130000
BC_Old 170000
HC_Old 130000
NG_CC 65000
NG_ST 60000
NG_GT 50000
O_ST 60000
O_GT 50000
CC_New 70000
NG_GT_New 50000
HC_Retro 110000
/
;
Parameter available(n) availabilitiy of plant in per cent of time
/
HYD 0.75
NUCL 0.86
HC_New 1
BC_Old 0.82
HC_Old 0.82
NG_CC 0.86
NG_ST 0.86
NG_GT 0.86
O_ST 0.84
O_GT 0.84
Appendix – Source Codes
157
CC_New 0.9
NG_GT_New 0.9
HC_Retro 1
/
;
Parameter MSD(n) marginal start-up or ramping depreciation cost in ct per kW
/
HYD 0
NUCL 0.17
HC_New 0.5
BC_Old 0.1
HC_Old 0.15
NG_CC 1
NG_ST 1
NG_GT 1
O_ST 0.5
O_GT 0.5
CC_New 1
NG_GT_New 1
HC_Retro 0.5
/
;
Parameter emf(n) emission factor in kg per kWh
/
HYD 0
NUCL 0
HC_New 0.34
BC_Old 0.4
HC_Old 0.34
NG_CC 0.2
NG_ST 0.2
NG_GT 0.2
O_ST 0.28
O_GT 0.28
CC_New 0.2
NG_GT_New 0.2
HC_Retro 0.36
/
;
Parameter dq_max(n) start-up or ramping limit in per cent
/
HYD 1
NUCL 0.15
HC_New 0.5
BC_Old 0.4
HC_Old 0.4
NG_CC 0.5
NG_ST 0.36
NG_GT 1
O_ST 0.36
O_GT 1
CC_New 0.55
NG_GT_New 1
HC_Retro 0.4
/
;
dq_max(n) = dq_max(n)*2;
Parameter s(n) start-up or ramping fuel requirement in kWh per kW
/
HYD 0
NUCL 16.7
HC_New 6.2
BC_Old 6.2
HC_Old 6.2
NG_CC 3.5
NG_ST 4.0
NG_GT 1.1
O_ST 4.0
O_GT 1.1
CC_New 2.9
NG_GT_New 1.1
HC_Retro 6.2
/
;
Parameter eta(n) efficiency in per cent
/
HYD 1
NUCL 0.34
HC_New 0.43
Appendix – Source Codes
158
BC_Old 0.38
HC_Old 0.34
NG_CC 0.56
NG_ST 0.4
NG_GT 0.35
O_ST 0.38
O_GT 0.33
CC_New 0.6
NG_GT_New 0.47
HC_Retro 0.38
/
;
Parameter oc(n) variable operation cost in ct per kWh
/
HYD 0.26
NUCL 0.04
HC_New 0.2
BC_Old 0.26
HC_Old 0.2
NG_CC 0.13
NG_ST 0.15
NG_GT 0.15
O_ST 0.15
O_GT 0.15
CC_New 0.13
NG_GT_New 0.15
HC_Retro 0.1
/
;
Table p_f(n,a) fuel price in ct per kWh
*IEA (2011) Scenarios with 15 scenarios
s0 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15
HYD 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
NUCL 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80
HC_New 0.65 0.67 0.60 0.70 0.54 0.71 0.71 0.73 0.47 0.72 0.72 0.76 0.45 0.73 0.73 0.77
BC_Old 0.29 0.32 0.32 0.32 0.33 0.33 0.33 0.33 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34
HC_Old 0.65 0.67 0.60 0.70 0.54 0.71 0.71 0.73 0.47 0.72 0.72 0.76 0.45 0.73 0.73 0.77
NG_CC 1.66 2.13 2.44 2.30 2.64 2.46 2.46 2.17 2.79 2.59 2.59 2.15 2.88 2.68 2.68 2.08
NG_ST 1.66 2.13 2.44 2.30 2.64 2.46 2.46 2.17 2.79 2.59 2.59 2.15 2.88 2.68 2.68 2.08
NG_GT 1.66 2.13 2.44 2.30 2.64 2.46 2.46 2.17 2.79 2.59 2.59 2.15 2.88 2.68 2.68 2.08
O_ST 3.02 3.94 4.57 4.20 4.92 4.39 4.39 3.75 5.20 4.54 4.54 3.75 5.41 4.64 4.64 3.75
O_GT 3.02 3.94 4.57 4.20 4.92 4.39 4.39 3.75 5.20 4.54 4.54 3.75 5.41 4.64 4.64 3.75
CC_New 1.66 2.13 2.44 2.30 2.64 2.46 2.46 2.17 2.79 2.59 2.59 2.15 2.88 2.68 2.68 2.08
NG_GT_New 1.66 2.13 2.44 2.30 2.64 2.46 2.46 2.17 2.79 2.59 2.59 2.15 2.88 2.68 2.68 2.08
HC_Retro 0.65 0.67 0.60 0.70 0.54 0.71 0.71 0.73 0.47 0.72 0.72 0.76 0.45 0.73 0.73 0.77
;
Table sv(n,a) Exogenous salvage value in ct with fixed full-load hours
s0 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15
HYD 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
NUCL 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
HC_New 7867 13052 16469 16469 18721 18721 18721 18721 20973 20973 20973 20973 22579 22579 22579 22579
BC_Old 4683 7770 9804 9804 11839 11839 11839 11839 13873 13873 13873 13873 15907 15907 15907 15907
HC_Old 4594 7621 9617 9617 11612 11612 11612 11612 13607 13607 13607 13607 15603 15603 15603 15603
NG_CC 0 0 5377 5377 8922 8922 8922 8922 11257 11257 11257 11257 11725 11725 11725 11725
NG_ST 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
NG_GT 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
O_ST 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
O_GT 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
CC_New 0 0 5781 5781 9592 9592 9592 9592 12103 12103 12103 12103 12606 12606 12606 12606
NG_GT_New 0 0 4714 4714 7820 7820 7820 7820 9868 9868 9868 9868 10277 10277 10277 10277
HC_Retro 0 0 0 0 0 0 0 0 4158 4158 4158 4158 8316 8316 8316 8316
;
sv(n,a)=0;
Parameter phi(a) emission price in ct per kg (IEA 2011)
/
s0 2.00
s1 2.50
s2 3.00
s3 4.50
s4 3.50
s5 3.50
s6 3.50
s7 7.50
s8 4.00
s9 4.00
s10 4.00
s11 9.50
s12 4.50
s13 4.50
s14 4.50
Appendix – Source Codes
159
s15 12.00
/
;
phi(a) = scaling_cost*phi(a);
* Assignment of parameter values to marginal values
MSE(n) = emf(n)*s(n);
ME(n) $eta(n) = emf(n)/(eta(n));
MC(n,a) $eta(n) = scaling_cost*( p_f(n,a)/(eta(n))+oc(n) + ME(n)*phi(a));
MSC(n,a) = scaling_cost*( p_f(n,a)*s(n)+msd(n) + MSE(n)*phi(a) );
Parameter prob(a) probability of scenario node a in model
/
s0 1
s1 1
s2 0.5
s3 0.5
s4 0.25
s5 0.25
s6 0.25
s7 0.25
s8 0.25
s9 0.25
s10 0.25
s11 0.25
s12 0.25
s13 0.25
s14 0.25
s15 0.25
/
;
$ontext
Parameter prob_2(a) probability for calculation of expected profits;
loop(year,
prob_2(a)$P_Matrix(year,a) = 1 / sum(aa$P_Matrix(year,aa), 1 )
);
;
$offtext
Parameter P0_list(t) Reference price
/
1 3.337
2 2.844
3 3.357
4 4.549
5 5.207
6 5.395
7 4.980
8 4.561
9 4.984
10 5.412
11 4.692
12 4.066
/
;
Parameter P0(t,a) Reference price;
P0(t,'s0')=1*scaling_kw*P0_list(t);
P0(t,'s1')=1.025*scaling_kw*P0_list(t);
P0(t,'s2')=1.05*scaling_kw*P0_list(t);
P0(t,'s3')=1.05*scaling_kw*P0_list(t);
P0(t,'s4')=1.075*scaling_kw*P0_list(t);
P0(t,'s5')=1.075*scaling_kw*P0_list(t);
P0(t,'s6')=1.075*scaling_kw*P0_list(t);
P0(t,'s7')=1.075*scaling_kw*P0_list(t);
P0(t,'s8')=1.1*scaling_kw*P0_list(t);
P0(t,'s9')=1.1*scaling_kw*P0_list(t);
P0(t,'s10')=1.1*scaling_kw*P0_list(t);
P0(t,'s11')=1.1*scaling_kw*P0_list(t);
P0(t,'s12')=1.125*scaling_kw*P0_list(t);
P0(t,'s13')=1.125*scaling_kw*P0_list(t);
P0(t,'s14')=1.125*scaling_kw*P0_list(t);
P0(t,'s15')=1.125*scaling_kw*P0_list(t);
sigma(t) = 1.15*1/p0_list(t);
Parameter D0_list(t) Reference demand
/
1 46931
2 46439
3 49381
4 56684
5 60467
6 62074
7 60580
Appendix – Source Codes
160
8 58722
9 59658
10 60721
11 56698
12 50942
/
;
Parameter D0(t,a) reference demand in year a;
D0(t,'s0')=1*scaling_kw*D0_list(t);
D0(t,'s1')=1.025*scaling_kw*D0_list(t);
D0(t,'s2')=1.05*scaling_kw*D0_list(t);
D0(t,'s3')=1.05*scaling_kw*D0_list(t);
D0(t,'s4')=1.075*scaling_kw*D0_list(t);
D0(t,'s5')=1.075*scaling_kw*D0_list(t);
D0(t,'s6')=1.075*scaling_kw*D0_list(t);
D0(t,'s7')=1.075*scaling_kw*D0_list(t);
D0(t,'s8')=1.1*scaling_kw*D0_list(t);
D0(t,'s9')=1.1*scaling_kw*D0_list(t);
D0(t,'s10')=1.1*scaling_kw*D0_list(t);
D0(t,'s11')=1.1*scaling_kw*D0_list(t);
D0(t,'s12')=1.125*scaling_kw*D0_list(t);
D0(t,'s13')=1.125*scaling_kw*D0_list(t);
D0(t,'s14')=1.125*scaling_kw*D0_list(t);
D0(t,'s15')=1.125*scaling_kw*D0_list(t);
Parameter RES_table(t) Feed-in of renewable energy
/
1 14589
2 14508
3 14775
4 16453
5 18842
6 19809
7 18985
8 17002
9 15192
10 14655
11 14717
12 14718
/
;
Parameter RES(t,a) renewables output;
RES(t,'s0')=1*scaling_kw*RES_table(t);
RES(t,'s1')=1.434*scaling_kw*RES_table(t);
RES(t,'s2')=2.033*scaling_kw*RES_table(t);
RES(t,'s3')=2.033*scaling_kw*RES_table(t);
RES(t,'s4')=2.371*scaling_kw*RES_table(t);
RES(t,'s5')=2.371*scaling_kw*RES_table(t);
RES(t,'s6')=2.371*scaling_kw*RES_table(t);
RES(t,'s7')=2.371*scaling_kw*RES_table(t);
RES(t,'s8')=2.865*scaling_kw*RES_table(t);
RES(t,'s9')=2.865*scaling_kw*RES_table(t);
RES(t,'s10')=2.865*scaling_kw*RES_table(t);
RES(t,'s11')=2.865*scaling_kw*RES_table(t);
RES(t,'s12')=3.06*scaling_kw*RES_table(t);
RES(t,'s13')=3.06*scaling_kw*RES_table(t);
RES(t,'s14')=3.06*scaling_kw*RES_table(t);
RES(t,'s15')=3.06*scaling_kw*RES_table(t);
* 2000 2005 2010 2015 2020 2025 2030 2035
* Germany RES Inst Cap (MW; PRIMES 2012) 22757 48964 77392 110974 157345 183523 221737 236834
* 2010 Index x x 1 1.434 2.033 2.371 2.865 3.06
Parameter alpha(year) Minimum average price expected in each year in cent per kWh
/
2010 4
2015 5
2020 6
2025 7
2030 8
2035 8.5
/
;
Variables
P(t,a) Price in period t
Positive variables
INVESTMENT(f,n,a) Investment
q(f,n,t,a) Production
DIMq(f,n,t,a) Strictly positive Production
dq(f,n,t,a) Load gradient
Appendix – Source Codes
161
lambda(f,n,t,a) Shadow price of startup restriction
kappa(f,n,t,a) Shadow price of capacity restriction
theta(f,t,a) Market share
delta(f,n,t,a) Dual of upper ramp limit
gamma(t,a) Dual of minimum reserve capacity requirement
omega(year) Dual of minmimum average price constraint
;
* Fixing ramping variables - there is no ramping constraint in the first period, so no need for a dual variable:
lambda.fx(f,n,t,a)$( ORD(t) = 1 ) = 0 ;
dq.fx(f,n,t,a)$( ORD(t) = 1 ) = 0 ;
delta.fx(f,n,t,a)$( ORD(t) = 1 ) = 0 ;
gamma.fx(t,a)$( ORD(t) = 1 ) = 0 ;
*===============================================================================
* Equations - Stochastic Model
*===============================================================================
Equation profit(f,n,t,a) Stationarity production - perpendicular to q;
profit(f,n,t,a)..
weeks(a)*discount(a)*prob(a)*MC(n,a) +lambda(f,n,t,a)-lambda(f,n,t+1,a)+kappa(f,n,t,a)+gamma(t,a)
=g=
weeks(a)*discount(a)*prob(a)*
P(t,a)*(1-(theta(f,t,a)/(sigma(t)))$(nash1*nash(f)))
;
Equation profit_inv(f,n,a) Stationarity investment - perpendicular to Investment;
profit_inv(f,n,a).. # kappas und lambdas hier auf nachfolgejahre/knoten beschränkt. Auch bei Ruud Egging ist das so. Ausserdem investitionskosten nicht
mit *discount(a)*weeks(a) - INVESTITIONSKOSTEN NICHT MIT PROB MULTIPLIZIEREN?
investment_cost(n)*discount(a)*prob(a) -sv(n,a)*prob(a)
=g=
sum((t), sum(aa$Ancestor_Matrix(a,aa), (1/1.09)**(yearnumber(aa)-yearnumber(a)+2.5)*(kappa(f,n,t,aa) + gamma(t,a) + dq_max(n)*delta(f,n,t,aa)) )
)*available(n)
;
Equation Profit_loadgradient(f,n,t,a) Stationarity load gradient - perpendicular to dq;
Profit_loadgradient(f,n,t,a)$( ORD(t) ge 2 ).. # There is no ramping in the first hour
weeks(a)*discount(a)*prob(a)*MSC(n,a) - lambda(f,n,t,a) + delta(f,n,t,a)
=g=
0
;
Equation market(t,a) Market balance - perpendicular to p;
market(t,a)$(p0(t,a))..
sum((f,n),q(f,n,t,a))
=e=
- RES(t,a) + D0(t,a)* (P(t,a)/(P0(t,a)))**(-sigma(t))
;
Equation market_share(f,t,a) Market share - perpendicular to theta;
market_share(f,t,a)$(nash(f)*nash1)..
theta(f,t,a)*sum(ff,sum(n,q(ff,n,t,a)$(nash(ff)*nash1)))
=e=
sum(n,q(f,n,t,a))
;
Equation capacity_restriction(f,n,t,a) Production capacity restriction - perpendicular to kappa;
capacity_restriction(f,n,t,a)..
(q_max(f,n,a)+ sum(aa$(Ancestor_Matrix(aa,a)),INVESTMENT(f,n,aa)) )*available(n)
=g=
q(f,n,t,a)
;
Equation ramp_restriction(f,n,t,a) Ramping restriction - perpendicular to delta;
ramp_restriction(f,n,t,a)$(ord(t) >= 2).. # There is no ramp-up constraint in the first hour
(dq_max(n)*q_max(f,n,a)+ sum(aa$(Ancestor_Matrix(aa,a)),dq_max(n)*INVESTMENT(f,n,aa)))*available(n)
=g=
dq(f,n,t,a)
;
Equation load_gradient(f,n,t,a) Load gradient definition- perpendicular to lambda;
load_gradient(f,n,t,a)$( ORD(t) ge 2 ).. # There is no ramp-up constraint in the first hour
dq(f,n,t,a)
=g=
q(f,n,t,a)-q(f,n,t-1,a)
;
Equation reserve_capacity(t,a) Minimum reserve capacity requirement - perpendicular to gamma;
reserve_capacity(t,a)$( ORD(t) ge 2 )..
sum((f,n), (q_max(f,n,a)+ sum(aa$(ord(a) > ord(aa)),INVESTMENT(f,n,aa)))*available(n) -q(f,n,t,a)) - q_min(a)
=g=
0
;
Equation risk_aversion(year) Minimum average price constraint - perpendicular to omega;
risk_aversion(year)..
Appendix – Source Codes
162
sum(a$(P_Matrix(year,a)),prob(a)*sum(t,P(t,a)/card(t)) )
=g=
alpha(year)-omega(year)
;
model esymmetry2011
/
profit.Q,
profit_inv.INVESTMENT,
profit_loadgradient.DQ,
market.P,
market_share.theta,
capacity_restriction.kappa,
ramp_restriction.delta,
load_gradient.lambda,
reserve_capacity.gamma
*,risk_aversion.omega
/
;
*===============================================================================
* Fix values, set starting values, post-calculate parameters
*===============================================================================
P.l(t,a)=p0(t,a);
dq.l(f,n,t,a)=0;
P.lo(t,a)=0.0000001;
INVESTMENT.up(f,n,a) = 40000;
*INVESTMENT.up('DE_Dummy',n,a) = 0;
INVESTMENT.up(f,'HC_Retro',a)$(ord(a) ge 2) = q_max(f,'HC_New',a-1)-q_max(f,'HC_New',a);
INVESTMENT.fx(f,'HYD',a) = 0;
INVESTMENT.fx(f,'NUCL',a) = 0;
INVESTMENT.fx(f,'BC_Old',a) = 0;
INVESTMENT.fx(f,'HC_Old',a) = 0;
INVESTMENT.l(f,'NG_CC',a) = 0;
INVESTMENT.l(f,'NG_ST',a) = 0;
INVESTMENT.l(f,'NG_GT',a) = 0;
INVESTMENT.l(f,'O_ST',a) = 0;
q.l(f,n,t,a)=q_max(f,n,a);
q.l(f,'BC_Old',t,a)=q_max(f,'BC_Old',a)*available('BC_Old');
q.l(f,'HC_Old',t,a)=q_max(f,'HC_Old',a)*available('HC_Old');
q.l(f,'HC_New',t,a)= q_max(f,'HC_New',a)*available('HC_New') ;
q.l(f,'HYD',t,a)=q_max(f,'HYD',a)*available('HYD');
q.l(f,'NUCL',t,a)=q_max(f,'NUCL',a)*available('NUCL');
q.l(f,'NG_ST',t,a)= 0 ;
q.l(f,'NG_GT',t,a)= 0 ;
q.l(f,'NG_CC',t,a)= 0 ;
q.l(f,'CC_New',t,a)= q_max(f,'CC_New',a)*available('CC_New') ;
q.l(f,'NG_GT_New',t,a)= q_max(f,'NG_GT_New',a)*available('NG_GT_New') ;
q.l(f,'O_ST',t,a)= 0 ;
q.l(f,'O_GT',t,a)= 0 ;
$ontext
*===============================================================================
* Fix starting values to previous runs
*===============================================================================
Parameter
q_starting_value(f,n,t,a)
dq_starting_value(f,n,t,a)
INVESTMENT_starting_value(f,n,a)
p_starting_value(t,a)
;
*$libinclude xlimport q_starting_value .\output-stochastic.xls q!b3:s7803
*$libinclude xlimport dq_starting_value .\output-stochastic.xls dq!b3:s7803
*$libinclude xlimport INVESTMENT_starting_value .\output-stochastic.xls INVESTMENT!b3:r68
*$libinclude xlimport p_starting_value .\output-stochastic.xls price!b3:q123
Q.l(f,n,t,a)=q_starting_value(f,n,t,a);
DQ.l(f,n,t,a)=dq_starting_value(f,n,t,a);
INVESTMENT.l(f,n,a)=INVESTMENT_starting_value(f,n,a);
P.l(t,a)=p_starting_value(t,a);
$offtext
* Tell GAMS that Investment in last model year must be zero. Otherwise empty equation profit_inv without dual fixed.
INVESTMENT.fx(f,n,'s12')=0;
INVESTMENT.fx(f,n,'s13')=0;
INVESTMENT.fx(f,n,'s14')=0;
INVESTMENT.fx(f,n,'s15')=0;
*===============================================================================
* Fix investment levels for calculation of Value of Stochastic Solution
Appendix – Source Codes
163
*===============================================================================
*Parameter
*INVESTMENT_deterministic(f,n,a);
*$libinclude xlimport INVESTMENT_deterministic .\output-deterministic.xls INVESTMENT-for-VSS-Calculation!b3:s68
*INVESTMENT.fx(f,n,a)=INVESTMENT_deterministic(f,n,a);
*===============================================================================
* Solve statement
*===============================================================================
solve esymmetry2011 using mcp;
*===============================================================================
* Excel Output
*===============================================================================
TC(f,a)= sum((n,t), q.l(f,n,t,a)*MC(n,a)+dq.l(f,n,t,a)*MSC(n,a))*weeks(a) + sum(n, investment_cost(n)*INVESTMENT.l(f,n,a));
TRev(f,a)= sum(t,P.l(t,a)*sum(n,q.l(f,n,t,a)))*weeks(a);
TP(f,a)= TRev(f,a)-TC(f,a);
Expected_profits(f)=sum(a, TP(f,a)*prob(a)*discount(a));
e(a) = sum(f,sum(n,sum(t,q.l(f,n,t,a)*emf(n)/(eta(n)+0.001)+ s(n)*emf(n)*dq.l(f,n,t,a))));
TQ_tech(t,a,n)=sum(f, Q.l(f,n,t,a));
TQ_tech_s1(t,n)=sum(f, Q.l(f,n,t,'s1'));
TQ(t,a)=sum((f,n), Q.l(f,n,t,a));
FullLoadHour(n,a)= sum((f,t), Q.l(f,n,t,a))/( (sum(f, q_max(f,n,a)+ 0.0001 + sum(aa$(ord(a) > ord(aa)),INVESTMENT.l(f,n,aa)))) *card(t)) *8760;
AveragePrice(a)=sum(t,P.l(t,a))/card(t);
Renewable_share(a)=sum(t,RES(t,a)+sum(f,Q.l(f,'HYD',t,a)))/sum(t,sum((f,n),Q.l(f,n,t,a))+0.0001+RES(t,a));
Yearly_demand(a)=sum(t,sum((f,n),Q.l(f,n,t,a))+RES(t,a))*8760/card(t)*1/1000000;
display Q.l, DQ.L, TQ, TQ_tech_s1, RES, P.l, mc, msc, FullLoadHour, AveragePrice, Renewable_share, Yearly_demand, INVESTMENT.l, Expected_profits,TP,
TC, TRev;
*** Write zeros in EXCEL file
TQ(t,a)$(not TQ(t,a)) = eps;
P.l(t,a)$(not P.l(t,a)) = eps;
q_max(f,n,a)$(not q_max(f,n,a)) = eps;
INVESTMENT.l(f,n,a)$(not INVESTMENT.l(f,n,a)) = eps;
TQ_tech_s1(t,n)$(not TQ_tech_s1(t,n)) = eps;
lambda.l(f,n,t,a)$(not lambda.l(f,n,t,a)) = eps;
delta.l(f,n,t,a)$(not delta.l(f,n,t,a)) = eps;
kappa.l(f,n,t,a)$(not kappa.l(f,n,t,a)) = eps;
q.l(f,n,t,a)$(not q.l(f,n,t,a)) = eps;
dq.l(f,n,t,a)$(not dq.l(f,n,t,a)) = eps;
*** Write output in EXCEL file
$libinclude xldump P.l output-stochastic.xls price!b3
$libinclude xldump TQ_tech_s1 output-stochastic.xls production!b3
$libinclude xldump INVESTMENT.l output-stochastic.xls INVESTMENT!b3
$libinclude xldump Expected_profits output-stochastic.xls PROFITS!b3
GAMS Code of the model in Chapter 5
*===============================================================================
* Andreas Schroeder November 2012
* Model EMELIE-ESY as contribution to EMF 28
* Scenario EU1/ 40%DEF of EMF28
* Model run requires access to the file “Input_Esy_2050-2012-08-28.xls” and to the file “Set-E-2.dat” and the file “NTC-2012-08-31.xls”
*===============================================================================
option mcp = path;
option iterlim = 10000000;
option reslim = 30000;
$batinclude Set-E-2.dat
set
f Firm
t Time step /1*24/
y Period /2010,2020,2030,2040,2050/
n Technology /BC_old, HC_old, BC_SCP, HC_SCP, G_CC, G_GT, NUC_NEW, BC_CCS, HC_IGCCCCS, O_ST, O_GT, G_ST, NUC_old, G_CCS,
HYD /
r Region
link(r,r) Interregional exchange possibility
local(f,r) Assigns regions to firms
nash(f) Firmen die sich nach Nash verhalten;
nash(f):=no;
scalar nash1 Nash-Verhalten von Firmen /0/ ;
alias (f,ff),(r,rr),(n,nn),(y,yy);
Appendix – Source Codes
164
link(r,rr) = yes;
link(r,r) = no;
parameter
g(y) Year indication /2010 2010, 2020 2020, 2030 2030, 2040 2040, 2050 2050/
exlim(y,r,rr) Installed export capacity
q_max(y,f,n) Installed capacity of firm f and technology n
i_max(y,f,n) Planned construction of firm f and technology n
D0(r,t) Reference demand in region r and period t
P0(r,t) Reference price in region r and period t
psi(r) Ten year demand growth rate
*energy efficiency ref
/Germany 0.1, Austria 0.1, Switzerland 0.1, France 0.1, Italy 0.1, Poland 0.2, Netherlands 0.1, Belgium 0.1, Czech
0.2, Norway 0.1, BALTIC 0.2, BRIT 0.1, SEAST 0.2, IBERIA 0.1, NORDIC 0.1/
*energy efficiency high
*/Germany 0.05, Austria 0.05, Switzerland 0.05, France 0.1, Italy 0.05, Poland 0.1, Netherlands 0.1, Belgium 0.1,
Czech 0.1, Norway 0.05, BALTIC 0.1, BRIT 0.05, SEAST 0.1, IBERIA 0.05, NORDIC 0.05/
s(n) Ramp up fuel requirement
dq_max(n) Maximum load gradient
p_f(y,n) Fuel cost of tech n in cent pro kwh
emf(n) Emissions factor
eta(n) Degree of efficiency of tech n
oc(n) Operating cost of tech n in t
a(n) Availability of technology n
epsilon0 Demand elasticity /0.3/
RES(y,r,t) Inelastic supply of RES
delta Private discount rate /0.08/
MC(y,n) Marginal Costs
ME(n) Marginal Emissions
MSD(n) Marginal ramp up depreciation
MSC(y,n) Marginal ramp up costs
MSE(n) Marginal ramp up emissions
FC(y,n) Fix costs of investment in technology n in cent per kW
rep Factor to transform represented production period into investment horizon
hcs(n,f,t) Firm specific regional availability hydro correction factor
cap(y) Emission cap in period y
*mitigation 1 scenario
*/2010 1.265, 2020 0.956, 2030 0.647, 2040 0.338, 2050 0.029/
*reference scenario
/2010 1.265, 2020 1.0576, 2030 0.8502, 2040 0.6427, 2050 0.4353/
resf(y) Renewables up scaling
* reference RES
/2010 0, 2020 0, 2030 0, 2040 0, 2050 0/
* high RES
*/2010 0, 2020 0, 2030 0.1, 2040 0.2, 2050 0.3/
;
$libinclude xlimport FC .\Input_Esy_2050-2012-08-28.xls a2:p7
$libinclude xlimport p_f .\Input_Esy_2050-2012-08-28.xls a10:p15
$libinclude xlimport eta .\Input_Esy_2050-2012-08-28.xls a20:o21
$libinclude xlimport oc .\Input_Esy_2050-2012-08-28.xls a24:o25
$libinclude xlimport s .\Input_Esy_2050-2012-08-28.xls a28:o29
$libinclude xlimport dq_max .\Input_Esy_2050-2012-08-28.xls a32:o33
$libinclude xlimport emf .\Input_Esy_2050-2012-08-28.xls a36:o37
$libinclude xlimport MSD .\Input_Esy_2050-2012-08-28.xls a40:o41
$libinclude xlimport a .\Input_Esy_2050-2012-08-28.xls a44:o45
$libinclude xlimport D0 .\Input_Esy_2050-2012-08-28.xls a50:y65
$libinclude xlimport P0 .\Input_Esy_2050-2012-08-28.xls a70:y85
$libinclude xlimport RES .\Input_Esy_2050-2012-08-28.xls a90:z165
$libinclude xlimport q_max .\Input_Esy_2050-2012-08-28.xls a180:k255
$libinclude xlimport i_max .\Input_Esy_2050-2012-08-28.xls r180:y255
;
display q_max, D0, P0, RES;
resf(y)=0;
MC(y,n)=p_f(y,n)/eta(n)+oc(n);
ME(n)=emf(n)/eta(n);
rep =(sum(y$(ord(y)=2),g(y))-sum(y$(ord(y)=1),g(y))) *8760/card(t);
MSC(y,n)= p_f(y,n)*s(n)+MSD(n);
MSE(n)=emf(n)*s(n);
parameter slope(r,t,y) Slope of demand function;
slope(r,t,y)$D0(r,t) = P0(r,t)/(-epsilon0*D0(r,t)*(1+psi(r))**(ord(y)-1))
;
parameter intercept(r,t,y) Intercept of demand function;
intercept(r,t,y)$D0(r,t) = P0(r,t)-D0(r,t)*(1+psi(r))**(ord(y)-1)*slope(r,t,y)
;
display intercept, slope;
*******************************************************************************
*** Export limits (NTCs)
Appendix – Source Codes
165
*******************************************************************************
Parameter NTC_2010(r,rr);
Parameter NTC_2040(r,rr);
Parameter NTC_2020(r,rr);
Parameter NTC_2030(r,rr);
Parameter NTC_2050(r,rr);
$libinclude xlimport NTC_2010 .\NTC-2012-08-31.xls a4:p19
$libinclude xlimport NTC_2020 .\NTC-2012-08-31.xls a23:p38
$libinclude xlimport NTC_2030 .\NTC-2012-08-31.xls a42:p57
$libinclude xlimport NTC_2040 .\NTC-2012-08-31.xls a61:p76
$libinclude xlimport NTC_2050 .\NTC-2012-08-31.xls a80:p95
display NTC_2010;
display NTC_2020;
display NTC_2030;
display NTC_2040;
display NTC_2050;
exlim('2010',r,rr)=NTC_2010(r,rr);
exlim('2020',r,rr)=NTC_2020(r,rr);
exlim('2030',r,rr)=NTC_2030(r,rr);
exlim('2040',r,rr)=NTC_2040(r,rr);
exlim('2050',r,rr)=NTC_2050(r,rr);
*******************************************************************************
*** Variables
*******************************************************************************
Variable
P(r,t,y) Price in region r and period t in Period y
;
positive
variables
Po(y,r,t) Ordered prices for output
i(f,n,y) Investment of firm f in technology n in period y
q(y,f,n,t) Production of firm f in technology n in step t and Period y
theta(y,f,t,r) Market share dual
x(r,rr,t,y) Export of region r to region rr in step t and Period y
e(y,f) Annual Emissions from sectoral production in period y in tons
phi(y) Carbon Dioxide emissions price
DIMi(r,y) Imports of region r in Period y
DIMx(rr,y) Export of region r in Period y
dq(y,f,n,t) Load gradient of firm f in technology n in step t and Period y
lambda(y,f,n,t) Shadow price of load-gradient restriction of firm f in technology n in step t and Period y
kappa(y,f,n,t) Shadow price of capacity restriction of firm f in technology n in step t and Period y
rho(y,f,n,t) Shadow price of ramping requirement
tau(r,rr,t,y) Shadow price of transmission r to rr in step t and Period y
iota(f,n,y) Shadow price of investment restriction
;
* WARUM IST EXPORT IMMER POSITIV? KEIN IMPORT?
equations
profit_i(f,n,y)
profit_q(y,f,n,t)
profit_dq(y,f,n,t)
profit_x(r,rr,t,y)
trans(r,rr,t,y)
market(r,t,y)
market_share(y,f,t,r)
emission(y,f)
emission_market(y)
capacity_restriction(y,f,n,t)
load_gradient_restriction(y,f,n,t)
ramp_requirement(y,f,n,t)
investment_constraint(f,n,y)
;
*******************************************************************************
*** Equations
*******************************************************************************
profit_q(y,f,n,t)..
MC(y,n)+phi(y)*ME(n)
+kappa(y,f,n,t)
- sum(r$local(f,r),P(r,t,y))
+((1/epsilon0)*sum(r$local(f,r),(P0(r,t)/(D0(r,t)*(1+psi(r))**(ord(y)-1))))*sum(nn,q(y,f,nn,t)))$(nash1*nash(f))
+rho(y,f,n,t)$(ord(t)>1)-rho(y,f,n,t+1)
=g= 0
;
market_share(y,f,t,r)$(local(f,r)*nash(f)*nash1)..
theta(y,f,t,r)*(D0(r,t)*(1+psi(r))**(ord(y)-1))=e=sum(n,q(y,f,n,t))
Appendix – Source Codes
166
;
market(r,t,y)..
sum(n,sum(f$local(f,r),q(y,f,n,t)))+sum(rr$link(r,rr),x(rr,r,t,y)-x(r,rr,t,y))
+ (1+resf(y))*RES(y,r,t)
- (D0(r,t)*(1+psi(r))**(ord(y)-1))-((D0(r,t)*(1+psi(r))**(ord(y)-1))/P0(r,t))*(P0(r,t)-P(r,t,y))*(1/epsilon0)**(-1)
=e=0
;
profit_i(f,n,y)..
(FC(y,n)+iota(f,n,y))- (rep*(sum(yy$(ord(yy)>=ord(y)),sum(t,(kappa(yy,f,n,t)+lambda(yy,f,n,t)*dq_max(n)) *a(n)*(1/(1+delta))**(g(yy)-g(y)+4)))))
=g=0
*letzter Term für Diskontierung mit dem 4. Jahr einer Periode als Referenzjahr für die Berechnung der Diskontierung
;
profit_dq(y,f,n,t)$( ORD(t) > 1 )..
MSC(y,n)+MSE(n)*phi(y)+lambda(y,f,n,t)-rho(y,f,n,t) =g=0
;
investment_constraint(f,n,y)..
i_max(y,f,n)
-i(f,n,y)=g= 0
;
profit_x(r,rr,t,y)..
P(r,t,y)=g= P(rr,t,y)-tau(r,rr,t,y)
;
trans(r,rr,t,y)..
exlim(y,r,rr)- x(r,rr,t,y)=g= 0
;
emission_market(y)..
cap(y)-sum(f,e(y,f))=g=0
;
emission(y,f)..
e(y,f)=e=sum(t, sum(n, q(y,f,n,t)*ME(n)+ dq(y,f,n,t)*MSE(n))) *(rep/10)*1/1000000000
;
capacity_restriction(y,f,n,t)..
(q_max(y,f,n)+sum(yy$(ord(yy)<=ord(y)),i(f,n,yy)))*a(n) - q(y,f,n,t)
=g= 0
;
load_gradient_restriction(y,f,n,t)$( ORD(t) > 1 )..
dq_max(n)*(q_max(y,f,n)+sum(yy$(ord(yy)<=ord(y)),i(f,n,yy)))*a(n)-(q(y,f,n,t)-q(y,f,n,t-1)$(ord(t)>1) )=g= 0
;
ramp_requirement(y,f,n,t)$( ORD(t) > 1 )..
dq(y,f,n,t)-(q(y,f,n,t)-q(y,f,n,t-1)$(ord(t)>1))=g= 0
;
lambda.fx(y,f,n,t)$( ORD(t) = 1 ) = 0
;
rho.fx(y,f,n,t)$( ORD(t) = 1 ) = 0
;
dq.fx(y,f,n,t)$( ORD(t) = 1 ) = 0
;
model EMELIE_Esy_2050
/
profit_q.q,
profit_dq.dq,
profit_i.i,
profit_x.x,
trans.tau,
market.p,
market_share.theta,
emission.e,
emission_market.phi,
investment_constraint.iota,
capacity_restriction.kappa,
load_gradient_restriction.lambda,
ramp_requirement.rho
/
;
*******************************************************************************
*** Set starting values
*******************************************************************************
Appendix – Source Codes
167
P.l(r,t,y)=5;
phi.l(y)=1;
i.l(f,n,y)=0;
q.l(y,f,n,t)=q_max(y,f,n)*a(n);
* Fix first-period investment
i.fx(f,n,'2010')=0;
* Set minimum price to avoid infeasibility under iso-elastic demand function
*P.lo(r,t,y)= 0.000001;
*******************************************************************************
*** Solve and report
*******************************************************************************
solve EMELIE_Esy_2050 using mcp;
Po.l(y,r,t):= P.l(r,t,y);
DIMx.l(r,y):=sum(t,sum(rr,x.l(r,rr,t,y)))+0.000000001;
DIMi.l(r,y):=sum(t,sum(rr,x.l(rr,r,t,y)))+0.000000001;
P.l(r,t,y)$(not P.l(r,t,y)) = eps;
i.l(f,n,y)$(not i.l(f,n,y)) = eps;
q.l(y,f,n,t)$(not q.l(y,f,n,t)) = eps;
x.l(r,rr,t,y)$(not x.l(r,rr,t,y)) = eps;
e.l(y,f) $(not e.l(y,f )) = eps;
phi.l(y) $(not phi.l(y)) = eps;
Parameter
qtot(y,f,n) Production of firm f in Period y;
qtot(y,f,n):=sum(t,q.l(y,f,n,t))*360/1000000;
Parameter
PRODUCTION(f,y) Production in TWh per Year
P_EMF(r,y) Price in 2010 EUR per GJ
I_EMF(n,f,y) Capacity Investment in GW
Q_FOSSILS(n,f,y) Production in EJ per year
EXPORT_EMF(r,y) Trade Export in EJ per year
IMPORT_EMF(r,y) Trade Import in EJ per year
EMISSIONPRICE(y) Emission price in EUR per t CO2
EMISSIONS(f,y) Emissions in Mt CO2 per year
CUM_CAPACITY(n,f,y) Cumulative Capacity in GW per year
EFFICIENCY(n) Efficiency in percent
FULL_LOAD_HOURS(f,n,y) Yearly full load hours
AVERAGE_PRICE(r,y) Yearly average price in EUR per MWh
Annuity(n) Annuity for capital cost
LCoE(f,n,y) Levelized cost of electricity in EUR per MWh
INVESTMENT(f,y) Investment in billion EUR per year
lifetime(n) Lifetime of power plants in years
/BC_old 50, HC_old 50, BC_SCP 50, HC_SCP 50, G_CC 40, G_GT 35, O_ST 50, O_GT 35, G_ST 50, NUC_old 50, NUC_New 50, BC_CCS 50, HC_IGCCCCS
50, G_CCS 40, HYD 100/
;
PRODUCTION(f,y)=sum((t,n), Q.l(y,f,n,t)+(1+resf(y))*sum(r$local(f,r),RES(y,r,t)))*8760/card(t)*1/1000000;
P_EMF(r,y)=sum(t, P.l(r,t,y))/card(t)*10;
I_EMF(n,f,y)=i.l(f,n,y)/1000;
Q_FOSSILS(n,f,y)=sum(t, Q.l(y,f,n,t))*0.0000000036*8760/card(t);
EXPORT_EMF(r,y)=sum((rr,t),X.l(r,rr,t,y))*0.0000000036*8760/card(t);
IMPORT_EMF(r,y)=sum((rr,t),X.l(rr,r,t,y))*0.0000000036*8760/card(t);
EMISSIONPRICE(y)=phi.l(y)*10;
EMISSIONS(f,y)=e.l(y,f)*1000;
CUM_CAPACITY(n,f,y)=(q_max(y,f,n)+sum(yy$(ord(yy)<=ord(y)),i.l(f,n,yy)))/1000;
EFFICIENCY(n)=eta(n);
FULL_LOAD_HOURS(f,n,y)=sum(t,q.l(y,f,n,t))/((q_max(y,f,n)+sum(yy$(ord(yy)<=ord(y)),i.l(f,n,yy))+0.0001)*card(t))*8760;
ANNUITY(n)=(1+delta)**lifetime(n)*delta/((1+delta)**lifetime(n)-1);
LCOE(f,n,y)=ANNUITY(n)*FC(y,n)*10/(FULL_LOAD_HOURS(f,n,y)+0.000001)+MC(y,n)*10+phi.l(y)*ME(n)*10;
INVESTMENT(f,y)=sum(n,i.l(f,n,y)*1000*FC(y,n)/1000000000000);
I_EMF(n,f,y)$(not I_EMF(n,f,y)) = eps;
Q_FOSSILS(n,f,y)$(not Q_FOSSILS(n,f,y)) = eps;
EXPORT_EMF(r,y)$(not EXPORT_EMF(r,y)) = eps;
IMPORT_EMF(r,y)$(not IMPORT_EMF(r,y)) = eps;
CUM_CAPACITY(n,f,y)$(not CUM_CAPACITY(n,f,y)) = eps;
EFFICIENCY(n)$(not EFFICIENCY(n)) = eps;
INVESTMENT(f,y)$(not INVESTMENT(f,y))=eps;
display MSC, MC, ME, MSE, P_EMF, I_EMF, Q_FOSSILS, EXPORT_EMF, IMPORT_EMF, EMISSIONS,
EMISSIONPRICE, CUM_CAPACITY, EFFICIENCY, FULL_LOAD_HOURS, ANNUITY, LCOE, INVESTMENT, PRODUCTION;
$libinclude xldump P_EMF .\EMF_EU1.xls Price
$libinclude xldump I_EMF .\EMF_EU1.xls New_Capacity
$libinclude xldump Q_FOSSILS .\EMF_EU1.xls Production
Appendix – Source Codes
168
$libinclude xldump EXPORT_EMF .\EMF_EU1.xls Export
$libinclude xldump IMPORT_EMF .\EMF_EU1.xls Import
$libinclude xldump EMISSIONS .\EMF_EU1.xls Emissions
$libinclude xldump EMISSIONPRICE .\EMF_EU1.xls CO2price
$libinclude xldump CUM_CAPACITY .\EMF_EU1.xls Cum_Capacity
$libinclude xldump EFFICIENCY .\EMF_EU1.xls Efficiency
$libinclude xldump LCoE .\EMF_EU1.xls LCOE
$libinclude xldump INVESTMENT .\EMF_EU1.xls Investment
$libinclude xldump FULL_LOAD_HOURS .\EMF_EU1.xls FullLoadHours
;
GAMS Code of the model in Chapter 6
*===============================================================================
* Andreas Schröder – May 2012
* Projektstudium 2011 – Model on grid congestion in Germany and the effects of HVDC lines and the strategic placement of generation resources
* Model run requires access to the file “input.xls”
*===============================================================================
sets
n Node or Zone /PT,ES,FR,NL,BE,LX,DK-W,CH,AU,IT,PL,CZ,SK,HU,SN,CR,UA,21,22,23,24,25,26,41,42,71,72,73,74,75,76,81,82,83,84,SE,DK-
E,NO,GB/
Ger(n) Nodes in Germany /21,22,23,24,25,26,41,42,71,72,73,74,75,76,81,82,83,84/
dcl DC Line /dc1*dc12,dc18*dc34,dc36*dc50,dc51*dc53/
t Time /t1*t1008/
st Storage /pump,battery,acaes/
s Type of plant
/
Lignite
Coal
Gas
Oil
Nuclear
Biomass
/
Flexible(s) Subset of flexible plants /Gas,Oil/
Fossil(s) Subset of fossil-fired plants /Coal,Gas,Nuclear/
CHP_technologies(s) Subset of CHP-able technology plants /Coal,Gas,Nuclear,Biomass/
l Ordinary AC Line /Line2*line3643/
;
Alias (t,tt),(n,nn);
option reslim = 120000000;
option iterlim = 100000000;
option
limrow = 0,
limcol = 0,
solprint = off,
sysout = off;
option savepoint=1 ;
$onecho > cplex.opt
threads 4
$offecho
*------------------------------------------------------------------------------*
* Some parameters
*------------------------------------------------------------------------------*
scalars
epsilon Demand elasticity at reference point / -0.2/
loadfactor Factor to define load levels / 1.0 /
windfactor Factor to define wind generation / 1.0 /
pvfactor Factor to define pv generation / 1.0 /
trm Transmission reliability margin / 0.2 /
c_dsm_l DSM costs low / 3 /
c_dsm_m DSM costs medium / 5 /
c_dsm_h DSM costs high / 10 /
;
parameter revision(s) Factor defining the availabilty of plant types
/
Lignite 0.9
Coal 0.9
Gas 0.95
Oil 0.95
Nuclear 0.9
Biomass 0.95
/
;
Appendix – Source Codes
169
display revision;
*------------------------------------------------------------------------------*
* Line parameters
*------------------------------------------------------------------------------*
parameter
AC_P_max(l) Maximum Capacity of line dcl
PTDF(l,n) Power Transfer Distribution Factor
;
$call GDXXRW "input.xls" par=AC_P_max rng=AC_Capacity!A2:b263 cdim=0 rdim=1
$gdxin input.gdx
$load AC_P_max
;
$call GDXXRW "input.xls" par=PTDF rng=PTDF!A1:AN263 cdim=1 rdim=1
$gdxin input.gdx
$load PTDF
;
Parameter AC_Incidence(l,n);
$call GDXXRW "input.xls" par=AC_Incidence rng=AC_Capacity!m1:AZ263 cdim=1 rdim=1
$gdxin input.gdx
$load AC_Incidence
;
AC_P_max(l) = (1-trm) * AC_P_max(l);
display AC_P_max, PTDF;
Parameter DC_P_max(dcl) Maximum Capacity of line dcl;
*NEP DC
*$call GDXXRW "input.xls" par=DC_P_max rng=DC_Capacity!A2:b45 cdim=0 rdim=1
*OHNE DC
*$call GDXXRW "input.xls" par=DC_P_max rng=DC_Capacity!A2:b30 cdim=0 rdim=1
*Selektierte HGÜ
$call GDXXRW "input.xls" par=DC_P_max rng=DC_Capacity!A2:b32 cdim=0 rdim=1
$gdxin input.gdx
$load DC_P_max
;
Parameter DC_Incidence(dcl,n);
*NEP DC
*$call GDXXRW "input.xls" par=DC_Incidence rng=DC_Incidence!A1:AN45 cdim=1 rdim=1
*OHNE DC
*$call GDXXRW "input.xls" par=DC_Incidence rng=DC_Incidence!A1:AN30 cdim=1 rdim=1
*Selectierte HGÜ
$call GDXXRW "input.xls" par=DC_Incidence rng=DC_Incidence!A1:AN32 cdim=1 rdim=1
$gdxin input.gdx
$load DC_Incidence
;
display DC_Incidence, DC_P_max;
*------------------------------------------------------------------------------*
* Generation capacities
*------------------------------------------------------------------------------*
Parameter g_max(s,n) Generation capacities of current fossil plants;
$call GDXXRW "input.xls" par=g_max rng=g_max!A2:Ao8 cdim=1 rdim=1
$gdxin input.gdx
$load g_max
;
display g_max;
Parameter Wind_max(t,n) Wind generation;
$call GDXXRW "input.xls" par=Wind_max rng=Wind!A2:AN1010 cdim=1 rdim=1
$gdxin input.gdx
$load Wind_max
Parameter PV_max(t,n) PV generation;
$call GDXXRW "input.xls" par=PV_max rng=PV!A2:AN1010 cdim=1 rdim=1
$gdxin input.gdx
$load PV_max
Parameter Hydro_max(t,n) Hydro-electric generation;
$call GDXXRW "input.xls" par=Hydro_max rng=Hydro!A2:AN1010 cdim=1 rdim=1
$gdxin input.gdx
$load Hydro_max
*------------------------------------------------------------------------------*
Appendix – Source Codes
170
* Reference demand (linear demand fucntion p = a + m*q )
*------------------------------------------------------------------------------*
parameter q_ref(t,n) Average demand;
$call GDXXRW "input.xls" par=q_ref rng=demand!A2:AN1010 cdim=1 rdim=1
$gdxin input.gdx
$load q_ref
;
display q_ref;
Parameter p_ref(t) Reference price for demand function;
$call GDXXRW "input.xls" par=p_ref rng=Price!A3:B1010 cdim=0 rdim=1
$gdxin input.gdx
$load p_ref
;
display p_ref;
parameter m(t,n) Slope of demand function;
m(t,n)$q_ref(t,n) = p_ref(t)/(epsilon*loadfactor*q_ref(t,n))
;
parameter a(t,n) Intercept of demand function;
a(t,n)$q_ref(t,n) = p_ref(t)-loadfactor*q_ref(t,n)*m(t,n)
;
display m,a;
*------------------------------------------------------------------------------*
* Generation costs
*------------------------------------------------------------------------------*
Parameter c(s) Erzeugungskosten der Kraftwerkstypen in EUR per MW including carbon cost
/
Lignite 25
Coal 35
Gas 55
Oil 95
Nuclear 25
Biomass 70
/
;
Parameter ramp_percentage(s)
/
Lignite 0.5
Coal 0.5
Gas 1
Oil 1
Nuclear 0.33
Biomass 1
/
;
Parameter ramp_cost(s) marginal ramping cost
/
Lignite 25
Coal 35
Gas 55
Oil 95
Nuclear 25
Biomass 70
/
;
Parameter ramp_limit(s,n);
ramp_limit(s,n)=ramp_percentage(s)*g_max(s,n);
*------------------------------------------------------------------------------*
* Storage parameters
*------------------------------------------------------------------------------*
Parameter S_eff(st) Conversion efficiency storage
/
pump 0.75
battery 0.8
acaes 0.7
/
;
Appendix – Source Codes
171
Parameter Scap_max(st,n) Storage capacity limit;
$call GDXXRW "input.xls" par=Scap_max rng=storage_cap!A1:an4 cdim=1 rdim=1
$gdxin input.gdx
$load Scap_max
;
Parameter Sin_max(st,n) Storage capacity limit;
$call GDXXRW "input.xls" par=Sin_max rng=storage_inflow!A1:an4 cdim=1 rdim=1
$gdxin input.gdx
$load Sin_max
;
Parameter Sout_max(st,n) Storage outflow power limit;
Sout_max(st,n) = Sin_max(st,n)
;
display S_eff, Sin_max, Scap_max, Sout_max;
*AUSSCHALTEN
*Sin_max('battery',n) = 0;
*Sin_max('acaes',n) = 0;
*Sout_max('battery',n)=0;
*Sout_max('acaes',n)=0;
*------------------------------------------------------------------------------*
* Demand-Side-Management parameters
*------------------------------------------------------------------------------*
Parameter dsm_max_l(t,n) Limit;
dsm_max_l(t,n)=0.02*q_ref(t,n);
Parameter dsm_max_m(t,n) Limit;
dsm_max_m(t,n)=0.02*q_ref(t,n);
Parameter dsm_max_h(t,n) Limit;
dsm_max_h(t,n)=0.01*q_ref(t,n);
display dsm_max_l, dsm_max_m, dsm_max_h;
*AUSSCHALTEN
*dsm_max_l(t,n)=0;
*dsm_max_m(t,n)=0;
*dsm_max_h(t,n)=0;
*------------------------------------------------------------------------------*
* Variables and equations
*------------------------------------------------------------------------------*
Variables
w Welfare
q_area(t) Area under demand function
variablecost(t) Total cost
AC_lineflow(l,t) Lineflow on l
AC_netinput(t,n) Net input at node n
DC_lineflow(dcl,t) Lineflow on dcl
DC_netinput(t,n) Net input at node n
;
Positive Variables
q(t,n) Demand at node n
g(t,s,n) Generation of plant type s of firm f at node n
SIN(st,n,t) Storage inflow
SOUT(st,n,t) Storage outflow
g_up(t,s,n) Generation change from one period to the next
S_LEVEL(st,n,t) Storage level
DSM_out_l(n,t) DSM shifting load
DSM_in_l(n,t) DSM adding load
DSM_out_m(n,t) DSM shifting load
DSM_in_m(n,t) DSM adding load
DSM_out_h(n,t) DSM shifting load
DSM_in_h(n,t) DSM adding load
;
Equations
objective Zielfunktion der Maximierung (Wohlfahrtsfunktion)
nodal_balance(t,n) Nebenbedingung1: Erzeugung = Nachfrage + NetInput
gen_constraint(t,s,n) Nebenbedingung3: kein Kraftwerk darf mehr Erzeugen als es kann
ramp_limit_constraint(t,s,n) Ramping limits for power plants
ramp_up_constraint(t,s,n) Ramping up constraint for power plants
AC_Constraint_LineFlow(l,t) power flow for each line [MW]
Appendix – Source Codes
172
AC_Constraint_LineFlow_pos(l,t) transmission limit positive [MW]
AC_Constraint_LineFlow_neg(l,t) transmission limit negative [MW]
AC_NetInput_Constraint(t) Net inputs have to sum to zero over all nodes
*DC_NetInput_Constraint(t) Net inputs have to sum to zero over all nodes
DC_Constraint_LineFlow(n,t) power flow for each line [MW]
DC_Constraint_LineFlow_pos(dcl,t) transmission limit positive [MW]
DC_Constraint_LineFlow_neg(dcl,t) transmission limit negative [MW]
Spowerlimit_in1(st,t,n) Power limit storage inflow
Spowerlimit_out1(st,t,n) Power limit storage outflow
Storage_level(st,t,n) Storage level at time t and node n
Slimit_upper1(st,t,n) Capacity limit storage outflow (kann nicht mehr rein als capacity limit)
Storage_Balance(st,n,t) Storage Balance
DSMlimit_upper_l(t,n) Maximum of (positive) demand-side management
DSMlimit_lower_l(t,n) Maximum of (negative) demand-side management
DSMlimit_upper_m(t,n) Maximum of (positive) demand-side management
DSMlimit_lower_m(t,n) Maximum of (negative) demand-side management
DSMlimit_upper_h(t,n) Maximum of (positive) demand-side management
DSMlimit_lower_h(t,n) Maximum of (negative) demand-side management
DSMbalance_l(t,n) Demand-side management balance restricts the period within which load can be shifted
DSMbalance_m(t,n) Demand-side management balance restricts the period within which load can be shifted
DSMbalance_h(t,n) Demand-side management balance restricts the period within which load can be shifted
CHP_constraint_lignite CHP condition for lignite
CHP_constraint_coal CHP condition for coal
CHP_constraint_biomass CHP condition for biomass
CHP_constraint_gas_oil CHP condition for gas and oil
;
objective.. w =e= ( sum(t, sum (n, (a(t,n)*q(t,n)+0.5*m(t,n)*sqr(q(t,n)))) - sum((s,n), g(t,s,n)*c(s))
- sum(n, c_dsm_l*DSM_out_l(n,t))-sum(n,c_dsm_m*DSM_out_m(n,t))-sum(n,c_dsm_h*DSM_out_h(n,t))
- sum((s,n),g_up(t,s,n)*ramp_cost(s))) ) / 1
;
nodal_balance(t,n).. sum((s),g(t,s,n))
- DSM_in_l(n,t)+ DSM_out_l(n,t)- DSM_in_m(n,t)+ DSM_out_m(n,t)- DSM_in_h(n,t)+ DSM_out_h(n,t)
+ sum(st, SOUT(st,n,t) - SIN(st,n,t))
+ wind_max(t,n) + hydro_max(t,n) + pv_max(t,n) - q(t,n) + AC_NetInput(t,n) + DC_NetInput(t,n) =e= 0
;
gen_constraint(t,s,n).. revision(s) * (g_max(s,n)) =g= g(t,s,n)
;
ramp_limit_constraint(t,s,n)$(ord(t) ge 1).. ramp_limit(s,n) =g= g(t,s,n) - g(t-1,s,n)
;
ramp_up_constraint(t,s,n)$(ord(t) ge 1).. g_up(t,s,n) =g= g(t,s,n) - g(t-1,s,n)
;
* LINES
AC_Constraint_LineFlow(l,t).. AC_LineFlow(l,t) - SUM(n, PTDF(l,n) * AC_NetInput(t,n)) =e= 0
;
AC_Constraint_LineFlow_pos(l,t).. AC_P_max(l) =g= AC_LineFlow(l,t)
;
AC_Constraint_LineFlow_neg(l,t).. AC_LineFlow(l,t) =g= - AC_P_max(l)
;
AC_NetInput_Constraint(t).. sum(n, AC_NetInput(t,n)) =e= 0
;
*DC_NetInput_Constraint(t).. sum(n, DC_NetInput(t,n)) =e= 0
*;
DC_Constraint_LineFlow(n,t).. DC_NetInput(t,n) - sum(dcl, DC_LineFlow(dcl,t) * DC_Incidence(dcl,n) ) =e= 0
;
DC_Constraint_LineFlow_pos(dcl,t).. DC_P_max(dcl) =g= DC_LineFlow(dcl,t)
;
DC_Constraint_LineFlow_neg(dcl,t).. DC_LineFlow(dcl,t) =g= - DC_P_max(dcl)
;
* STORAGE
Spowerlimit_in1(st,t,n).. 0 =g= SIN(st,n,t) - Sin_max(st,n)
;
Spowerlimit_out1(st,t,n).. 0 =g= SOUT(st,n,t) - Sout_max(st,n)
;
Storage_level(st,t,n)$(ord(t) ge 2).. S_LEVEL(st,n,t) - (S_LEVEL(st,n,t-1) -SOUT(st,n,t) + SIN(st,n,t)* S_eff(st) ) =e= 0
;
Slimit_upper1(st,t,n).. Scap_max(st,n) =g= S_LEVEL(st,n,t)
;
Storage_Balance(st,n,t).. S_LEVEL(st,n,t)=g= 0
;
* DEMAND-SIDE-MANAGEMENT
DSMlimit_upper_l(t,n).. 0 =g= DSM_in_l(n,t) - dsm_max_l(t,n)
;
DSMlimit_lower_l(t,n).. 0 =g= DSM_out_l(n,t) - dsm_max_l(t,n)
;
DSMlimit_upper_m(t,n).. 0 =g= DSM_in_m(n,t) - dsm_max_m(t,n)
;
DSMlimit_lower_m(t,n).. 0 =g= DSM_out_m(n,t) - dsm_max_m(t,n)
;
Appendix – Source Codes
173
DSMlimit_upper_h(t,n).. 0 =g= DSM_in_h(n,t) - dsm_max_h(t,n)
;
DSMlimit_lower_h(t,n).. 0 =g= DSM_out_h(n,t) - dsm_max_h(t,n)
;
DSMbalance_l(t,n)$(ord(t) ge 2).. sum(tt$((ord(tt) >= ord(t)-1) and (ord(tt)<=ord(t)+1)),
DSM_in_l(n,tt)-DSM_out_l(n,tt)) =e= 0
;
DSMbalance_m(t,n)$(ord(t) ge 2).. sum(tt$((ord(tt) >= ord(t)-1) and (ord(tt)<=ord(t)+1)),
DSM_in_m(n,tt)-DSM_out_m(n,tt)) =e= 0
;
DSMbalance_h(t,n)$(ord(t) ge 2).. sum(tt$((ord(tt) >= ord(t)-1) and (ord(tt)<=ord(t)+1)),
DSM_in_h(n,tt)-DSM_out_h(n,tt)) =e= 0
;
* COMBINED HEAT AND POWER
CHP_constraint_coal.. sum((t,Ger), g(t,'coal',Ger)) =g= 0.14*15.000
*0.28*sum((t,Ger),q(t,Ger))
;
CHP_constraint_lignite.. sum((t,Ger), g(t,'lignite',Ger)) =g= 0.20*15.000
*0.28*sum((t,Ger),q(t,Ger))
;
CHP_constraint_biomass.. sum((t,Ger), g(t,'biomass',Ger)) =g= 0.33*15.000
*0.28*sum((t,Ger),q(t,Ger))
;
CHP_constraint_gas_oil.. sum((t,Ger), g(t,'gas',Ger)) + sum((t,Ger), g(t,'oil',Ger)) =g= 0.27*15.000
*0.28*sum((t,Ger),q(t,Ger))
;
*------------------------------------------------------------------------------*
* Rest *
*------------------------------------------------------------------------------*
model projektstudium2011 /all/;
g.fx(t,'Biomass',n) = revision('Biomass') * g_max('Biomass',n) ;
S_LEVEL.fx(st,n,'t1') = 0 ;
S_LEVEL.fx('pump','NO','t1') = 0.5*Scap_max('pump','NO') ;
SOUT.up(st,n,'t1') = S_LEVEL.l(st,n,'t1');
*S_LEVEL.fx(st,n,'1008') = 0;
*S_LEVEL.lo(st,'NO','1008') = 0;
*SWITCH THE FOLLOWING FIXED VARIABLES ON AND OFF DEPENDING ON SCENARIO
*SIN.fx('battery',n,t)=0;
*SIN.fx('acaes',n,t)=0;
*SOUT.fx('battery',n,t)=0;
*SOUT.fx('acaes',n,t)=0;
*DSM_in_l.fx(n,t)=0;
*DSM_in_m.fx(n,t)=0;
*DSM_in_h.fx(n,t)=0;
*DAS gibt iwie immer comp errors
$ontext
*S_LEVEL.fx('pump','19a','t1') = Scap_max('pump','19a') ;
*S_LEVEL.fx(st,n,'t%t_max%') = 0 ;
*S_LEVEL.l('pump','19c','t%t_max%') = 1 ;
*S_LEVEL.l('pump','19a','t%t_max%') = 1 ;
$offtext
solve projektstudium2011 maximizing w using qcp;
parameter p(n,t) Nodalpreis;
p(n,t) = - nodal_balance.m(t,n) *1 ;
Parameter total_generation(t,s);
total_generation(t,s) = sum(n, g.l(t,s,n));
Parameter total_german_generation(t,s);
total_german_generation(t,s) = sum(Ger, g.l(t,s,Ger));
Parameter total_german_demand(t);
total_german_demand(t)=sum(s,total_german_generation(t,s));
Parameter total_german_reference_demand(t);
total_german_reference_demand(t) = sum(Ger, q_ref(t,Ger));
Parameter german_renewable_share;
german_renewable_share=sum(t,sum(Ger,(g.l(t,'Biomass',Ger)+wind_max(t,Ger)+hydro_max(t,Ger)+pv_max(t,Ger))))/sum((s,t),total_german_generation(t,s))
;
Appendix – Source Codes
174
Parameter full_load_hours(s);
full_load_hours(s)= sum((t,n), g.l(t,s,n))/sum(n,g_max(s,n)*card(t)*revision(s))*8760;
Parameter german_average_export_rate;
german_average_export_rate=sum(t,sum(s,total_german_generation(t,s))+sum(Ger,wind_max(t,Ger)+hydro_max(t,Ger)+pv_max(t,Ger)))/sum(t,total_german
_demand(t));
Parameter average_price(n);
average_price(n)=sum(t,p(n,t))/card(t);
Parameter german_average_price;
german_average_price=sum((t,Ger),p(Ger,t))/(card(t)*card(Ger));
Parameter total_DSM_in(n,t);
total_DSM_in(n,t)=DSM_in_l.l(n,t)+DSM_in_m.l(n,t)+DSM_in_h.l(n,t);
Parameter total_DSM_out(n,t);
total_DSM_out(n,t)=DSM_out_l.l(n,t)+DSM_out_m.l(n,t)+DSM_out_h.l(n,t);
Parameter use_rate_AC_line(l);
use_rate_AC_line(l)=sum(t, abs(AC_LineFlow.l(l,t)))/ (AC_P_max(l)*card(t));
Parameter average_use_rate_AC_line;
average_use_rate_AC_line=sum(l,use_rate_AC_line(l))/card(l);
Parameter use_rate_DC_line(dcl);
use_rate_DC_line(dcl)=sum(t, abs(DC_LineFlow.l(dcl,t)))/ (DC_P_max(dcl)*card(t));
Parameter average_use_rate_DC_line;
average_use_rate_DC_line=sum(dcl,use_rate_DC_line(dcl)/card(dcl));
Parameter congestion_shadow_cost_AC;
congestion_shadow_cost_AC=sum((l,t),AC_Constraint_LineFlow_pos.m(l,t))-sum((l,t),AC_Constraint_LineFlow_neg.m(l,t)) ;
Parameter congestion_shadow_cost_DC;
congestion_shadow_cost_DC=sum((dcl,t),DC_Constraint_LineFlow_pos.m(dcl,t))-sum((dcl,t),DC_Constraint_LineFlow_neg.m(dcl,t)) ;
Parameter AC_flow_matrix(n,nn);
AC_flow_matrix(n,nn)=sum((l,t),AC_Incidence(l,n)*AC_Incidence(l,nn)*AC_LineFlow.l(l,t));
Parameter AC_capacity_matrix(n,nn);
AC_capacity_matrix(n,nn)=sum((l),AC_Incidence(l,n)*AC_Incidence(l,nn)*AC_P_max(l)*card(t));
Parameter AC_use_rate_matrix(n,nn);
AC_use_rate_matrix(n,nn)$(AC_capacity_matrix(n,nn))=AC_flow_matrix(n,nn)/AC_capacity_matrix(n,nn);
Parameter DC_flow_matrix(n,nn);
DC_flow_matrix(n,nn)=sum((dcl,t),DC_Incidence(dcl,n)*DC_Incidence(dcl,nn)*DC_LineFlow.l(dcl,t));
Parameter DC_capacity_matrix(n,nn);
DC_capacity_matrix(n,nn)=sum((dcl),DC_Incidence(dcl,n)*DC_Incidence(dcl,nn)*DC_P_max(dcl)*card(t));
Parameter DC_use_rate_matrix(n,nn);
DC_use_rate_matrix(n,nn)$(DC_capacity_matrix(n,nn))=DC_flow_matrix(n,nn)/DC_capacity_matrix(n,nn);
Parameter AC_congestion_cost_matrix(n,nn);
AC_congestion_cost_matrix(n,nn)=sum((l,t),AC_Incidence(l,n)*AC_Incidence(l,nn)*(AC_Constraint_LineFlow_pos.m(l,t)+AC_Constraint_LineFlow_neg.m(l,t
)));
*Zaehlen der congested hours und in Knotenmatrix machen
Parameter AC_congestion_hour_matrix(n,nn);
AC_congestion_hour_matrix(n,nn)=sum((l,t),AC_Incidence(l,n)*AC_Incidence(l,nn)*(1$(AC_Constraint_LineFlow_pos.m(l,t)<-
0.1)+(1$(AC_Constraint_LineFlow_neg.m(l,t)<-0.1))));
Parameter DC_congestion_cost_matrix(n,nn);
DC_congestion_cost_matrix(n,nn)=sum((dcl,t),DC_Incidence(dcl,n)*DC_Incidence(dcl,nn)*(DC_Constraint_LineFlow_pos.m(dcl,t)+DC_Constraint_LineFlow
_neg.m(dcl,t)));
Parameter DC_congestion_hour_matrix(n,nn);
DC_congestion_hour_matrix(n,nn)=sum((dcl,t),DC_Incidence(dcl,n)*DC_Incidence(dcl,nn)*(1$(DC_Constraint_LineFlow_pos.m(dcl,t)<-
0.1)+(1$(DC_Constraint_LineFlow_neg.m(dcl,t)<-0.1))));
Parameter flow_matrix(n,nn);
flow_matrix(n,nn)=(DC_flow_matrix(n,nn)+AC_flow_matrix(n,nn))*8760/card(t);
Display DC_LineFlow.l, pv_max, hydro_max, wind_max, DC_NetInput.l, q.l,
g.l,SIN.l,SOUT.l,S_LEVEL.l,p, total_DSM_out, total_DSM_in, nodal_balance.m,
AC_Constraint_LineFlow_pos.m, AC_Constraint_LineFlow_neg.m,AC_LineFlow.l,
total_german_demand, total_german_reference_demand,w.l,german_renewable_share,german_average_export_rate,full_load_hours,
german_average_price,average_price,average_use_rate_AC_line,average_use_rate_DC_line,
congestion_shadow_cost_AC,congestion_shadow_cost_DC,use_rate_AC_line,use_rate_DC_line,
DC_use_rate_matrix,AC_use_rate_matrix,AC_congestion_cost_matrix,DC_congestion_cost_matrix,flow_matrix;
*** Write zeros in EXCEL file
g.l(t,s,n)$(not g.l(t,s,n)) = eps;
Appendix – Source Codes
175
Q.l(t,n)$(not Q.l(t,n)) = eps;
P(n,t)$(not P(n,t)) = eps;
AC_Constraint_LineFlow_pos.m(l,t)$(not AC_Constraint_LineFlow_pos.m(l,t)) = eps;
AC_Constraint_LineFlow_neg.m(l,t)$(not AC_Constraint_LineFlow_neg.m(l,t)) = eps;
DC_Constraint_LineFlow_pos.m(dcl,t)$(not DC_Constraint_LineFlow_pos.m(dcl,t)) = eps;
DC_Constraint_LineFlow_neg.m(dcl,t)$(not DC_Constraint_LineFlow_neg.m(dcl,t)) = eps;
total_DSM_in(n,t)$(not total_DSM_in(n,t)) = eps;
SIN.l(st,n,t)$(not SIN.l(st,n,t)) = eps;
SOUT.l(st,n,t)$(not SOUT.l(st,n,t)) = eps;
AC_LineFlow.l(l,t)$(not AC_LineFlow.l(l,t)) = eps;
AC_NetInput.l(t,n)$(not AC_NetInput.l(t,n)) = eps;
DC_NetInput.l(t,n)$(not DC_NetInput.l(t,n)) = eps;
DC_LineFlow.l(dcl,t)$(not DC_LineFlow.l(dcl,t)) = eps;
total_generation(t,s)$(not total_generation(t,s)) = eps;
total_german_generation(t,s)$(not total_german_generation(t,s)) = eps;
pv_max(t,n)$(not pv_max(t,n)) = eps;
hydro_max(t,n)$(not hydro_max(t,n)) = eps;
wind_max(t,n)$(not wind_max(t,n)) = eps;
total_DSM_in(n,t)$(not total_DSM_in(n,t)) = eps;
AC_use_rate_matrix(n,nn)$(not AC_use_rate_matrix(n,nn))=eps;
DC_use_rate_matrix(n,nn)$(not DC_use_rate_matrix(n,nn))=eps;
AC_congestion_cost_matrix(n,nn)$(not AC_congestion_cost_matrix(n,nn))=eps;
DC_congestion_cost_matrix(n,nn)$(not DC_congestion_cost_matrix(n,nn))=eps;
AC_congestion_hour_matrix(n,nn)$(not AC_congestion_hour_matrix(n,nn))=eps;
DC_congestion_hour_matrix(n,nn)$(not DC_congestion_hour_matrix(n,nn))=eps;
flow_matrix(n,nn)$(not flow_matrix(n,nn))=eps;
*** Write output in EXCEL file
$libinclude xldump g.l output-NEP-2012.xlsx generation!b3
$libinclude xldump total_generation output-NEP-2012.xlsx total_generation!b3
$libinclude xldump total_german_generation output-NEP-2012.xlsx total_german_generation!b3
$libinclude xldump q.l output-NEP-2012.xlsx demand!b3
$libinclude xldump P output-NEP-2012.xlsx price!b3
$libinclude xldump AC_Constraint_LineFlow_neg.m output-NEP-2012.xlsx AC_Constraint_LineFlow_neg!b3
$libinclude xldump AC_Constraint_LineFlow_pos.m output-NEP-2012.xlsx AC_Constraint_LineFlow_pos!b3
$libinclude xldump DC_Constraint_LineFlow_neg.m output-NEP-2012.xlsx DC_Constraint_LineFlow_neg!b3
$libinclude xldump DC_Constraint_LineFlow_pos.m output-NEP-2012.xlsx DC_Constraint_LineFlow_pos!b3
$libinclude xldump AC_LineFlow.l output-NEP-2012.xlsx AC_LineFlow!b3
$libinclude xldump AC_NetInput.l output-NEP-2012.xlsx AC_NetInput!b3
$libinclude xldump DC_NetInput.l output-NEP-2012.xlsx DC_NetInput!b3
$libinclude xldump DC_LineFlow.l output-NEP-2012.xlsx DC_LineFlow!b3
$libinclude xldump total_DSM_in output-NEP-2012.xlsx DSM_in!b3
$libinclude xldump SIN.l output-NEP-2012.xlsx SIN!b3
$libinclude xldump SOUT.l output-NEP-2012.xlsx SOUT!b3
$libinclude xldump S_LEVEL.l output-NEP-2012.xlsx S_Level!b3
$libinclude xldump pv_max output-NEP-2012.xlsx pv_max!b3
$libinclude xldump hydro_max output-NEP-2012.xlsx hydro_max!b3
$libinclude xldump wind_max output-NEP-2012.xlsx wind_max!b3
$libinclude xldump w.l output-NEP-2012.xlsx welfare!b3
$libinclude xldump total_DSM_out output-NEP-2012.xlsx DSM_out!b3
$libinclude xldump use_rate_AC_line output-NEP-2012.xlsx use_rate_AC_line!b3
$libinclude xldump use_rate_DC_line output-NEP-2012.xlsx use_rate_DC_line!b3
$libinclude xldump AC_use_rate_matrix output-NEP-2012.xlsx use_rate_AC!a1
$libinclude xldump DC_use_rate_matrix output-NEP-2012.xlsx use_rate_DC!a1
$libinclude xldump congestion_shadow_cost_AC output-NEP-2012.xlsx congestion_cost_AC!b3
$libinclude xldump congestion_shadow_cost_DC output-NEP-2012.xlsx congestion_cost_DC!b3
$libinclude xldump AC_congestion_cost_matrix output-NEP-2012.xlsx congestion_cost_matrix_AC!a1
$libinclude xldump DC_congestion_cost_matrix output-NEP-2012.xlsx congestion_cost_matrix_DC!a1
$libinclude xldump AC_congestion_hour_matrix output-NEP-2012.xlsx congestion_hour_matrix_AC!a1
$libinclude xldump DC_congestion_hour_matrix output-NEP-2012.xlsx congestion_hour_matrix_DC!a1
$libinclude xldump flow_matrix output-NEP-2012.xlsx flow_matrix_AC_DC!a1
GAMS Code of the model in Chapter 7
*===============================================================================
* Andreas Schröder – October 2012
* Model on Grid Congestion and the effects of HVDC lines and power plant investment
* Model run requires access to the file “input-8760h.gdx”
* Input data can be obtained from the author upon request
*===============================================================================
sets
n Node or Zone /PT,ES,FR,NL,BE,LX,DK-
W,CH,AU,IT,PL,CZ,SK,HU,SN,CR,UA,21,22,23,24,25,26,41,42,71,72,73,74,75,76,81,82,83,84,SE,DK-E,NO,GB/
Ger(n) Nodes in Germany /21,22,23,24,25,26,41,42,71,72,73,74,75,76,81,82,83,84/
dcl DC Line /dc1*dc12,dc18*dc34,dc36*dc50/
*,dc36*dc50/
*dc51*dc52/
t Time /t1*t8760/
st Storage /pump,battery,acaes/
Appendix – Source Codes
176
s Type of plant
/
Lignite
Coal
Gas
Oil
Nuclear
Biomass
/
Flexible(s) Subset of flexible plants /Gas,Oil/
Fossil(s) Subset of fossil-fired plants /Coal,Gas,Nuclear/
CHP_technologies(s) Subset of CHP-able technology plants /Coal,Gas,Nuclear,Biomass/
l Ordinary AC Line
/
line2
line3
line4
line6
line9
line10
line12
line13
line14
line17
line20
line21
line24
line27
line31
line34
line35
line36
line39
line40
line42
line44
line45
line49
line50
line51
line62
line64
line72
line74
line78
line85
line86
line88
line90
line91
line92
line94
line95
line98
line101
line108
line109
line110
line121
line129
line140
line147
line148
line150
line153
line155
line156
line165
line176
line177
line180
line181
line184
line189
line196
Appendix – Source Codes
177
line208
line209
line213
line215
line218
line267
line275
line277
line278
line279
line281
line289
line290
line291
line292
line298
line338
line340
line341
line344
line352
line463
line464
line475
line478
line479
line487
line494
line497
line498
line499
line500
line503
line505
line508
line510
line512
line534
line535
line545
line567
line570
line571
line572
line575
line579
line601
line607
line629
line640
line641
line643
line646
line655
line656
line672
line673
line705
line707
line708
line709
line710
line711
line712
line715
line716
line719
line726
line731
line734
line736
line737
line745
line746
line748
Appendix – Source Codes
178
line749
line766
line772
line773
line775
line778
line779
line780
line781
line786
line791
line792
line793
line795
line844
line906
line907
line965
line973
line1011
line1079
line1103
line1108
line1118
line1160
line1350
line1369
line1516
line1542
line1580
line1584
line1659
line1746
line1873
line1875
line1876
line1877
line1878
line1879
line1880
line1881
line1882
line1885
line2192
line2205
line2206
line2210
line2220
line2227
line2244
line2248
line2249
line2250
line2278
line2294
line2295
line2300
line2326
line2327
line2393
line2394
line2395
line2396
line2397
line2400
line2401
line2402
line2403
line2404
line2511
line2521
line2522
line2523
line2524
line2525
Appendix – Source Codes
179
line2526
line2527
line2528
line2530
line2533
line2540
line2541
line3288
line3292
line3444
line3449
line3456
line3459
line3460
line3468
line3469
line3476
line3478
line3483
line3484
line3489
line3490
line3496
line3498
line3503
line3504
line3525
line3527
line3535
line3536
line3538
line3543
line3559
line3560
line3562
line3565
line3566
line3584
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line3602
line3606
line3621
line3630
line3633
line3636
line3637
line3641
line3642
line3643
/
;
Alias (t,tt),(n,nn);
option reslim = 120000000;
option iterlim = 100000000;
option
limrow = 0,
limcol = 0,
solprint = off,
sysout = off;
option savepoint=1 ;
$onecho > cplex.opt
threads 1
$offecho
*------------------------------------------------------------------------------*
* Some parameters
*------------------------------------------------------------------------------*
Appendix – Source Codes
180
scalars
epsilon Demand elasticity at reference point / -0.1 /
loadfactor Factor to define load levels / 1.0 /
windfactor Factor to define wind generation / 1.0 /
pvfactor Factor to define pv generation / 1.0 /
trm Transmission reliability margin / 0.2 /
c_dsm_l DSM costs low / 3 /
c_dsm_m DSM costs medium / 5 /
c_dsm_h DSM costs high / 10 /
;
parameter revision(s) Factor defining the availabilty of plant types
/
Lignite 0.9
Coal 0.9
Gas 0.95
Oil 0.95
Nuclear 0.9
Biomass 0.95
/
;
display revision;
*------------------------------------------------------------------------------*
* Line parameters
*------------------------------------------------------------------------------*
Parameter
AC_P_max(l) Maximum Capacity of line dcl
PTDF(l,n) Power Transfer Distribution Factor
AC_Incidence(l,n) AC Incidence Matrix
DC_P_max(dcl) Maximum Capacity of line dcl
DC_Incidence(dcl,n) Incidence Matrix of DC lines
;
*------------------------------------------------------------------------------*
* Generation capacities
*------------------------------------------------------------------------------*
Parameter g_max(s,n) Generation capacities of current fossil plants;
Parameter Wind_max(t,n) Wind generation;
Parameter PV_max(t,n) PV generation;
Parameter Hydro_max(t,n) Hydro-electric generation;
*------------------------------------------------------------------------------*
* Reference demand (linear demand fucntion p = a + m*q )
*------------------------------------------------------------------------------*
Parameter q_ref(t,n) Average demand;
Parameter p_ref(t,n) Reference price for demand function;
*------------------------------------------------------------------------------*
* Investment parameters
*------------------------------------------------------------------------------*
Parameter invest_cost_total(s) Overnight investment cost in EUR per kW
/
Lignite 1700
Coal 1200
Gas 600
Oil 400
Nuclear 6000
Biomass 2300
/
;
Parameter life_length(s) Life length of technology in years
/
Lignite 40
Coal 40
Gas 35
Oil 30
Appendix – Source Codes
181
Nuclear 50
Biomass 30
/
;
Parameter invest_limit(s) Limit for installed capacity in Europe per technology in MW accroding to Roadmap 2050 Part 1 p. 78
/
Lignite 1000000
Coal 1000000
Gas 200000
Oil 50000
Nuclear 150000
Biomass 80000
/
;
Parameter annuity_factor(s) annuity factor;
Parameter invest_cost(s) annuity or week investment cost;
Scalar r interest rate /0.09/;
annuity_factor(s) = (1+r)**(life_length(s))*r /((1+r)**(life_length(s)) - 1);
invest_cost(s) = invest_cost_total(s)*1000*annuity_factor(s)*card(t)/8760;
*------------------------------------------------------------------------------*
* Generation costs
*------------------------------------------------------------------------------*
Parameter c(s) Erzeugungskosten der Kraftwerkstypen in EUR per MW including carbon cost
/
Lignite 66.9
Coal 68.2
Gas 75
Oil 170
Nuclear 25
Biomass 35
/
;
Parameter ramp_percentage(s)
/
Lignite 0.5
Coal 0.5
Gas 1
Oil 1
Nuclear 0.33
Biomass 1
/
;
Parameter ramp_cost(s) marginal ramping cost
/
Lignite 60
Coal 60
Gas 10
Oil 10
Nuclear 60
Biomass 10
/
;
*------------------------------------------------------------------------------*
* Storage parameters
*------------------------------------------------------------------------------*
Parameter S_eff(st) Conversion efficiency storage
/
pump 0.75
battery 0.8
acaes 0.7
/
;
Parameter Scap_max(st,n) Storage capacity limit;
Appendix – Source Codes
182
Parameter Sin_max(st,n) Storage capacity limit;
*------------------------------------------------------------------------------*
* Call GDX File
*------------------------------------------------------------------------------*
$onecho >temp.txt
par=AC_P_max rng=AC_Capacity!A2:b263 cdim=0 rdim=1
par=PTDF rng=PTDF!A1:AN263 cdim=1 rdim=1
par=AC_Incidence rng=AC_Capacity!m1:AZ263 cdim=1 rdim=1
par=DC_P_max rng=DC_Capacity!A2:b45 cdim=0 rdim=1
par=DC_Incidence rng=DC_Incidence!A1:AN45 cdim=1 rdim=1
par=g_max rng=g_max!A2:Ao8 cdim=1 rdim=1
par=Wind_max rng=Wind!A2:AN8762 cdim=1 rdim=1
par=PV_max rng=PV!A2:AN8762 cdim=1 rdim=1
par=Hydro_max rng=Hydro!A2:AN8762 cdim=1 rdim=1
par=q_ref rng=demand!A2:AN8762 cdim=1 rdim=1
par=p_ref rng=Price!A2:AN8762 cdim=1 rdim=1
par=Scap_max rng=storage_cap!A1:an4 cdim=1 rdim=1
par=Sin_max rng=storage_inflow!A1:an4 cdim=1 rdim=1
$offecho
*$call GDXXRW "input-8760h.xls" @temp.txt
$gdxin input-8760h.gdx
$load AC_P_max,PTDF,AC_Incidence,DC_P_max,DC_Incidence,g_max
;
$load Wind_max,PV_max,Hydro_max,p_ref,q_ref,Scap_max,Sin_max
;
*------------------------------------------------------------------------------*
* Calculations of parameters after GDX call
*------------------------------------------------------------------------------*
AC_P_max(l) = (1-trm) * AC_P_max(l);
parameter m(t,n) Slope of demand function;
m(t,n)$q_ref(t,n) = p_ref(t,n)/(epsilon*loadfactor*q_ref(t,n))
;
parameter a(t,n) Intercept of demand function;
a(t,n)$q_ref(t,n) = p_ref(t,n)-loadfactor*q_ref(t,n)*m(t,n)
;
Parameter dsm_max_l(t,n) DSM Limit;
dsm_max_l(t,n)=0.02*q_ref(t,n);
Parameter dsm_max_m(t,n) DSM Limit;
dsm_max_m(t,n)=0.02*q_ref(t,n);
Parameter dsm_max_h(t,n) DSM Limit;
dsm_max_h(t,n)=0.01*q_ref(t,n);
Parameter Sout_max(st,n) Storage outflow power limit;
Sout_max(st,n) = Sin_max(st,n)
;
Parameter ramp_limit(s,n) Ramping limits;
ramp_limit(s,n)=ramp_percentage(s)*g_max(s,n);
*------------------------------------------------------------------------------*
* Variables and equations
*------------------------------------------------------------------------------*
Variables
w Welfare
q_area(t) Area under demand function
variablecost(t) Total cost
AC_lineflow(l,t) Lineflow on l
AC_netinput(t,n) Net input at node n
DC_lineflow(dcl,t) Lineflow on dcl
DC_netinput(t,n) Net input at node n
;
Positive Variables
Appendix – Source Codes
183
q(t,n) Demand at node n
g(t,s,n) Generation of plant type s of firm f at node n
SIN(st,n,t) Storage inflow
SOUT(st,n,t) Storage outflow
g_up(t,s,n) Generation change from one period to the next
S_LEVEL(st,n,t) Storage level
DSM_out_l(n,t) DSM shifting load
DSM_in_l(n,t) DSM adding load
DSM_out_m(n,t) DSM shifting load
DSM_in_m(n,t) DSM adding load
DSM_out_h(n,t) DSM shifting load
DSM_in_h(n,t) DSM adding load
INVEST(s,n) Investment into generation capacity
;
Equations
objective Zielfunktion der Maximierung (Wohlfahrtsfunktion)
nodal_balance(t,n) Nebenbedingung1: Erzeugung = Nachfrage + NetInput
gen_constraint(t,s,n) Nebenbedingung3: kein Kraftwerk darf mehr Erzeugen als es kann
ramp_limit_constraint(t,s,n) Ramping limits for power plants
ramp_up_constraint(t,s,n) Ramping up constraint for power plants
AC_Constraint_LineFlow(l,t) power flow for each line [MW]
AC_Constraint_LineFlow_pos(l,t) transmission limit positive [MW]
AC_Constraint_LineFlow_neg(l,t) transmission limit negative [MW]
AC_NetInput_Constraint(t) Net inputs have to sum to zero over all nodes
*DC_NetInput_Constraint(t) Net inputs have to sum to zero over all nodes
DC_Constraint_LineFlow(n,t) power flow for each line [MW]
DC_Constraint_LineFlow_pos(dcl,t) transmission limit positive [MW]
DC_Constraint_LineFlow_neg(dcl,t) transmission limit negative [MW]
Spowerlimit_in1(st,t,n) Power limit storage inflow
Spowerlimit_out1(st,t,n) Power limit storage outflow
Storage_level(st,t,n) Storage level at time t and node n
Slimit_upper1(st,t,n) Capacity limit storage outflow (kann nicht mehr rein als capacity limit)
Storage_Balance(st,n,t) Storage Balance
DSMlimit_upper_l(t,n) Maximum of (positive) demand-side management
DSMlimit_lower_l(t,n) Maximum of (negative) demand-side management
DSMlimit_upper_m(t,n) Maximum of (positive) demand-side management
DSMlimit_lower_m(t,n) Maximum of (negative) demand-side management
DSMlimit_upper_h(t,n) Maximum of (positive) demand-side management
DSMlimit_lower_h(t,n) Maximum of (negative) demand-side management
DSMbalance_l(t,n) Demand-side management balance restricts the period within which load can be shifted
DSMbalance_m(t,n) Demand-side management balance restricts the period within which load can be shifted
DSMbalance_h(t,n) Demand-side management balance restricts the period within which load can be shifted
*CHP_constraint_lignite CHP condition for lignite
*CHP_constraint_coal CHP condition for coal
*CHP_constraint_biomass CHP condition for biomass
*CHP_constraint_gas_oil CHP condition for gas and oil
Investment_constraint(s) Upper limit potential for investments
Demand_minimum_Germany To ensure comparability to NEP calculations
;
objective.. w =e= ( sum(t, sum (n, (a(t,n)*q(t,n)+0.5*m(t,n)*sqr(q(t,n)))) - sum((s,n), g(t,s,n)*c(s))
- sum(n, c_dsm_l*DSM_out_l(n,t))-sum(n,c_dsm_m*DSM_out_m(n,t))-sum(n,c_dsm_h*DSM_out_h(n,t))
- sum((s,n),g_up(t,s,n)*ramp_cost(s))) -sum((s,n),invest_cost(s)*INVEST(s,n)) ) / 1
;
nodal_balance(t,n).. sum((s),g(t,s,n))
- DSM_in_l(n,t)+ DSM_out_l(n,t)- DSM_in_m(n,t)+ DSM_out_m(n,t)- DSM_in_h(n,t)+ DSM_out_h(n,t)
+ sum(st, SOUT(st,n,t) - SIN(st,n,t))
+ wind_max(t,n) + hydro_max(t,n) + pv_max(t,n) - q(t,n) + AC_NetInput(t,n) + DC_NetInput(t,n) =e= 0
;
gen_constraint(t,s,n).. revision(s) * (g_max(s,n)+INVEST(s,n)) =g= g(t,s,n)
;
ramp_limit_constraint(t,s,n)$(ord(t) ge 1).. ramp_percentage(s)*(g_max(s,n)+INVEST(s,n)) =g= g(t,s,n) - g(t-1,s,n)
;
ramp_up_constraint(t,s,n)$(ord(t) ge 1).. g_up(t,s,n) =g= g(t,s,n) - g(t-1,s,n)
;
* LINES
AC_Constraint_LineFlow(l,t).. AC_LineFlow(l,t) - SUM(n, PTDF(l,n) * AC_NetInput(t,n)) =e= 0
;
AC_Constraint_LineFlow_pos(l,t).. AC_P_max(l) =g= AC_LineFlow(l,t)
Appendix – Source Codes
184
;
AC_Constraint_LineFlow_neg(l,t).. AC_LineFlow(l,t) =g= - AC_P_max(l)
;
AC_NetInput_Constraint(t).. sum(n, AC_NetInput(t,n)) =e= 0
;
*DC_NetInput_Constraint(t).. sum(n, DC_NetInput(t,n)) =e= 0
*;
DC_Constraint_LineFlow(n,t).. DC_NetInput(t,n) - sum(dcl, DC_LineFlow(dcl,t) * DC_Incidence(dcl,n) ) =e= 0
;
DC_Constraint_LineFlow_pos(dcl,t).. DC_P_max(dcl) =g= DC_LineFlow(dcl,t)
;
DC_Constraint_LineFlow_neg(dcl,t).. DC_LineFlow(dcl,t) =g= - DC_P_max(dcl)
;
* STORAGE
Spowerlimit_in1(st,t,n).. 0 =g= SIN(st,n,t) - Sin_max(st,n)
;
Spowerlimit_out1(st,t,n).. 0 =g= SOUT(st,n,t) - Sout_max(st,n)
;
Storage_level(st,t,n)$(ord(t) ge 2).. S_LEVEL(st,n,t) - (S_LEVEL(st,n,t-1) -SOUT(st,n,t) + SIN(st,n,t)* S_eff(st) ) =e= 0
;
Slimit_upper1(st,t,n).. Scap_max(st,n) =g= S_LEVEL(st,n,t)
;
Storage_Balance(st,n,t).. S_LEVEL(st,n,t)=g= 0
;
* DEMAND-SIDE-MANAGEMENT
DSMlimit_upper_l(t,n).. 0 =g= DSM_in_l(n,t) - dsm_max_l(t,n)
;
DSMlimit_lower_l(t,n).. 0 =g= DSM_out_l(n,t) - dsm_max_l(t,n)
;
DSMlimit_upper_m(t,n).. 0 =g= DSM_in_m(n,t) - dsm_max_m(t,n)
;
DSMlimit_lower_m(t,n).. 0 =g= DSM_out_m(n,t) - dsm_max_m(t,n)
;
DSMlimit_upper_h(t,n).. 0 =g= DSM_in_h(n,t) - dsm_max_h(t,n)
;
DSMlimit_lower_h(t,n).. 0 =g= DSM_out_h(n,t) - dsm_max_h(t,n)
;
DSMbalance_l(t,n)$(ord(t) ge 2).. sum(tt$((ord(tt) >= ord(t)-1) and (ord(tt)<=ord(t)+1)),
DSM_in_l(n,tt)-DSM_out_l(n,tt)) =e= 0
;
DSMbalance_m(t,n)$(ord(t) ge 2).. sum(tt$((ord(tt) >= ord(t)-1) and (ord(tt)<=ord(t)+1)),
DSM_in_m(n,tt)-DSM_out_m(n,tt)) =e= 0
;
DSMbalance_h(t,n)$(ord(t) ge 2).. sum(tt$((ord(tt) >= ord(t)-1) and (ord(tt)<=ord(t)+1)),
DSM_in_h(n,tt)-DSM_out_h(n,tt)) =e= 0
;
Investment_constraint(s).. invest_limit(s) - sum(n, g_max(s,n) + INVEST(s,n)) =g= 0
;
$ontext
* COMBINED HEAT AND POWER
CHP_constraint_coal.. sum((t,Ger), g(t,'coal',Ger)) =g= 0.14*0.28*sum((t,Ger),q(t,Ger))
;
CHP_constraint_lignite.. sum((t,Ger), g(t,'lignite',Ger)) =g= 0.20*0.28*sum((t,Ger),q(t,Ger))
;
CHP_constraint_biomass.. sum((t,Ger), g(t,'biomass',Ger)) =g= 0.33*0.28*sum((t,Ger),q(t,Ger))
;
CHP_constraint_gas_oil.. sum((t,Ger), g(t,'gas',Ger)) + sum((t,Ger), g(t,'oil',Ger)) =g= 0.27*0.28*sum((t,Ger),q(t,Ger))
;
$offtext
Demand_minimum_Germany.. sum((t,Ger),q(t,Ger))*8760/card(t)*1/1000000 =e= 535
;
*------------------------------------------------------------------------------*
* Solve statement and starting values
Appendix – Source Codes
185
*------------------------------------------------------------------------------*
model projektstudium2011 /all/;
S_LEVEL.fx(st,n,'t1') = 0 ;
S_LEVEL.fx('pump','NO','t1') = 0.99*Scap_max('pump','NO') ;
SOUT.up(st,n,'t1') = S_LEVEL.l(st,n,'t1');
INVEST.l(s,n)=0;
INVEST.fx('Biomass',n)=0;
*SWITCH THE FOLLOWING FIXED VARIABLES ON AND OFF DEPEDNING ON SCENARIO
SIN.fx('battery',n,t)=0;
SIN.fx('acaes',n,t)=0;
SOUT.fx('battery',n,t)=0;
SOUT.fx('acaes',n,t)=0;
DSM_in_l.fx(n,t)=0;
DSM_in_m.fx(n,t)=0;
DSM_in_h.fx(n,t)=0;
INVEST.fx(s,n)=0;
*DAS gibt iwie immer comp errors
option qcp=CPLEX;
projektstudium2011.optfile=1;
solve projektstudium2011 maximizing w using qcp;
*------------------------------------------------------------------------------*
* Write Results *
*------------------------------------------------------------------------------*
parameter p(n,t) Nodalpreis;
p(n,t) = - nodal_balance.m(t,n) *1 ;
Parameter total_generation(t,s);
total_generation(t,s) = sum(n, g.l(t,s,n));
Parameter total_german_generation(t,s);
total_german_generation(t,s) = sum(Ger, g.l(t,s,Ger));
Parameter total_german_demand(t);
total_german_demand(t)=sum(s,total_german_generation(t,s));
Parameter total_german_reference_demand(t);
total_german_reference_demand(t) = sum(Ger, q_ref(t,Ger));
Parameter german_renewable_share Indicated as share of German generation;
german_renewable_share=sum(t,sum(Ger,(g.l(t,'Biomass',Ger)+wind_max(t,Ger)+hydro_max(t,Ger)+pv_max(t,Ger))))/sum(t,
sum(s,total_german_generation(t,s)) + sum(Ger, wind_max(t,Ger)+hydro_max(t,Ger)+pv_max(t,Ger)));
Parameter full_load_hours(s);
full_load_hours(s)= sum((t,n), g.l(t,s,n))/sum(n,(g_max(s,n)+INVEST.l(s,n))*card(t)*revision(s)+0.0001)*8760;
Parameter german_average_export_rate;
german_average_export_rate=sum(t,sum(s,total_german_generation(t,s))+sum(Ger,wind_max(t,Ger)+hydro_max(t,Ger)+pv_max(t,Ger)))/
sum(t,total_german_demand(t)+0.0001);
Parameter average_price(n);
average_price(n)=sum(t,p(n,t))/card(t);
Parameter german_average_price;
german_average_price=sum((t,Ger),p(Ger,t))/(card(t)*card(Ger));
Parameter total_DSM_in(n,t);
total_DSM_in(n,t)=DSM_in_l.l(n,t)+DSM_in_m.l(n,t)+DSM_in_h.l(n,t);
Parameter total_DSM_out(n,t);
total_DSM_out(n,t)=DSM_out_l.l(n,t)+DSM_out_m.l(n,t)+DSM_out_h.l(n,t);
Parameter use_rate_AC_line(l);
use_rate_AC_line(l)=sum(t, abs(AC_LineFlow.l(l,t)))/ (AC_P_max(l)*card(t));
Parameter average_use_rate_AC_line;
average_use_rate_AC_line=sum(l,use_rate_AC_line(l))/card(l);
Appendix – Source Codes
186
Parameter use_rate_DC_line(dcl);
use_rate_DC_line(dcl)$(DC_P_max(dcl))=sum(t, abs(DC_LineFlow.l(dcl,t)))/ (DC_P_max(dcl)*card(t));
Parameter average_use_rate_DC_line;
average_use_rate_DC_line=sum(dcl,use_rate_DC_line(dcl)/card(dcl));
Parameter congestion_shadow_cost_AC;
congestion_shadow_cost_AC=sum((l,t),AC_Constraint_LineFlow_pos.m(l,t))-sum((l,t),AC_Constraint_LineFlow_neg.m(l,t)) ;
Parameter congestion_shadow_cost_DC;
congestion_shadow_cost_DC=sum((dcl,t),DC_Constraint_LineFlow_pos.m(dcl,t))-sum((dcl,t),DC_Constraint_LineFlow_neg.m(dcl,t)) ;
Parameter AC_flow_matrix(n,nn);
AC_flow_matrix(n,nn)=sum((l,t),AC_Incidence(l,n)*AC_Incidence(l,nn)*AC_LineFlow.l(l,t));
Parameter AC_capacity_matrix(n,nn);
AC_capacity_matrix(n,nn)=sum((l),AC_Incidence(l,n)*AC_Incidence(l,nn)*AC_P_max(l)*card(t));
Parameter AC_use_rate_matrix(n,nn);
AC_use_rate_matrix(n,nn)$(AC_capacity_matrix(n,nn))=AC_flow_matrix(n,nn)/AC_capacity_matrix(n,nn);
Parameter DC_flow_matrix(n,nn);
DC_flow_matrix(n,nn)=sum((dcl,t),DC_Incidence(dcl,n)*DC_Incidence(dcl,nn)*DC_LineFlow.l(dcl,t));
Parameter DC_capacity_matrix(n,nn);
DC_capacity_matrix(n,nn)=sum((dcl),DC_Incidence(dcl,n)*DC_Incidence(dcl,nn)*DC_P_max(dcl)*card(t));
Parameter DC_use_rate_matrix(n,nn);
DC_use_rate_matrix(n,nn)$(DC_capacity_matrix(n,nn))=DC_flow_matrix(n,nn)/DC_capacity_matrix(n,nn);
Parameter AC_congestion_cost_matrix(n,nn);
AC_congestion_cost_matrix(n,nn)=sum((l,t),AC_Incidence(l,n)*AC_Incidence(l,nn)*(AC_Constraint_LineFlow_pos.m(l,t)+AC_Constraint_
LineFlow_neg.m(l,t)));
Parameter AC_congestion_hour_matrix(n,nn);
AC_congestion_hour_matrix(n,nn)=sum((l,t),AC_Incidence(l,n)*AC_Incidence(l,nn)*(1$(AC_Constraint_LineFlow_pos.m(l,t)<-
0.1)+(1$(AC_Constraint_LineFlow_neg.m(l,t)<-0.1))));
Parameter DC_congestion_cost_matrix(n,nn);
DC_congestion_cost_matrix(n,nn)=sum((dcl,t),DC_Incidence(dcl,n)*DC_Incidence(dcl,nn)*(DC_Constraint_LineFlow_pos.m(dcl,t)+DC_
Constraint_LineFlow_neg.m(dcl,t)));
Parameter DC_congestion_hour_matrix(n,nn);
DC_congestion_hour_matrix(n,nn)=sum((dcl,t),DC_Incidence(dcl,n)*DC_Incidence(dcl,nn)*(1$(DC_Constraint_LineFlow_pos.m(dcl,t)<-
0.1)+(1$(DC_Constraint_LineFlow_neg.m(dcl,t)<-0.1))));
Parameter flow_matrix(n,nn);
flow_matrix(n,nn)=(DC_flow_matrix(n,nn)+AC_flow_matrix(n,nn))*8760/card(t);
Parameter Yearly_Production_TWh(n);
Yearly_Production_TWh(n)=sum(t,sum(s,g.l(t,s,n))+wind_max(t,n)+hydro_max(t,n)+pv_max(t,n))*8760/card(t)*1/1000000;
Parameter Yearly_Demand_TWh(n);
Yearly_Demand_TWh(n)=sum(t,q.l(t,n))*8760/card(t)*1/1000000;
Display w.l,german_renewable_share,german_average_export_rate,full_load_hours,Yearly_Production_TWh,Yearly_Demand_TWh,
german_average_price,average_price,average_use_rate_AC_line,average_use_rate_DC_line,
DC_use_rate_matrix,AC_use_rate_matrix,AC_congestion_cost_matrix,DC_congestion_cost_matrix,flow_matrix
INVEST.l,invest_cost;
*** Write zeros
g.l(t,s,n)$(not g.l(t,s,n)) = eps;
Q.l(t,n)$(not Q.l(t,n)) = eps;
P(n,t)$(not P(n,t)) = eps;
AC_Constraint_LineFlow_pos.m(l,t)$(not AC_Constraint_LineFlow_pos.m(l,t)) = eps;
AC_Constraint_LineFlow_neg.m(l,t)$(not AC_Constraint_LineFlow_neg.m(l,t)) = eps;
DC_Constraint_LineFlow_pos.m(dcl,t)$(not DC_Constraint_LineFlow_pos.m(dcl,t)) = eps;
DC_Constraint_LineFlow_neg.m(dcl,t)$(not DC_Constraint_LineFlow_neg.m(dcl,t)) = eps;
total_DSM_in(n,t)$(not total_DSM_in(n,t)) = eps;
SIN.l(st,n,t)$(not SIN.l(st,n,t)) = eps;
SOUT.l(st,n,t)$(not SOUT.l(st,n,t)) = eps;
AC_LineFlow.l(l,t)$(not AC_LineFlow.l(l,t)) = eps;
Appendix – Source Codes
187
AC_NetInput.l(t,n)$(not AC_NetInput.l(t,n)) = eps;
DC_NetInput.l(t,n)$(not DC_NetInput.l(t,n)) = eps;
DC_LineFlow.l(dcl,t)$(not DC_LineFlow.l(dcl,t)) = eps;
total_generation(t,s)$(not total_generation(t,s)) = eps;
total_german_generation(t,s)$(not total_german_generation(t,s)) = eps;
pv_max(t,n)$(not pv_max(t,n)) = eps;
hydro_max(t,n)$(not hydro_max(t,n)) = eps;
wind_max(t,n)$(not wind_max(t,n)) = eps;
total_DSM_in(n,t)$(not total_DSM_in(n,t)) = eps;
AC_use_rate_matrix(n,nn)$(not AC_use_rate_matrix(n,nn))=eps;
DC_use_rate_matrix(n,nn)$(not DC_use_rate_matrix(n,nn))=eps;
AC_congestion_cost_matrix(n,nn)$(not AC_congestion_cost_matrix(n,nn))=eps;
DC_congestion_cost_matrix(n,nn)$(not DC_congestion_cost_matrix(n,nn))=eps;
AC_congestion_hour_matrix(n,nn)$(not AC_congestion_hour_matrix(n,nn))=eps;
DC_congestion_hour_matrix(n,nn)$(not DC_congestion_hour_matrix(n,nn))=eps;
flow_matrix(n,nn)$(not flow_matrix(n,nn))=eps;
INVEST.l(s,n)$(not INVEST.l(s,n))=eps;
execute_unload "results-8760h.gdx"
german_renewable_share,german_average_export_rate,full_load_hours,Yearly_Production_TWh,Yearly_Demand_TWh,
german_average_price,average_price,average_use_rate_AC_line,average_use_rate_DC_line,
DC_LineFlow,g,total_generation,total_german_generation,q,P,total_DSM_in,SIN,SOUT,
S_LEVEL,pv_max,hydro_max,wind_max,w,total_DSM_out,use_rate_AC_line,use_rate_DC_line,
AC_use_rate_matrix,DC_use_rate_matrix,congestion_shadow_cost_AC,congestion_shadow_cost_DC,
AC_congestion_cost_matrix,DC_congestion_cost_matrix,AC_congestion_hour_matrix,DC_congestion_hour_matrix,
flow_matrix,INVEST,invest_cost
;
