Levelized cost of electricity: key drivers and valuation methods

RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS AND INVESTMENT VALUATION METHODS ENERGY ECONOMICS ARTICULO DE INVESTIGACION Luis María Abadie, José Manuel Chamorro, Renewables Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 1 / 12 ESTIMACIONES DEL COSTE DE LA ELECTRICIDAD: FACTORES DETERMINANTES Y MÉTODOS DE VALORACIÓN Luis María Abadie1, José Manuel Chamorro2 1Basque Centre for Climate Change (BC3), Sede Building 1, 1st floor, Scientific Campus, University of the Basque Country, 48940 Leioa, Spain. E-mail: lm.aba[email protected]rg 2University of the Basque Country UPV/EHU, Dpt. Financial Economics II, and Institute of Public Economics, Av. Lehendakari Aguirre 83, 48015 Bilbao, Spain. E-mail: [email protected] Received: 24/Apr/2019--Reviewing: 6/Sep/2019--Accepted: 13/Sep/2019—DOI: http://dx.doi.org/10.6036/9223 LEVELIZED COST OF ELECTRICITY: KEY DRIVERS AND VALUATION METHODS ABSTRACT: The aim of this paper is to propose an improvement over traditional approaches to the levelized cost of electricity (LCOE). Basically there are two methods available. The first one considers a yearly timeframe, so it yields a yearly estimate of the LCOE. The second one, instead, keeps the whole lifetime of the facility when computing its LCOE; it thus results in a life-cycle estimate. This said, they share some features, for example, their reliance on the net-present-value methodology and the scant use of market prices. Unfortunately, they also stumble on some common issues, such as the proper way to account for risk. The focus here falls on two power generating technologies from renewable sources, namely wind and solar. Section 1 gives a quick overview of their widespread deployment across the world. Section 2 provides a thorough review of the two approaches to the LCOE at a theoretical level. It also includes some remarks about their underlying assumptions and pinpoints some of their limitations. Section 3 shows numerical estimates of LCOE for different technologies and countries following the two approaches. It also looks at recent trends of LCOE estimates over time. Then Section 4 presents a proposal for an improved LCOE, one that uses public information available on the markets and deals with the discounting of risk more properly. There is also a numerical application to a standard wind park. Section 5 concludes. Key Words: Electricity generation, renewable energies, solar farms, wind farms, investment valuation, futures markets RESUMEN: Este trabajo presenta una alternativa al cálculo tradicional del coste de la electricidad, también conocido como LCOE por sus siglas en inglés (levelized cost of electricity). Dentro de la práctica tradicional se pueden distinguir dos enfoques. El primero de ellos considera un horizonte temporal de un año en sus cálculos (y aporta una estimación anual). El segundo, en cambio, abarca toda la vida de la instalación (y da una estimación de ciclo vital). Estos enfoques tienen varios rasgos comunes. Por ejemplo, ambos se basan en la noción del valor actual neto y hacen un uso limitado de los precios de mercado. En parte por ello, ambos adolecen de limitaciones importantes, como la manera en que tratan y valoran el riesgo. Este artículo se centra principalmente en la estimación del LCOE en el caso particular de las tecnologías eólica y solar. La Sección 1 presenta el desarrollo de las tecnologías renovables a nivel mundial. La Sección 2 analiza los dos enfoques del LCOE a nivel teórico, prestando especial atención a los supuestos subyacentes y las debilidades que de ahí se derivan. La Sección 3 muestra estimaciones numéricas del LCOE para diferentes tecnologías y países en base a los dos métodos. También analiza las tendencias recientes de las estimaciones del LCOE. La Sección 4 presenta una propuesta para el cálculo de un LCOE mejorado. La mejora pasa por hacer más uso de la información pública disponible en los mercados y abordar el descuento del riesgo de manera más adecuada. La propuesta se ilustra por medio de una aplicación a un parque eólico típico. Las conclusiones se encuentran en la Sección 5. Palabras Clave: Generación de electricidad, energías renovables, parques eólicos, parques solares, valoración de inversiones, mercados de futuros 1.- INTRODUCTION During the last fifteen years, renewable energy has played an ever more prominent role. In the particular case of electricity, this fact can be observed both in terms of installed capacity and generation levels [1]. Several factors have contributed to the broader deployment of these technologies: growth in world electricity demand [2], concerns about security of supply and climate change, energy prices, technological progress, public support… RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS AND INVESTMENT VALUATION METHODS ENERGY ECONOMICS ARTICULO DE INVESTIGACION Luis María Abadie, José Manuel Chamorro, Renewables Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 2 / 12 Fig. 1. Renewable electricity generation (percentage share of world total). Source: Own elaboration on data from International Energy Agency [2]. Figure 1 shows the percentage of renewable electricity delivered by the world generation park. Its relative share has risen from 18% in 2003 to 24.4% in 2016, making it easier to meet the growing energy demand. Only since 2013 the share of coal-based generation started to decline significantly (from 41.1% in that year to 38.3% in 2016). It will take time for renewable electricity to reach a higher market share of total generation than 24.4%. Yet its development will not come without its own set of problems, e.g. the intermittent, unpredictable nature of renewable sources, in addition to their variations over space and time (e.g. seasonal behavior). These features, coupled with insufficient storage capacity, can give rise to power shortages at times of peak demand [3] if renewable generation falters. RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS AND INVESTMENT VALUATION METHODS ENERGY ECONOMICS ARTICULO DE INVESTIGACION Luis María Abadie, José Manuel Chamorro, Renewables Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 3 / 12 Fig. 2. Distribution of world renewable power generation in 2016. Source: Own elaboration on data from International Energy Agency [2]. Figure 2 displays the world mix of renewable generation in 2016. Hydropower generation provided 4,170,035 GWh, about 68% of total renewable generation. Wind generation came second, with 957,694 GWh, or 15.6%. Solar (both photovoltaic, PV, and thermal) accounted for 5.5% of total. Other technologies like liquid biofuels, industrial waste, and tide, wave and ocean fell still further behind in the world electricity generation park. At the world level, the installed capacities of both wind and solar PV are growing over time, but their capacity factor is relatively low (it measures a plant’s actual power generation compared to the maximum amount it could generate in a given period of time without any downtime); in the case of wind, it can be about 30% depending on the plant’s location. In 2017 the generation capacity of offshore wind was 18.8 GW, a mere 3.5% of total wind power capacity; nonetheless it also displays an acceleration. This is due to some positive characteristics, for example stronger and less intermittent winds at sea, which in turn enables larger turbines. Yet installation costs (depending on seafloor depth and site characteristics), the need of grid infrastructure, and maintenance costs are major drawbacks. The chief flaw of solar is that it works only when the sun shines. In this paper the traditional methods for estimating the levelized cost of electricity (LCOE) are analyzed and an alternative is proposed, which is based on electricity futures market quotes (i.e. observed market prices for future delivery of electricity). The LCOE is an estimate of the average cost of producing electricity with a particular technology. It can be useful when making investment decisions (especially in regulated, vertically integrated power systems). Section 2 provides a thorough review of the two approaches to the LCOE at a theoretical level. It also includes some remarks about their underlying assumptions and pinpoints some of their limitations. Section 3 shows numerical estimates of LCOE for different technologies and countries following the two approaches. It also looks at recent trends of LCOE estimates over time. Then Section 4 presents a proposal for an improved LCOE, one that uses public information available on the markets and deals with the discounting of risk more properly. There is also a numerical application to a standard wind park. Section 5 concludes. RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS AND INVESTMENT VALUATION METHODS ENERGY ECONOMICS ARTICULO DE INVESTIGACION Luis María Abadie, José Manuel Chamorro, Renewables Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 4 / 12 2. APPROACHES TO THE LEVELIZED COST OF ELECTRICITY (LCOE) There are a number of alternative power generation technologies. Consequently, power companies and/or policy makers have looked for metrics that allow rank those technologies according to their generation cost. The metrics of choice has typically been the so-called levelized cost of electricity (LCOE). It was first proposed in 1984 by the International Atomic Energy Agency [4] to compare costs across generating units. The LCOE aims to measure the unit cost of the power generated at a given facility in a particular system. The concept looks rather simple in principle, yet different institutions define it in a different way. Hence one must be careful to avoid the ‘easy to use, easy to confuse/misuse’ trap. Besides, one must ensure that it is measured uniformly across the technologies being compared. For this purpose, two different criteria to classify them are adopted, namely costs base and time dimension. At one level, the calculation can be framed either in a single year of operation (which gives rise to an annual cost) or the whole life of the project (a lifetime cost). On the other hand, the calculation can well take into account only the costs incurred by the facility’s owner, in which case a narrow-based estimate of the LCOE arises; nonetheless, any power generation asset is a mere part of a broader system, and the project’s impact at the system level too could be considered when computing the LCOE. An even broader estimate would include the costs to society of whatever ‘external effects’ emanate from power generation (e.g. greenhouse gas emissions, impacts on public health). In this paper the issue is addressed from the owner’s viewpoint using market prices of futures contracts on electricity. 2.1.- SINGLE-PERIOD PLANT-LEVEL LCOE First the single-period plant-level calculation of LCOE is reviewed, which is a standard often used in the electrical industry. The US National Renewable Energy Laboratory (NREL) [5] defines the ‘simple LCOE (sLCOE)’, which is measured in $/kWh, and allows the comparison of the combination of capital costs, operations and maintenance, performance, and fuel costs: 𝑠𝐿𝐶𝑂𝐸=𝑜𝑣𝑒𝑟𝑛𝑖𝑔ℎ𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑐𝑜𝑠𝑡∗𝐶𝑅𝐹+𝐹𝑂𝑀 8760∗𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟 + 𝑓𝑢𝑒𝑙 𝑐𝑜𝑠𝑡∗ ℎ𝑒𝑎𝑡 𝑟𝑎𝑡𝑒+ 𝑉𝑂𝑀. (1) Overnight Capital Cost is measured in dollars per installed kilowatt ($/kW). CRF is the capital recovery factor. It measures the ratio of a constant annuity to the present value of receiving that annuity for a given length of time [6]; the financial formula for computing it with an interest rate i over the next t years is: 𝐶𝑅𝐹=1 1 𝑖−1 𝑖(1+𝑖)𝑡=𝑖(1+𝑖)𝑡 (1+𝑖)𝑡−1 (2) Fixed Operation and Maintenance (FOM) costs are in dollars per kilowatt-year ($/kW-yr). Variable Operation and Maintenance (VOM) costs are in dollars per kilowatt-hour ($/kWh). In the denominator, 8760 = 365 × 24 is the number of hours in a year. The Capacity Factor is the portion of a year that the power plant is generating power (0≤CF≤1). Equation (1) is a standard one for LCOE. It states the equality between the present value of income (or revenue) and the present value of costs when calculating the LCOE. However, as NREL points out, this metrics does not include financing issues, discount issues, future replacement or degradation costs, etc. 2.2.- MULTI-PERIOD PLANT-LEVEL LCOE Unlike the U.S. NREL, the International Energy Agency [7] follows a levelized average lifetime cost approach; in common with the former, it uses the discounted cash flow (DCF) valuation method. For this purpose, it adopts three discount rates (3%, 7% and 10%). Transmission and distribution costs are left aside. RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS AND INVESTMENT VALUATION METHODS ENERGY ECONOMICS ARTICULO DE INVESTIGACION Luis María Abadie, José Manuel Chamorro, Renewables Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 5 / 12 The results include a carbon cost of US $30/tonne; beyond this, LCOE calculation does not capture other externalities or systemic costs. The foundation of LCOE computation is the equivalence of the present value of the sum of discounted revenues and the present value of the sum of discounted costs: ∑𝑃𝑀𝑊ℎ×𝑀𝑊ℎ (1+𝑟)𝑡 𝑛 𝑡=1 =∑𝐶𝑡+𝑂&𝑀𝑡+𝐹𝑢𝑒𝑙𝑡+𝐶𝑂2𝑡+𝐷𝑡 (1+𝑟)𝑡 𝑛 𝑡=1 . (3) Here, PMWh denotes the constant lifetime remuneration to the supplier for electricity; MWh is the amount of electricity produced (in MWh), assumed constant; (1+r)-t is the discount factor for year t (reflecting payments to capital); Ct stands for total capital construction costs in year t; CO2t reflects carbon costs in year t; and Dt captures decommissioning and waste management costs in year t; O&Mt are the operation and maintenance costs in year t; Fuelt is the fuel price in year t. All of the variables are real, i.e. net of inflation. Discounting takes place on a yearly basis (the discount rate must be real for consistency). Since PMWh is constant over time it can be brought out of the summation; this yields: 𝐿𝐶𝑂𝐸≡𝑃𝑀𝑊ℎ=∑[(𝐶𝑡+𝑂&𝑀𝑡+𝐹𝑢𝑒𝑙𝑡+𝐶𝑂2𝑡+𝐷𝑡)×(1+𝑟)−𝑡] 𝑛 𝑡=1 ∑𝑀𝑊ℎ×(1+𝑟)−𝑡 𝑛 𝑡=1 . (4) This is the formula used by IEA to calculate the levelized cost of producing baseload electricity at the plant level. On the other hand, the California Energy Commission [8] has developed its Cost of Generation Model (CGM). It is an Excel spreadsheet model that calculates LCOE for utility-scale electric generating technologies. These levelized costs are meant to be the total costs of building and operating a power plant over the economic life converted to equal annual payments in both energy (dollars per megawatt-hour) and capacity (dollars per kilowatt-year) terms. The CGM first calculates the costs for a technology on an annual basis, finds the present value of each yearly cost, sums the present values of the cost components, and then calculates the levelized cost thereof, i.e. the annual payment (under the interest, or discount, rate r) required to pay off that present value over the specified period T. The formula is as follows (the capital recovery factor shows up here again): 𝐿𝐶𝑂𝐸=∑𝐶𝑜𝑠𝑡𝑡 (1+𝑟)𝑡 𝑇 𝑡=1 𝑟(1+𝑟)𝑡 (1+𝑟)𝑡−1 (5) The results are presented as a cost per unit of generation over the period considered (in $/MWh or cents/kWh). These calculations are done by dividing the costs by the sum of all the expected generation over the time horizon being analyzed. LCOE estimates account for the total costs to generating power. Total costs are the sum of fixed costs (i.e. independent of the number of operating hours) and variable costs. In the end, total LCOE estimates are calculated as a function of who the developer is: merchant, investor-owned utility, or publicly owned utility (financing costs and corporate taxes change depending on the type of developer). Now, the UK Department for Business, Energy and Industrial Strategy [9] defines the LCOE as “the discounted lifetime cost of ownership and use of a generation asset, converted into an equivalent unit of cost of generation in £/MWh”: 𝐿𝐶𝑂𝐸= 𝑃𝑉(𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡𝑠) 𝑃𝑉(𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛) (6) RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS AND INVESTMENT VALUATION METHODS ENERGY ECONOMICS ARTICULO DE INVESTIGACION Luis María Abadie, José Manuel Chamorro, Renewables Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 6 / 12 Total costs are the sum of ‘Capex costs’ and ‘Opex costs’. Capital expenditure costs comprise: predevelopment costs, construction costs, and infrastructure cost (the last two adjusted over time for learning). Operation expenditure costs comprise: fixed opex (adjusted for learning), variable opex, insurance, connection costs, carbon transport and storage costs, decommissioning fund costs, heat revenues (for combined heat-andpower plants), fuel prices, and carbon costs. Regarding the denominator, expected generation data take into account: capacity of plant, expected availability, expected efficiency, expected load factor (all assumed baseload). Both total costs and electricity generation are expressed in net present value terms (i.e. future costs and outputs are discounted at a rate r when compared to costs and outputs today). Following Aldersey-Williams and Rubert [10], in finance the internal rate of return (IRR) on an investment project is the discount rate that makes its Net Present Value (NPV) equal to zero: 𝑁𝑃𝑉=𝑃𝑉(𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠)−𝑃𝑉 (𝑐𝑜𝑠𝑡𝑠)=0→𝑃𝑉(𝑐𝑜𝑠𝑡𝑠)=𝑃𝑉(𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠) (7) Hence, when r = IRR the LCOE can be equivalently defined as: 𝐿𝐶𝑂𝐸=𝑃𝑉(𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠) 𝑃𝑉(𝑒𝑛𝑒𝑟𝑔𝑦) =𝑃𝑉(𝑒𝑛𝑒𝑟𝑔𝑦×𝑝𝑟𝑖𝑐𝑒) 𝑃𝑉(𝑒𝑛𝑒𝑟𝑔𝑦) . (8) Thus, the LCOE can naturally be interpreted as the electricity price required for the project to have a zero NPV, or, in other words, for the revenues from the project to provide a return (IRR) that exactly matches the discount rate (r). This same reasoning underlies the calculation of LCOE according to NREL [11]. Analytically: 𝐿𝐶𝑂𝐸×∑𝐸𝑡 (1+𝑟)𝑡 𝑛 𝑡=1 =∑𝐶𝑡 (1+𝑟)𝑡 𝑛 𝑡=1 . (9) In any case, whenever the costs considered are real (i.e. as seen from time 0, in constant currency units, or unadjusted for future inflation) the LCOE measures the minimum constant real price of electricity for the project to make sense economically; needless to say, both IRR and r are real too for consistency. By the same token, using nominal costs (i.e. in current dollars, or adjusted for inflation) along with a nominal discount rate yields the average nominal price over the project’s lifetime that provides the required nominal return. Henceforth the focus is on electricity from two renewable sources, namely solar and wind. Thus, in Section 4 only capital expenses (Ct) and fixed operating costs (Ot) are considered in the analysis of LCOE (instead, variable operating costs, carbon costs, and decommissioning and waste management costs are left aside). Specifically, Equation (10) is used, which is a simplified version of the one used in [7]: 𝐿𝐶𝑂𝐸=∑𝐶𝑡+𝑂𝑡 (1+𝑟)𝑡 𝑛 𝑡=1 ∑𝐸𝑡 (1+𝑟)𝑡 𝑛 𝑡=1 . (10) 2.3.- REMARKS ON THE UNDERLYING ASSUMPTIONS The above formulas for LCOE raise two importants problems at least. The first one involves the behavior of costs and prices over time. The second one has to do with choice of the appropriate rate to discount future, uncertain cash flows back to the present when making investment decisions. a) Cost inflation is not much of a problem for the LCOE formula if inflation is constant and applies equally to every cost factor. In this case it is necessary to turn the real discount rate into a nominal one by adjusting the former for inflation: (1 + nominal rate) = (1 + real rate)×(1 + inflation rate). The LCOE formula will then yield a nominal electricity price. Yet the earlier assumption is an stringent one. On the other hand, inflation accumulates over time. This implies that power technologies with the bulk RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS AND INVESTMENT VALUATION METHODS ENERGY ECONOMICS ARTICULO DE INVESTIGACION Luis María Abadie, José Manuel Chamorro, Renewables Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 7 / 12 of their costs earlier in time are less affected by inflation than those in which most of the expenditure will take place further into the future. Thus, all else equal, renewable stations can show a lower LCOE than thermal ones (owing to the greater importance of fuel and operation costs for the latter). Besides, the electricity price is not constant. Standard features are seasonality, mean reversion, jumps, among others. The electricity price can also depend on the country/market at hand. Further, the electricity price (or revenues) and generation costs can well be affected by different inflation rates. b) The discount rate is controversial too. According to finance theory, each future cash flow must be dicounted at a rate commensurate with its risk. Therefore, a single discount rate (for every outflow of cash and constant through the plant’s lifetime) is hardly adequate. This applies irrespective of whether the rate is ‘subjective’ (based on management’s expert judgement) or ‘objective’ (like the weighted average cost of the capital invested in the plant). Anyway, a higher perceived risk (and ensuing discount rate) in some power technologies will translate into a higher LCOE for those technologies. In this regard, IEA [7] uses three discount rates across all technologies: 3% (corresponding to the social cost of capital), 7% (market rate in deregulated o restructured electricity markets), and 10% (investment in a high-risk environment). BEIS [9] focuses on LCOE estimates using a hurdle rate of 10% along with estimates at 7% and 3.5% hurdle rates for comparative purposes with international publications. CEC [8] defines the discount rate as the after-tax wighted average cost of capital (WACC) and uses a 6.17% real rate in its mid case scenario (changing to 10.57% and 4.28% in the high case and low case, respectively). These rates can be controversial and significantly affect the valuation process. Below a methodology to address some of these problems is proposed. It is possible to sidestep this issue to some extent by using observed prices in futures markets on commodities. These prices can be discounted at the risk-free rate (because of the hedging potential that these markets offer to their players). In the euro area the German debt rate can be adopted for this purpose. c) Another problem is that renewable technologies do not operate regularly through time. In addition to uncertain, they are intermittent and display seasonal behaviors (over different time frames). Thus, the power price that they get can well be different from the average market price. d) Energy and environmental policy can also pose a problem to using the LCOE formula. In principle, if there is a government push in favor of renewable generation expansion (e.g. feed-in tariffs, production tax credits, investment tax credits), one can easily add its present value to Equation (10); if public support measures are certain, the risk-free rate must be used to discount them. But policy measures cannot always be taken for granted over long time horizons as required by energy projects. This said, all of the above models account for technological development of generating technologies through their respective learning curves. The learning factor typically results in decreasing capital costs; the effect depends on the type of technology and the date when the plant enters service. For example, from 2022 to 2040 NREL [5] projects large LCOE reductions for onshore wind (9%), offshore wind (16%), and solar PV (16%). Similarly, IEA [7] assumes a learning rate of 7% for onshore wind; for offshore wind, cost reductions of about 40% could be expected in the cost of electricity generation by 2030, though uncertainties remain. Similarly, CEC [8] and BEIS [9] use technology-specific learning rates. RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS AND INVESTMENT VALUATION METHODS ENERGY ECONOMICS ARTICULO DE INVESTIGACION Luis María Abadie, José Manuel Chamorro, Renewables Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 8 / 12 3. EMPIRICAL RESULTS This section presents numerical LCOE estimates according to the two methodologies explained above and analyzes their recent trends. 3.1.- SINGLE-PERIOD PLANT-LEVEL LCOE The analysis in NREL [5] draws on three sources, namely the U.S. Energy Information Administration (EIA) [7], the National Renewable Energy Laboratory (NREL) [11] or National Energy Technology Laboratory (NETL) [12], and Lazard [13]. Then NREL computes U.S. estimates for LCOEs for selected generation technologies using cost and heat rate data ranges from these three sources (in the case of non-dispatchable technologies the heat rate is zero). Operating characteristics, such as fuel costs (zero for non-dispatchable technologies) and capacity factors, differ too for each technology; the estimates for LCOE consider the lowest and highest assumptions reported across the three primary sources. On top of this, NREL applies the same financial characteristics across all technologies; in this regard, the minimum and maximum cost of capital from these sources are used as inputs to the LCOE. The resulting LCOE ranges for wind and solar are shown in Table 1; these values do not include tax credits. They reflect wide variation of resource quality across the U.S. Table 1. Current U.S. LCOE ranges of wind and solar technologies (2013$/MWh). Source: NREL [5]. EIA NREL Lazard Technology Low High Low High Low High Wind, onshore 37.09 117.76 35.36 88.87 26.30 81.86 Wind, offshore 117.22 279.25 114.75 241.09 81.27 218.10 Solar PV, utility-scale 80.00 430.52 54.94 171.03 46.06 132.61 Solar CSP 140.20 271.89 82.61 207.35 104.44 249.46 3.2.- MULTI-PERIOD PLANT-LEVEL LCOE The analysis within IEA [7] draws on data for 181 power plants in 22 countries (19 OECD countries plus Brazil, China and South Africa). All cost figures are given in 2013 US dollars. The assumed commissioning date is 2020. Table 2 displays the LCOE estimates for onshore wind, solar thermal, and the three categories of solar PV in the study (residential, commercial, and large, ground-mounted) in the case of Spain. Table 2. Levelized costs of electricity for generating plants in Spain (2013$/MWh). Source: IEA [7]. Technology Capital costs O&M costs LCOE 3% 7% 10% 3%-7%-10% 3% 7% 10% Wind, onshore 53.65 74.32 92.09 27.86 81.51 102.19 119.96 Solar PV, residential rooftop 64.99 100.43 131.11 35.61 100.60 136.02 166.70 Solar PV, commercial rooftop 53.61 82.85 108.16 49.35 102.97 132.01 157.21 Solar PV, large, ground-mounted 41.57 64.35 84.12 45.75 87.33 109.92 129.57 Solar thermal (CSP) no storage 175.93 260.88 335.14 87.46 263.39 348.35 422.60 3.3.- EVOLUTION OF LCOE ESTIMATES OVER TIME As already mentioned in Section 2.2, the focus is on electricity from solar and wind energies. The evolution of the LCOE in the U.S. has been analyzed by Lazard [13]. It shows a consistent reduction over time, but at an ever slower pace. This suggests a proximity to an equilibrium. The mean values for 2017 are 45 US$/MWh for RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS AND INVESTMENT VALUATION METHODS ENERGY ECONOMICS ARTICULO DE INVESTIGACION Luis María Abadie, José Manuel Chamorro, Renewables Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 9 / 12 onshore wind and 50 US$/MWh for solar at utility scale. The estimate for offshore wind in the same year is 113 US$/MWh. The IEA [7] shows a number of LCOE estimates for each country and technology in the sample. These calculations depend on the values of irradiation and latitude, but this information, though used in the calculations, is not supplied by IEA [7].In the Spanish case the LCOE for solar PV (large, ground-mounted) is 87.33 US$/MWh, or 65.50 EUR/MWh using the exchange rate in the report [7]. For onshore wind it is 81.51 US$/MWh, or 61.13 EUR/MWh. Now, these LCOEs can be compared with the price of electricity for future delivery (i.e. the price in the futures market for electricity). The LCOEs are higher than the futures prices. For example, Table 3 shows the annual futures quotes on 10/31/2018 for electricity to be delivered in Spain. An open question is if an increasing renewable generation can lead to a decline in electricity prices. Table 3. Futures electricity prices (EUR/MWh) for Spain on 10/31/2018. Source: www.omip.pt. Contract Name Reference Price FTB YR-19 60.30 FTB YR-20 53.60 FTB YR-21 50.60 FTB YR-22 48.30 FTB YR-23 46.70 In the case of offshore wind, the IEA data [7] also show an important dispersion in LCOE.s This technology shows a mean capacity factor of 38.72% (it is 34.66 for onshore wind and 16.66 for solar PV large, groundmounted). Yet its average LCOE is 136.39 US$/MWh, well above the futures prices on Table 3 4.- A PROPOSAL FOR AN ENHANCED MULTI-PERIOD LCOE 4.1.- PROPOSED METHODOLOGY Next, an alternative valuation methodology to those in Section 2.2 is proposed. The starting point is the standard NPV formula, i.e. the difference between the present value of cash inflows and the present value of cash outflows, but with specific discount rates that apply to each component: 𝑁𝑃𝑉=∑ 𝑝𝑡×𝐸𝑡 (1+𝑟1)𝑡− ∑ [𝐶𝑡 (1+𝑟2)𝑡+𝑂𝑡 (1+𝑟3)𝑡] (11) Equation (11) shows the NPV in discrete time. This is similar to Equation (3), but in this case the discount rate and the future electricity future are obtained from market information (they are not subjective values). Note that when futures market prices are used, revenues can be discounted at the riskless rate. Note also that, consistent with financial theory, the costs known with certainty can be discounted too at the riskfree rate. Alternatively Equation (12) in continuous time can be used: 𝑁𝑃𝑉=∫ 𝑝𝑡×𝐸𝑡×𝑒−𝑟1 ∗𝑑𝑡−∫ [𝐶𝑡×𝑒−𝑟2 ∗+𝑂𝑡×𝑒−𝑟3 ∗] (12) where the discount rates 𝑟1,𝑟2,𝑟3 correspond to the different markets. They are slightly different under continuous or discrete compounding. Castillo-Calzadilla et al. [14] assess a solar PV facility in a standalone services building in Spain. Here an onshore wind farm in Spain with the following characteristics is considered (values for (a)-(g) are taken