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IAEE Energy Forum Bergen Special 2016
Optimal Level of Supply Security in the Power Sector
with Growing Shares of Fluctuating Renewable Energy
By Aaron Praktiknjo and Lars Dittmar
In many countries a rapid expansion of intermittent renewable power generation has oc-
curred in recent years. Simultaneously, conventional power plants such as nuclear generators
are being phased-out of the energy system. Especially the German power system is character-
ized by these two developments.
In this context, appropriate methods for the assessment of the security of electricity supply
are more important than ever. In general, there are deterministic and probabilistic methods
to assess security of supply or generation adequacy respectively. In the past, the four German
transmission system operators (TSOs) have relied on a deterministic approach. However, while
there is a continuous debate about methodological details, it is widely acknowledged that
probabilistic approaches are more appropriate that deterministic ones especially in light of
the stochastic nature of intermittent renewables. We share this opinion and, therefore, revert
to probabilistic methods.
While policy makers in Germany circumvent the question of appropriate level supply security
by not defining it explicitly, we argue that rational policies must derive the level security from
economic considerations. Ideally, investments in supply security should only be made if the
resulting benefits outweigh the costs. With our research, we want to contribute to the economic
assessment of security of supply and thereby provide a rational guideline on how to derive an
economic efficient level of security.
SUPPLY SECURITY OF CONVENTIONAL GENERATORS
In order to assess the contribution of conventional plants to generation adequacy, we use the so-called
methodology of recursive convolution. The basic idea behind it is that single production units are allowed
to only be in two possible states: available and unavailable. With this, the state ‘non-available’ of a given
plant occurs with a specific probability of (p) while the state ‘available’ occurs with the complementary
probability of (1-p). We differentiate unavailability in scheduled (maintenances) and unscheduled
unavailability and formulate an econometric model to account for observed seasonalities, see figure 1.
Using the information of installed capacities and the probabilities of occurrences on availability and
unavailability, the result of our recursive convolution will be a cumulated distribution function of the
available generation capacity of the entire portfolio of conventional power plants.
CONTRIBUTION TO SUPPLY SECURITY OF RENEWABLE GENERATORS
The distribution of available capacity of renewable is rather continuous (ranging between 0 and
100%) than discrete binary. We therefore use aggregate data of the feed-in from renewable power
generators. We rely on hourly time series pub-
lished by the German TSOs for the feed-in of
wind and photovoltaic plants. The times series
for wind ranges from 2006 to 2014, whereas
the data for photovoltaic range from 2011 to
2014. In order to increase representativity of
our time series we employ two supplementary
approaches. First, we formulate a polynomial
regression model of order 3 using weather
data (e.g. wind speed) from over 60 stations as
independent variables and the TSO time series
for the period from 2006 to 2014 as dependent
variable. The regression yields a high goodness
of fit with exceeding 95% when pitted against
the actual data on feed-in from the TSOs from
2006-2014. Using this model, we extend our
data on feed-in to a period of over 21 years
Aaron Praktiknjo is with
RWTH Aachen University,
Institute for Future
Energy Consumer Needs
and Behavior (FCN),
Mathieustr. 10, 52074
Aachen, Germany, E-Mail:
aaron.praktiknjo@
rwth-aachen.de,
corresponding author.
Lars Dittmar is with
TU Berlin, Department
of Energy Engineering,
Chair of Energy
Systems, Einsteinufer
25 (TA 8), 10587 Berlin,
Germany, E-Mail: lars.
0
20
40
60
I II III IV I II III IV I II III IV I II III IV I II
2011 2012 2013 2014 2015
Uranium Lignite
Coal Natural Gas
0
5
10
15
20
I II III IV I II III IV I II III IV I II III IV I II
2011 2012 2013 2014 2015
Uranium Lignite
Coal Natural gas
Discrete binomial distribution
of available capacity
0 % capacity
100 % capacity
Scheduled unavailabilities
Unscheduled unavailabilities
Figure 1. Unscheduled and scheduled unavailabilities of generators
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International Association for Energy EconomicsBergen Special 2016
(from 1994 to 2004), see figure 2. Second, we apply the so-called sliding window technique to increase
representativeness of the data, including also feed-ins at times to proximity of the examination time.
Given the information presented above, we can express the available capacity of renewable genera-
tors in dependence of the probability of occurrence and time of the year. Therefore, we also receive a
cumulated distribution function.
THE OPTIMAL LEVEL OF SUPPLY SECURITY
From an economic and welfare perspective, the optimal level of supply security is achieved if marginal
cost for an increase in supply security is equal to marginal utility for an increase in supply security.
Ideally, investments in supply security should only be made if the resulting benefits from an increase
in supply security amounts at least to the investment outlay.
Supply security can be increased by installing
additional generation capacities. As we know,
the identification of the economically most viable
option for the choice of generation technology
depends among others on the annual full load
hours of operation. In the case of Germany with
its already relatively high level of supply security,
the full load hours would be very small. Thus, the
cheapest option would be to invest in gas turbines.
The marginal cost of supply security would be
almost equal to the capital cost of an additional
gas turbine.
As for the utility of increased supply security,
we can interpret it as the avoided cost of reliability
issues. In the electricity business, these avoided
costs correspond to the so-called value of lost load
(VOLL). In a previous publication, we showed that
the VOLL is dependent on the duration of an interruption in supply (VOLL increases significantly with
shorter durations of interruption) and estimated it for Germany.
Given the data on marginal cost and marginal utility for an increase in supply security, it becomes
possible to estimate the welfare optimal level of supply security.
RESULTS
We convolve cumulated the distribution functions of conventional and renewable generators using
Monte Carlo simulation techniques to obtain a cumulated probability density function for our total gen-
eration portfolio for every hour of the year. Figure 3 shows the result for the hour of the German peak
load in 2014 (79.1 GW on December 3, 2014 between 5 and 6 p.m.). Here, the probability of a deficit in
supply compared to the demand for the hour of the peak load alone is lower than 10-12.
After having calculated the secured capacity of the total portfolio of power plants, we evaluate the
contribution of the different types of generators to total supply
security. To do so, we estimate the so-called capacity credit. The
capacity credit represents the contribution of a group of generators
(at a predefined level of supply security) to the secured supply of
our total portfolio and can be interpreted as a kind of performance
indicator for our group of generators. Figure 4 schematically depicts
the methodology for the calculation of the capacity credit and shows
the result for the German peak load hour in 2014.
With our results, we can estimate that phasing-out nuclear power
plants, ceteris paribus, obviously leads to a decrease in supply se-
curity. For the peak load hour alone, the level of supply security
would drop from almost 100% to a level of about 95%.
Carrying out the assessment for the welfare optimal level of
supply security, our results indicate that the optimal level of supply
security over a year would be equal to about 99.99994%. Translated
to the level of supply security of the peak load hour, this would also amount to approximately 95%.
0
20
40
60
80
100
94 96 98 00 02 0 4 06 08 10 12 14
Data from over 60 weather
stations 1994-2014
Continuous distribution
of available capacity
Backcast 1994-2005 TSO 2006-2014
Wind feed-in
Hourly wind feed-in data for 21 years
0
20
40
60
80
100
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
Data from TSOs from
2006-2014
100 % capacity
0 % capacity
Figure 2. Availabilities of renewable generators
Figure 3. Cumulated probability density function for the
entire generation portfolio
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IAEE Energy Forum Bergen Special 2016
DISCUSSION AND CONCLUSION
Our results indicate that the overall level
of supply security in Germany in 2014 is
extremely high with a probability of a deficit
for the peak load hour alone of almost 0%
(below 10-12). Our results confirm that the
contribution of intermittent renewable ca-
pacities is much less than the contribution
of conventional generation capacities. For
the peak load hour, wind power contributes
to supply security only by about 7.2% of
the installed capacity, while conventional
capacities can contribute by about 95% of
the installed capacity. In other words, 1GW of
conventional power generation (e.g. nuclear
power) has the same contribution to system
adequacy as 13 to 14GW of installed wind power. At the peak load, photovoltaic generation does not
contribute to security of supply at all. This is caused by the fact that the peak load in Germany regularly
occurs is in the evening hours of the winter.
From our analysis we can conclude that the phase-out of nuclear power will ultimately lead to a
decrease in the total level of supply security (from 100% to 95% for the peak load hour) while the
installation of new renewable generators alone will hardly compensate for it. However, we have shown
that the theoretically optimal level of supply security is equal to 99.99994% in a year, which is equal to
approximately 95% for the peak load hour. Therefore, from an economic perspective, the decrease in
supply security resulting from the phase-out of nuclear power plants would still be at a tolerable level.
With this, new investments to re-increase the level of national supply security would be unnecessary
and a waste of funds. But in the end, it is the German society that will be the one to decide on the final
level of supply security, economic welfare or not.
Fuel type Capacity credit
in percent
Nuclear 98.9
Lignite 94.9
Coal 94.7
Natural Gas 96.2
Wind 7.2
Photovoltaic 0.0
Level of supply security
Secured supply in GW
Capacity credit for the
group of generators
Secured capacity
of all installed generators
except those in the group
Secured capacity
of all installed generators
including those in the group
Capacity credit for the time of
the annual peak load
Figure 4. Calculating the capacity credit (at a level of 95%)
Bergen Overview (continued) (Social Events)
On Tuesday evening the City of Bergen gave a reception in the magnificent Håkonshallen, King Håkon’s Hall, represented
by the Mayor of Bergen, Marte Mjøs Persen. Håkonshallen is a large medieval stone hall, built from 1247 to 1261 and inau-
gurated for the wedding of a King Magnus Håkonsson in 1261, with 2000 guests attending. The Mayor gave a brief account
of the history of the hall and then dwelt upon the importance of energy for the economic development of Bergen and the
region around it and the role of Bergen as the “energy capital” of Norway.
Bergen Conference Wrap-Up
All in all, the conference seemed to work well and many positive comments and feedback were received from conference
participants. The conference facilities at NHH functioned quite satisfactorily and NHH was most generous and supportive
in hosting the conference. Much praise was also received for the quality of the food served during the conference and for
the service.
Last but not least: A sincere word of thanks and appreciation to the conference sponsors for their financial support,
which made it possible to organize a qualitatively better conference than otherwise.
The Bergen Conference Team--Their hard work was instrumental to the conference’s success
