Quantifying the Combined Impact of Wind and Solar Power Penetration on the Optimal Generation Mix and Thermal Power Plant Cycling

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1 Quantifying the Combined Impact of Wind and Solar Power Penetration on the Optimal Generation Mix and Thermal Power Plant Cycling Fernando de Sisternes * Massachusetts Institute of Technology November 24 th, 2011 Abstract Mandated levels of wind and solar power penetration are substantially changing the operation of modern power systems. The variability introduced by wind and solar power affects the optimal mix of generation capacity, because greater operational flexibility from thermal generators is required to balance changes in net load. Capacity expansion planning models have traditionally neglected operational constraints (ramping constraints, minimum stable output level of the units, etc) and the additional costs incurred from an intensive cycling regime of the units. Consequently, utility companies and regulators need new tools that account for these effects to assist them in their respective decision-making processes. Extended unit commitment models unit commitment models incorporating extra variables that account for capacity building decisions allow us to capture the operational details of the power system while simultaneously designing the optimal generation mix. This paper presents an extended unit commitment model, assesses its performance with a realistic-sized system (ERCOT), and applies it to quantify the impact of different penetration levels of wind and solar power on the optimal generation mix and the cycling behavior of intermediate units. We provide wall times for different configurations of the model: level of renewable energy penetration and reserves, and wind curtailment possibilities. We demonstrate that greater amounts of wind and solar generation significantly increase the number of cycles of thermal units, which can have a significant impact on cost. I. INTRODUCTION The large-scale penetration of renewable energies wind power in particular experienced by many electricity systems has dramatically increased the variability and the uncertainty of the net load. This effect has radically changed the way electric systems are operated and has intensified the need for an alternative generation mix with more flexibility (Milligan, 2011; MIT, 2010:43). At a system level, operational flexibility has been defined as the ability to accommodate a variable and uncertain * Engineering Systems Division, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, ferds@mit.edu 1

2 net load (Denholm et al., 2010:27) and as the ability to increase the ramping capability and decrease the minimum load on conventional generators (Denholm and Margolis, 2007:4424). The International Energy Agency differentiates four potential sources of flexibility, namely: dispatchable power plants, demand side management and response, energy storage facilities and interconnection with adjacent markets (IEA, 2011). However, due to the early stage of development of some of these technologies and/or physical limitations in the system, energy storage facilities, demand side management instruments and interconnection capacity with other systems are not yet accessible to every electricity system. Accordingly, this paper will determine the optimal generation mix for different levels of penetration of renewables, assuming that the system s operational flexibility is entirely provided by the generation capacity. A generation capacity expansion problem is a long-term horizon problem that determines the optimal level of investment in each available generation technology to meet a future demand in a specific electricity system. In a centrally planned context, capacity expansion models allow regulators to plan the generation capacity that has to be built in order to meet the future electricity demand in a reliable and efficient manner and at the least possible cost. In a liberalized market setting, capacity expansion models are used by regulators as an instrument for indicative energy planning to inform them about which technologies are most suitable from a long-term strategy perspective, in order to assist them in regulatory decisions (Pérez- Arriaga and Linares, 2008). The marginal pricing economic theory demonstrates that the optimal solution in a competitive generation market is equal to the solution of a centrally planned system with a single decision-maker the regulator who minimizes investment plus operating costs to meet demand (Pérez-Arriaga, 1994; Pérez-Arriaga and Meseguer, 1997; Green, 2000). This equivalence validates the use of cost minimization models to represent competitive markets. While other more realistic models accounting for market imperfections can be constructed by introducing equilibrium conditions, these models significantly increase the complexity of the problem (Ventosa et al., 2005). This model will assume that measures preventing the exercise of market power have been introduced, and that the system is large enough to make possible a perfectly competitive market structure. The Classic Capacity Expansion: the Screening Curves Model Since the origins of capacity expansion problems, cost minimization models were introduced to determine the optimal investment policy taking into account the capital and the operational costs of each available generating technology according to an optimal operating schedule of the plants. Traditionally, the difficulty of accounting for operating costs in investment planning models has been overcome by the use of load duration curves (LDC) (Kirchmayer, 1958). LDCs represent the fraction of the year during which demand is at or above a certain level. This simplified treatment of the demand is the basis of the classic screening curves models. 2

3 Screening curves plot the total cost per unit power of each technology option as a function of their capacity factor. Then they map the crossing points onto the LDC to determine the optimal capacity to invest in each generating technology (Stoft, 2002). Nevertheless, the use of the LDC for operating cost calculations assumes that the cost and availability of supply depend only upon the magnitude of the load and not on the time at which the load occurs (Turvey and Anderson, 1977). The validity of this assumption is largely questionable in systems such as those with a substantial penetration of renewable energies, where net load varies significantly among hours. Extended Unit Commitment Models Net load variability is primarily caused by the fluctuating patterns of wind speed and solar insolation and it induces a different operational regime on other generating technologies in the system. The resulting new regime can be characterized by a greater frequency of plant cycling and steeper output ramps than in a system without renewables. A greater number of start-ups will have a direct impact on the costs incurred by that generator and, for gas-fired power plants, it will also affect operation and maintenance costs corresponding to the replacement of the turbine, as these costs are a function of the number of cycles performed by the unit. Besides, more pronounced ramps in the net load requires the system to have enough generating capacity capable of increasing their output by a large amount in a very short period of time, as well as reserves that balance the divergence of renewables forecasts and actual output. Consequently, it is necessary to account for all these features in a model that aims to determine the optimal generation mix in a system with renewables. In the past, only short-term models such as unit commitment models have captured the level of operational detail needed to study the effect of the intermittency of renewables on the system. On the other hand, long-term models such as capacity expansion models (whether with screening curves or some other technique) have done poorly in including such level of detail. Kirschen et al. (2011), and Palmintier & Webster (2011) have proposed two similar approaches to solve this problem that combine the operational detail of unit commitment models and the investment decisions of capacity expansion models. These models are based on a unit commitment problem formulation with a preceding stage where building decisions are made. The main difference between these two approaches is that Kirschen et al. use binary variables to represent building decisions, while Palmintier & Webster use integer variables to determine the number of plants of each technology that get built. Following the nomenclature in Kirschen et al. (2011), we will refer to this type of models as extended unit commitment models. This paper uses an extended unit commitment model to determine the optimal generating capacity of a real-sized system: the ERCOT region of Texas. This system has 60 GW of peak demand and very weak interconnections with neighboring 3

4 systems, which will make the need for operational flexibility more salient as it will have to be provided by the system itself. The paper will use Kirchen s approach in that it will consider individual unit building decisions. However, it will not assume any previously existing capacity and the solution provided by the model will be the actual optimal generating capacity mix. II. OPTIMIZATION MODEL This section describes the elements of the mathematical formulation of the optimization model proposed. Similar formulations can be found in Kirschen et al. (2011) and Palmintier & Webster (2011). A. Indices and variables Two indices will be used in this model: i I, where I is the set of generating units that can be potentially built; and, j J, where J is the set of hours in a year. In addition, W I, is the subset of wind units, and G I, is the subset of gas-fired power plants: combined cycle gas turbines and combustion turbines (CCGTs and CTs). Building decisions are represented by the variable y i {0,1}; commitment states are u i,j {0,1}; start-up decisions are z i,j {0,1}; shutting down decisions are t i,j R + ; power output decisions are x i,j R +. B. Objective Function The objective function must account not only for what has traditionally been considered as fixed and variable costs in screening curves models, but also for startup costs. Accordingly, the objective function can be formulated as a two-stage decision problem in which it is decided first whether or not to build an individual power plant and a second stage where start-up and energy dispatch decisions are made (1): m # n & min " % f i! y i + "( c i! x i,j! g j + a i! z i,j ) ( (1) i=1 $ j=1 ' t,u,x,y,z where f i represents the annualized capital cost, c i the variable cost and a i the start-up cost of each technology. C. Operational Constraints Our model will be subjected to the classic constraints included in unit commitment models: demand constraint (2), start-up constraint (3), minimum and maximum output constraints (4) (introducing the new variable w i,j = x i,j! u i,j " P i ), and ramp constraints (5) (6): 4

5 m! x i,j " d j #j (2) i=1 u i,j! u i,j!1 = z i,j! t i,j "i, j (3) w i,j! u i,j "( Pi # P i ) $i, j (4) w i,j! w i,j!1 " r i #i, j (5) w i,j!1! w i,j " r i #i, j (6) In addition to these constraints, a coupling constraint will be added to link the two decision stages building and operating in the model. This extra constraint allows generating only units that have been built. Mathematically: D. Treatment of renewables x i,j! P i " y i #i, j (6) Wind and solar PV energy output has been introduced in the model as a function of each technology s capacity factor (c f ). Capacity factors indicate the availability of wind or solar resources for a specific hour at a certain location. Hence, for a particular hour of the year, the output of the total wind or solar power in our system will be determined by the product of each technology s total capacity and its respective c f. One characteristic offered by this model is the possibility of introducing curtailment as an extra degree of freedom to help match generation with demand. This feature will be implemented for wind power by choosing from one of the following two equations (Eq. 7 would enable curtailment): x w,j! P w "c f j x w,j = P w!c f j #w, j (7) "w, j (8) As will be shown later, the computing time of the model changes slightly depending on whether curtailment has been introduced or not. E. Operating Reserves Constraints Power systems need to secure a certain amount of spinning and non-spinning capacity to guarantee that generation constantly meets demand and that the frequency level of the system lies within the reference values. These frequency values are established so that they secure the stability of the system. Reserves are categorized according to their response time and the duration of the event they are required to mitigate. However, every system uses its own classification of operating 5

6 reserves. Milligan et al. (2010) presented a survey of the use of reserves in a number of power systems and proposed a common naming convention. Here, operating reserves will be modeled in a more simplified way, by requiring the system to cope with the loss of the largest generator at every time period. In addition to the conventional deployment of reserves, power systems with a significant amount of renewables require an extra reserve capacity (a.k.a. ramping reserves or flexibility) to compensate for the difference between the renewable generation forecast and the actual power generated (Milligan et al., 2010; Dena, 2005). This model will consider this type of reserves, requiring the system to have a total positive and negative regulation capacity proportional to the amount of wind power installed. The ramping reserves capacity used in this model is the capacity requirement found in the Dena study (Dena, 2005). Accordingly, positive and negative regulation constraints are respectively as follows: ( ) G " u i,j P i! x i,j # max P i i g=1 ( ) W ( ) $ y w $ P w " %j (9) w=1 G W " u i,j x i,j! P i # 0.08$ y w $ P w g=1 w=1 " %j (10) Operational flexibility will be exclusively provided by gas-fired power plants for two reasons: i) the ramping capacity offered by the other thermal units (nuclear and coal) is significantly more limited; ii), the emission associated with coal cycling has an extremely negative environmental impact. F. Complexity For large systems, like most encountered in the real world, the number of binary and real variables explode with the number of power plants considered. If we consider the 8,760 hours of a year, each power plant will have associated 8,760 x 2 = 17,520 binary variables (counting commitment and start-up decisions at every hour) and 8,760 x 2 = 17,520 real variables (counting output and shut-down decisions at every hour). As it is suggested in the literature, one way to go around this problem is to choose representative days or weeks in a year and weigh them by the corresponding factor to account for a complete year. However, one has to be careful making this composition as it would be easy to obtain spurious results resulting from the boundary effects between weeks. G. Model Data 1) Generation data The total number of power plants considered in the problem is 270, distributed as follows: 30 nuclear power plants, 20 coal power plants, 115 combined cycle gas turbines (CCGTs), 35 combustion gas turbines (CTs), 50 wind farms of 1GW of maximum power each, and 20 solar PV farms of 1GWp of power each. The number 6

7 of potential non-renewable plants that could be installed has been decided by running the model iteratively until the final solution has plants with extra slack. This slack guarantees that the solution is not determined by an artificial constraint imposed on the model by limiting the amount of power plants in the initial set. The cost data used for nuclear power have been taken from EIA (2010), whereas the cost data for the remaining technologies have been obtained from IEA (2010). A summary of these data and the cost parameters used in the model (annualized capital cost and variable cost) are given in the following tables: TABLE I: FIXED COSTS OF THE THERMAL POWER PLANTS CONSIDERED Technology Capital cost Fixed O&M Annualized capital Life [years] WACC [k$/mw] [$/MW-year] cost [k$/mw year] Nuclear 2 5, % 88, Coal 1 3, % 35, CCGT % 14, CT % 6, Energy Information Administration (EIA), Updated Capital Cost Estimates for Electricity Generation Plants, Fixed costs of Nuclear: International Energy Agency (IEA), Energy Technology Perspectives, 2010 TABLE II: VARIABLE COSTS OF THE THERMAL POWER PLANTS CONSIDERED Technology Variable O&M Heat rate Fuel price Variable cost [$/MWh] [MBTU/MWh] [$/MBTU] [$/MWh] Nuclear Coal CCGT CT Likewise, the technical parameters used for each technology is summarized in the next table: TABLE III: TECHNICAL DATA AND START-UP COSTS OF THE THERMAL POWER PLANTS CONSIDERED Technology Carbon Emissions Maximum ramp Start-up costs P [tnco 2 /GWh] i [GW] P i [GW] [GW/h] 3 [M$/start-up] Nuclear Coal CCGT CT International Energy Agency (IEA), Harnessing Variable Renewables, ) Demand, wind and solar data This model uses real demand and wind data from the ERCOT system corresponding to the year Each week selected is a representative week for each season. Also, the weeks have been selected so as to avoid demand jumps between the 7

8 last hour in one week and the first hour of the following week. A value of non-served energy of $5,000/MWh has been used along the study. The wind capacity factor for every hour comes from dividing the actual wind production by the wind capacity installed in the ERCOT system at that time. The hourly solar insolation data used in the study corresponds to the Corpus Christi Intl Arpt siting during year 2005, and they have been obtained from the National Solar Radiation Database (NSRDB). III. RESULTS The extended unit commitment model was run using GAMS on a 64 bit dual socket hexcore (i.e. 12 physical cores, 12 virtual cores total) Intel nehalem (x5650) machine. The maximum optcr has been set to 0.01 in all runs. Two main configurations have been tested: allowing for wind curtailment (Table IV) and not allowing for wind curtailment (Table V); and several penetration scenarios of wind and solar power have been examined. TABLE IV: SIMULATION PERFORMANCE, INSTALLED CAPACITY AND CAPACITY FACTOR ALLOWING CURTAILMENT General Results Wind-Solar Case [GW] Solver time [hh:mm:ss] 0:59:30 1:07:32 0:52:13 0:48:54 0:49:18 1:18:15 Relative gap Total Cost [M$] 24,538 26,369 28,702 30,616 34,881 38,784 Emissions [tnco2] 5.72E E E E E E+07 Relative NSE 9.54E E E E E E-04 Wind Curtailed [%] 0 % 5.4% 1.5% 3.5% 1.4% 4.3% Installed Capacity Nuclear [units/gw] 24/24 23/23 20/20 17/17 8/8 2/2 Coal [units /GW] 9 /4.5 3/1.5 5/2.5 3/1.5 4/2 0/0 CCGT [units/gw] 83/ / / / / /45.2 CT [units/gw] 11/3.3 16/4.8 19/5.7 23/6.9 27/8.1 35/10.5 Wind [units/gw] 0/0 10/10 10/10 20/20 30/30 50/50 Solar [units/gw] 0/0 0/0 10/10 10/10 20/20 20/20 Generation Mix Nuclear [%] 63.90% 60.90% 53.20% 45.10% 21.30% 5.30% Coal [%] 10.60% 3.40% 6.00% 3.50% 5.00% 0.00% CCGT [%] 25.30% 28.60% 28.90% 32.60% 41.70% 50.50% CT [%] 0.10% 0.20% 0.20% 0.20% 1.30% 0.40% Wind [%] 0.00% 6.80% 7.10% 14.00% 21.40% 34.60% Solar [%] 0.00% 0.00% 4.60% 4.60% 9.20% 9.20% Capacity Factor Nuclear [%] 99.67% 99.12% 99.57% 99.31% 99.67% 99.20% Coal [%] 88.18% 84.85% 89.84% 87.34% 93.58% - CCGT [%] 28.53% 31.12% 32.20% 34.28% 39.42% 41.82% CT [%] 1.13% 1.56% 1.31% 1.09% 6.01% 1.43% Wind [%] % 26.58% 26.20% 26.70% 25.90% Solar [%] % 17.22% 17.22% 17.22% Start-Ups per Year Coal (avg/max) 7/26 9/13 13/13-13/13 - CCGT (avg/max) 39/104 64/130 47/104 56/117 56/104 72/130 8

9 CT (avg/max) 71/91 67/104 97/378 84/ /782 86/235 TABLE V: SIMULATION PERFORMANCE, INSTALLED CAPACITY AND CAPACITY FACTOR NOT ALLOWING CURTAILMENT General Results Wind-Solar Case [GW] Solver time [hh:mm:ss] 0:59:30 1:02:39 1:06:02 1:07:55 1:00:00 0:35:18 Relative gap Total Cost [M$] 24,538 26,659 28,705 30,681 34,834 38,843 Emissions [tnco2] 5.72E E E E E E+07 Relative NSE 9.54E E E E E E-04 Wind Curtailed [%] Installed Capacity Nuclear [units/gw] 24/24 19/19 18/18 14/14 4/4 2/2 Coal [units /GW] 9 /4.5 9/4.5 11/5.5 10/5 16/8 5/2.5 CCGT [units/gw] 83/ / / /36 98/ /42.4 CT [units/gw] 11/3.3 16/4.8 19/5.7 21/6.3 27/8.1 35/10.5 Wind [units/gw] 0/0 10/10 10/10 20/20 30/30 50/50 Solar [units/gw] 0/0 0/0 10/10 10/10 20/20 20/20 Generation Mix Nuclear [%] 63.90% 50.60% 48.00% 36.40% 10.00% 5.30% Coal [%] 10.60% 10.90% 13.20% 12.10% 19.90% 5.50% CCGT [%] 25.30% 31.00% 26.80% 32.30% 38.90% 45.30% CT [%] 0.10% 0.20% 0.20% 0.20% 0.20% 0.40% Wind [%] 0.00% 7.20% 7.20% 14.50% 21.70% 36.20% Solar [%] 0.00% 0.00% 4.60% 4.60% 9.20% 9.20% Capacity Factor Nuclear [%] 99.67% 99.69% 99.82% 97.33% 93.58% 99.20% Coal [%] 88.18% 90.67% 89.84% 90.59% 93.11% 82.35% CCGT [%] 28.53% 32.97% 30.59% 33.59% 37.15% 39.99% CT [%] 1.13% 1.56% 1.31% 1.19% 0.92% 1.43% Wind [%] % 26.95% 27.14% 27.08% 27.10% Solar [%] % 17.22% 17.22% 17.22% Start-Ups per Year Coal (avg/max) 7/26 6/13 6/13 22/39 33/39 - CCGT (avg/max) 39/104 46/91 48/104 50/91 54/91 70/103 CT (avg/max) 71/91 68/117 79/274 76/169 85/130 81/156 For all the cases studied, the wall times of the simulations sit at about one hour. Nevertheless, it can be noted that restricting curtailment slightly increases the computational time of the model. In general, larger penetration of renewables affects the optimal mix in two ways: first, nuclear capacity is displaced by renewables as renewables can provide part of the baseload capacity at a lower variable cost; second, more gas-fired power plants (CCGTs and CTs) are introduced to meet the reserves requirement, and to provide baseload generation when combined with renewables. These two effects are consistent with those found in the MIT Future of Natural Gas Study (MIT, 2010). Some of the instances were also run using GAMS on a commercial 2.4 GHz Intel Core 2 Duo machine with 4GB of memory, and the computing time experienced was in the order of 1.5 to 2 times that of the original machine. 9

10 The average capacity factor (or level of utilization of the power plants) varies significantly across technologies: nuclear plants maintain a level over 99% in most of the instances, coal plants lie roughly between 80-90%, CCGTs lie between 30-40%, and CTs are slightly over 1%. It is found that for larger levels of penetration of wind and solar plants, the capacity factor of CCGTs gradually increases. This result contradicts what was found in the MIT Future of Natural Gas Study, which suggests that gas-fired power plants might operate for a smaller number of hours. The fundamental reason for this divergence is that in the MIT study, the dispatch is performed with a fixed generation mix, adjusting only the wind output in each case. This results in a capacity mix that is not optimal for other levels of penetration of renewables considered in the first place. On the other hand, this paper optimizes the capacity mix for each different case, optimizing as well the way that power plants are operated. Yet, in practice, dynamically changing the capacity mix as the deployment of renewables increases might not be as economical, as it would involve the decommission of plants that have not been yet amortized. One of the major differences between the two cases (with and without curtailment) is that when curtailment is not allowed in the system, part of the flexibility is provided by coal units. This results in some of the nuclear capacity being substituted by coal, which in turn considerably increases the total emissions of the system. Lastly, results show that on average, larger levels of penetration of wind and solar increase the cycling regime of midrange units. Differences between the average number of cycles per year and the maximum number of cycles suggest that some power plants will be more affected than others by the change of operational regime. However, taking into account the extra fuel cost to stat-up each unit, it is demonstrated that larger deployment of renewables in the system will lead to higher cycling costs to the owners of the power plants. IV. CONCLUSIONS This paper uses an extended unit commitment model to study how different penetration levels of renewable energies (wind and solar) and curtailment options affect the optimal generation capacity and the cycling regime of the thermal units. The model starts from a set of plants that could be potentially built and decides on the optimal capacity mix, taking into account operational constraints and reserves requirements. Results indicate that greater levels of penetration of renewables require a smaller capacity of nuclear power and a larger amount of gas-fired power plants (CCGTs and CTs). This result suggests that power systems that are massively installing nuclear power capacity run the risk of becoming ill-adapted in the future, as large amounts of renewables will demand larger operational flexibility from the system and as nuclear power is displaced by renewables. 10

11 The paper also shows that wind curtailment is a valuable source of operational flexibility for the system since, to a certain extent, it avoids the need to install other more expensive and more polluting units that provide that flexibility. Finally, this study demonstrates that, in general, larger penetration of renewables will induce thermal units to have a more intense cycling regime which, in turn, could bring a higher cost to this type of power plants. V. ACKNOWLEDGEMENTS Prof. Mort Webster, Prof. Ignacio Pérez-Arriaga, Dr. John Parsons, Prof. Andrés Ramos, Dr. Carlos Batlle, Bryan Palmintier, Fundación Caja Madrid. VI. REFERENCES Bushnell, J. (2010) Building Blocks: Investment in Renewable and Nonrenewable Technologies in (eds.) R. Schmalensee, J Padilla and B. Moselle, Harnessing Renewable Energy, London, Earthscan DENA (2005) Energiewirtschaftliche Planung für die Netzintegrationvon Windenergie in Deutschland an Land und Offshore bis zum Jahr Dena, March EIA (2010) Updated Capital Cost Estimates for Electricity Generation Plants, U.S. Energy Information Administration, Office of Energy Analysis. U.S. Department of Energy, November 2010 Green, R. (2000) Competition in Generation: The Economic Foundations, Proceedings of the IEEE, Vol. 88, No. 2, February 2000 IEA (2010) Energy Technology Perspectives Scenarios and Strategies to 2050, International Energy Agency. ISBN : IEA (2011) Harnessing Variable Renewables. A Guide to the Balancing Challenge, International Energy Agency. ISBN Kirchmayer, L. K. (1958) Economic Operation of Power Systems, John Wiley. Kirschen, D. Ma, J., Silva, V. Belhomme, R. (2011) Optimizing the Flexibility of a Portfolio of Generating Plants to Deal with Wind Integration, IEEE Presented to the PES General Meeting, Detroit, MI, July 2011 Milligan, M. (2011) Costs of Integration for Wind and Solar Energy: Large-scale studies and implications. MIT Wind Integration Workshop, January 21st Presentation available at: Milligan, M., et al. (2010) Operating Reserves and Wind Power Integration: An International Comparison, NREL Conference Paper NREL/CP October

12 MIT (2010) The Future of Natural Gas. An Interdisciplinary MIT Study. Interim Report MIT Energy Initiative, Cambridge, MA. ISBN: Available at: MIT (2011) The Future of Nuclear Fuel Cycle. MIT Energy Initiative, Cambridge, MA. ISBN: Available at: National Solar Radiation Database (NSRDB), Palmintier, B., Webster, M. (2011) Impact of Unit Commitment Constraints on Generation Expansion Planning with Renewables, Presented to the IEEE, Power and Energy Society Conference, Detroit, MI, July 2011 Pérez-Arriaga I. J., Meseguer, C. (1997) Wholesale marginal prices in competitive generation markets. IEEE Transactions on Power Systems, vol. 12, no. 2, pp , May Pérez-Arriaga, J. I. (2007) Security of Electricity Supply in Europe in a Short, Medium and Long-Term Perspective. European Review of Energy Markets volume 2, issue 2, December 2007 Pérez-Arriaga, J.I., Linares, P. (2008) Markets vs. Regulation. A Role for Indicative Energy Planning, Institute for Research in Technology (IIT), Comillas University, Madrid, Spain Stoft, S. (2002) Power System Economics: Designing Markets for Electricity. IEEE Press & Wiley Interscience, ISBN Turvey, R., Anderson, D. (1977) Electricity Economics. Essays and Case Studies, The Johns Hopkins University Press. ISBN: Ventosa, M., Baillo, A., Ramos, A., Rivier, M. (2005) Electricity Market Modeling Trends, Energy Policy 33 (2005)