A Stochastic Two Settlement Equilibrium Model for Electricity Markets with Wind Generation

Transcription

1 1 A Stochastic Two Settlement Equilibrium Model or Electricity Markets with Wind Generation Sebastian Martin, Student Member, IEEE, Yves Smeers, and Jose A. Aguado, Member, IEEE (This article is under the IEEE Copyright Policy) Abstract Incentives to encourage the uptake o renewable energy generation have ostered wind energy in many power systems. These incentives usually take the orm o market instruments (e.g. eed-in tari or premium) that are not directly amenable to optimization representations o the market. In this paper, we propose an equilibrium model o the short term market to address the impact o wind operation under dierent structural assumptions. The model is ormulated or several price taking, risk averse irms in competition. It accounts or wind generation uncertainty and embeds a representation o the day ahead and balancing mechanisms. The consumer is modeled by a linear inverse demand unction. We ocus on eed-in premium as the incentive to wind as this is the instrument most avored today in European discussions. The model is ormulated as a stochastic equilibrium problem where the Karush-Kuhn-Tucker (KKT) conditions rom the optimization problem o each irm are simultaneously solved together with market clearing conditions on energy, capacity or reserve and energy or reserve. The problem or each irm consists o a two-stage stochastic optimization problem with a recourse unction based on the Conditional Value at Risk, (CV ar θ ), as a risk measure. Due to price taking assumptions the model is a single stage complementarity problem; it is implemented and solved using the sotware GAMS. An example based on a stylized simpliication o the Spanish power market and motivated by the impact o wind penetration on the revenue o conventional plants is used to illustrate the proposed approach. Index Terms CVaR, equilibrium, market, stochastic programming, Feed-in Premium. A. Indices and sets NOTATION, h, F Indices and set or irms,, h F. G Set o all the generators. G Set o generators belonging to irm. g Index or dispatchable generators, g G. l Index or wind generators, l G. k, Ω Index and set or scenarios, k Ω. B. Parameters A Upper bound or the requirement o committed upward reserve. In the Spanish System A = 110%. The work o S. Martin and J.A. Aguado was supported in part by the Spanish Ministry o Economy and Competitiveness through the project ENE S. Martin and J. A. Aguado are with the Department o Electrical Engineering, University o Malaga, Malaga, Spain ( smartin@uma.es; jaguado@uma.es) Y. Smeers is with the Center or Operations Research and Econometrics (CORE) at Université Catholique de Louvain (UCL), Belgium ( yves.smeers@uclouvain.be) A Lower bound or the requirement o committed upward reserve. In the Spanish System A = 90%. B Lower rate or committed downward reserve respect to the committed upward reserve. In the Spanish System B = 40%. R Upward ramping slope respect to the generation capacity, usually R [0.02, 0.53] per hour. R Downward ramping slope respect to the generation capacity, usually R [0.02, 0.53] per hour. cg g Linear coeicient o generation cost or dispatchable generator g, [e/mwh]. m y Balancing reserve actor or wind turbines. m x Balancing reserve actor or dispatchable generators. Pr k Probability o scenario k. X g Maximum generation capacity o dispatchable generator g, [MW]. X g Must-run capacity o dispatchable generator g, [MW]. In the case study X g = 0. Y k l Maximum generation capacity available or wind turbine l in scenario k, [MW]. Y k l Must-run capacity o wind turbine l in scenario k, [MW]. In the case study Y k l = 0. Y max l Installed capacity o wind turbine l, [MW]. α 0 Slope o the inverse demand unction [e/(mwh) 2 ]. θ Conidence level or irm CVaR, θ (0, 1). λ Level o risk aversion, λ [0, 1], λ = 0 risk neutral. ρ 0 Independent coeicient o the inverse demand unction, [e/mwh]. ρ + Premium associated with the scheduled wind generation, [e/mwh]. C. Variables Primal variables d Energy sales o irm in day ahead, [MWh]. Q k, Auxiliary variable or CV ar θ calculation. ru g Committed upward reserve rom dispatchable generator g, [MW]. rd g Committed downward reserve rom dispatchable generator g, [MW]. s k g Energy deployed rom upward reserve o dispatchable generator g at scenario k, [MWh]. u k g Energy deployed rom downward reserve o dispatchable generator g at scenario k, [MWh]. vl k Wind energy in excess over the scheduled generation or wind turbine l at scenario k, [MWh]. Scheduled generation o dispatchable unit g, [MWh]. x g

2 2 φ g φ k g y l Scheduled generation o wind turbine l, [MWh]. zl k Energy bought by wind turbine l at scenario k, [MWh]. ζ Auxiliary variable or CV ar θ calculation. Dual variables γ Upper bound or committed upward reserve. γ Upper bound or committed downward reserve. δ g Upper bound or upward reserve that generator g can supply. Ramping constraint. δ g Upper bound or downward reserve that generator g can supply. Ramping constraint. η k g Upper bound or the energy rom the committed upward reserve, dispatch. generator g, scenario k. η k Upper bound or the energy rom the committed g downward reserve, dispatch. generator g, scenario k. ι k l Upper bound or purchases o wind turbine l at scenario k. ι k l Lower bound or purchases o wind turbine l at scenario k. κ Lower bound or committed upward reserve [e/mwh]. κ Lower bound or committed downward reserve [e/mwh]. ν Power balance o irm. ξl k Upper bound or sales in excess o wind turbine l at scenario k. σ k CV ar θ constraint. τl k Constraint that relates the available wind in excess or wind turbine l and it use at scenario k. Upper bound capacity constraint o dispatchable generator g. Lower bound capacity constraint o dispatchable generator g at scenario k. χ k Balancing with excess o wind at scenario k. χ k Balancing with shortage o wind at scenario k. ψ l Upper bound capacity constraint o wind turbine l. ψ k l Lower bound capacity constraint o wind turbine l at scenario k. I. INTRODUCTION Rrenewable energy sources, in particular wind and solar, are seen as key technologies or mitigating climate change. Dierent economic instruments such as Green Targets and Certiicates, Feed-in Taris or Feed-in Premiums have been introduced to support the development o these technologies. These instruments raise interesting economic questions [1] [4], but can also sometimes lead to unintended consequences [5] [7]. This paper assumes a eed-in premium incentive throughout; it very occasionally touches on an unintended eect, but otherwise does not discuss the relative merits o these economic instruments. High rates o wind and solar generation in power systems also pose other, more micro economic and technical, challenges to market designers, system operators and generation irms [8] [10]. Variability and unpredictability in case o high wind penetration may cause operational problems [11], [12] that need to be handled by operational lexibility in real time. We here reer to an European system with a balancing mechanism but no real time market, and reer to lexibility reserve as the reserve used in that balancing mechanism to manage unpredictability (we deal with variability in another paper [13]) in the sense o deviations with respect to wind orecast errors. The determination o the optimal quantity and price o the lexibility reserve has been studied by several authors. In [14] a methodology that takes into account the uncertainty o the load and wind power orecasts and also the probability o generation ailures is proposed to quantiy the requirement or system reserve given a certain level o system reliability. This methodology is applied to the whole Irish power system as a case study. A common approach to deal with uncertainty is to rely on stochastic programming, as in [15] and [16]. The value o the operational lexibility is another important notion, which has been explored, or instance, in [17]. In [18] it is shown how to optimize the operation in a short-term orward electricity market using the concept o stochastic security. Conditions or an optimal balancing market have been studied by several authors, who conclude that cost-relectiveness with respect to the imbalance price is a key condition or a balancing market to be optimal [19], [20]. Generators act on both the day ahead and intraday markets as well as on balancing. Besides the literature on balancing, a number o strategies or optimal bidding in day ahead have been proposed in the academic literature. These strategies ocus on uncertainty in the system and are also oten based on stochastic programming. In [21], a model to derive the best oering strategy or a wind power producer is initially posed as a mixed-integer nonlinear program and inally reormulated and solved as an equivalent linear program. More microeconomic analysis o the behaviour o individual agents operating under uncertainty can be ound in the literature such as in [22]. The use o stochastic programming or determining optimal oering strategies o wind power producers under uncertainty gives results more accurate than other methods that consider less inormation. This is shown in [23] and also in [24] where the model is posed as a two-stage stochastic program taking into account network constraints and a pool with a signiicant number o wind producers. In [25], optimal oers in quantity are calculated or wind power producers through a two-stage stochastic program in which the inormation on prices and available wind energy is incorporated as exogenous parameters using a scenario tree. The CVaR is used or representing risk averse behavior. Other approaches include second-order cone programming as in [26], which is used to solve an optimal sel-scheduling problem or a single irm based on a security constrained optimal power low with risk aversion using a CVaR unction. The main contribution o this paper with respect to that literature can be summarized as ollows. In contrast with most o the literature that poses the problem o wind accommodation through stochastic [15], [16] or robust [26] optimization, we state it in equilibrium terms with risk averse agents. We justiy the departure rom optimization on several grounds. A irst reason is that wind penetration is generally supported by instruments that distort the market away rom perect

3 3 competition. This is the case o the eed-in premium which is the avorite EU proposal or reorming the support to renewable generation, as well as the eed-in tari which has been the rule in many European countries. These distortions are incompatible with the perect competition conditions implied by the pure optimization ormulation o the short term power markets (e.g. two prices or the same product in a single market). Equally relevant to justiy the move to an equilibrium model, European systems contain idiosyncrasies that add distortions to the standard competition paradigms. One o them, treated here, implies non backward recursive payos in the sense that day ahead prices are also used in balancing, notwithstanding the state o the world in real time. This orward passing o price is the opposite o the backward mechanisms that state day ahead prices as expectations o real time prices in stochastic programming. This again departs rom what can be done by optimization ormulations. Last, instruments such as eed-in premium or taris also generate risk exposures that can be quite dierent or conventional and wind generators. Barring a US type mechanism o the virtual bidding type that does not exist in Europe, these risks are not tradable. This requires a multi-agent setting where agents ace dierent non tradable risks. This is again not amenable to a single agent representation (whether by stochastic, robust or risk unction optimization) o the problem. Summing up, we believe that the combination o balancing markets and wind policies idiosyncrasies introduces enough departures rom the standard stochastic optimization paradigm to justiy an extension to the more general equilibrium ormulation at least when looking at the European market. The balancing mechanism is thus central in this analysis. It can be modeled through econometric relations giving balancing prices as unctions o energy or through undamental representations that could include an unit commitment [27]. Because balancing is an evolving process subject to continuous discussion, we do not rely on an econometric representation but introduce a undamental equilibrium model (without explicit unit commitment). This model can be adapted, sometimes at the cost o additional computational manipulation, to dierent market designs (e.g. dierent pricing schemes). This capability is also speciic to equilibrium models and would not be possible in an optimization ramework. This is discussed in more detail in Section II-D. The content o the paper can be summarized as ollows. We develop a short-term equilibrium-based model with high wind penetration where the wind producers beneit rom a eedin premium, and each generator solves a two-stage stochastic programming problem to optimize its proit. The Transmission System Operator (TSO) runs a day ahead market or reserve and a real time balancing mechanism. We use this set up to provide a irst insight into the loss o competitiveness o conventional capacity that accompanied the penetration o wind in Europe. We examine the combined impact o eed-in premium and adequate pricing o the reserve on the revenue o conventional plants, and come up with contrasting results. The possibility to contract abundant reserve or lexibility close to real time conirms the loss o competitiveness o conventional plants. In contrast, lexibility reserves that need to be committed many hours in advance provide revenue that compensate the losses on the energy market. The paper is organized as ollows. In Section II the model attributes and main assumptions or the day ahead, reserve and balancing market are given. In Section III the mathematical ormulation is described. An illustrative case study based on a stylized version o the Spanish power system is discussed in Sections IV and V. Conclusions close the paper. A. Assumptions II. MODEL FORMULATION Electricity markets deal with wind integration through a wide range o organizations. The proposed model is inspired by the Spanish case but presents some general eatures that are common to all European markets and hence may also be o interest to other countries supporting renewable energy [28]. We consider a two settlements system with a day ahead energy market and a real time balancing mechanism. The Power exchange (PX) clears the energy market in day-ahead under imperect wind orecast. The TSO deals with deviations with respect to these orecasts in real time. It does so through reserves that it procures in a day ahead market or reserve and uses in real time 1 in balancing. Flexibility reserves are o the upward and downward capacity type. Here we ocus on the operation mechanism in an hour, and simpliy the treatment by not explicitly considering any intra-day market. Reserve and balancing deal with deviations with respect to scheduled quantities in day ahead. This can be represented by a standard two stage stochastic tree. We represent deviations with respect to orecast by scenarios o wind power output realization in one hour 2.The model is set up or a day ahead time horizon with an hourly time granularity. Generators, consumers, and the TSO are the agents in the market. Generators operate dispatchable (conventional) generators with linear cost (without ixed operating cost) and wind turbines with zero generation cost. Deviations, up and down, are cleared by the TSO in real time within the reserve capacities procured in day ahead rom generators. Consumers are represented by a linear inverse demand unction in the day ahead energy market. They are charged a raction o the socialized cost o the reserve capacity through an ex-post network charge that, or the sake o simplicity, but also not unrealistically, is not taken into account in the model (this assumes that consumers do not react to ixed connection charge in the short run). The government subsidizes scheduled wind generation through a premium that is inanced by the general budget. The premium can be related to the spot price by a general unction (the higher the spot price the lower the premium) but it is here taken as an exogenous parameter in 1 In some electricity markets, like the Spanish market, there exists an intraday market with intermediate auctions in the time between day ahead and real time; these auctions contribute to reduce the cost associated with the wind orecast error [21], [29]. 2 Deviations o demand and generation contingencies can be included in the scenario tree at the cost o additional technical developments. In order to simpliy the presentation wind deviations constitute the only stochastic elements.

4 4 order to both simpliy the presentation and allow or sensitivity analysis. The model is posed as a two stage stochastic market equilibrium problem with risk averse generators. The irst stage variables o the equilibrium model are the demand and the energy bids rom conventional and wind generators in the energy market and the capacities in the lexibility reserve market. The second stage variables are those appearing in balancing and the auxiliary variables used to compute the risk unction o the generators (a CV ar involving the revenue rom balancing). We make the blanket assumption that agents are price takers in the day ahead energy and reserve market as well as in the real time balancing market. The energy market is typically modeled by a technology driven supply curve (marginal cost) and a linear demand unction (marginal willingness to pay). The need or reserves is represented by a set o upper and lower bound constraints, that equate the supply and demand o that energy in balancing. These are discussed in detail in Sections II-B, II-C and II-D. Finally, network constraints are not considered in this model where the TSO is only involved in the organization o the reserve market and the balancing mechanism. Many o these eatures can be technically removed or modiied to scale up the model or adapt it to other markets. The model is ormulated as a complementarity problem. B. Day ahead energy market and premium The PX clears the energy market on an hourly basis in day ahead. Day ahead outcomes depend on an imperect wind orecast but not on real time wind realization. The energy market is modeled by a standard technology driven supply curve (marginal cost) and a linear demand unction (marginal willingness to pay) represented by the inverse demand unction ρ = ρ 0 α 0 d T (1) where ρ is the price or energy in day ahead and d T is the total demand. The clearing o the day ahead energy market determines sales d h, scheduled wind y l and dispatchable generation x g. Scheduled wind generation y l receives a eed-in premium ρ + (exogenous parameter), that adds to the equilibrium price in the generators revenue. It is not directly paid by customers but charged to the general budget. Only the scheduled wind generation that is actually generated in real time receives the eed-in premium; the wind that was scheduled, but inally not generated, loses the eed-in premium in the balancing mechanism. No eed-in premium is paid to the wind energy that is generated in real time but was not scheduled. In the Spanish market this premium was given until 12th July 2013, by a piecewise linear unction with a loor and a cap, as described in [30]. We simpliy the mechanism and assume a ixed premium ρ +. The contribution o the day ahead energy market to the revenue o irm is y l (ρ + + ρ ) + x g (ρ cg g ) (2) l G where ρ is the value o the price ρ, cleared by the energy market. l G y l (ρ + + ρ ) is the revenue accruing to scheduled wind (eed-in premium and equilibrium price) and x g (ρ cg g ) is the revenue collected by the scheduled dispatchable generation (equilibrium price minus generation cost). C. Reserve Model The TSO clears the market or committed lexible reserves on an hourly basis in day ahead. Dierent types o reserves are used in real power systems. It is convenient to classiy them in two groups: i) those intervening or load-requency control are usually very ast (seconds) and automatically operated; ii) those devoted to load-ollowing operate on longer times (hours) and are part o the market [31]. This model concentrates on a load-ollowing requirements due to wind that we call lexibility reserve; these imply ramping requirements and balancing or accommodating deviations rom wind orecast. Flexibility reserve is procured by the TSO rom dispatchable generators in day ahead and results in two products: capacities o committed upward (ru g ) and downward (rd g ) reserves in the day ahead. In real power systems the requirement o lexibility reserves is usually based on deterministic and/or simple probabilistic approaches [32] with more than one criteria commonly used or sizing the load-ollowing reserves. We here ollow [33] and dynamically determine the required lexibility reserve on the basis o the generation scheduled rom dierent units. We use the linear unction R u = m y l G y l + m x x g o the scheduled generation to determine the upward reserve requirement R u by the TSO. The coeicients m y and m x appearing in this relation, called balancing reserve actors, are exogenous and relect the uncertain need or reserve associated with each technology. The whole set o constraints or reserve in the model is as ollows (3)-(6): ru g A m x x g + m y, (κ), (3) l G rd g B ru g, (κ), (4) ru g A m x x g + m y rd g l G y l y l, (γ), (5) ru g, (γ). (6) where (3) and (4) are the upper bound constraints or the upward and the downward reserve capacities respectively, and (5), (6) are the corresponding lower bound constraints. These constraints are inspired by the operation o real power systems, in particular the Spanish system. The revenue accruing to irm rom committing lexibility reserve in the TSO day ahead reserve market is: (ru g (κ + γ) + rd g (κ + γ)) (7)

5 5 where κ + γ (e/mw) is the shadow price o capacity or committed upward reserve, and κ + γ (e/mw) is the shadow price o capacity or committed downward reserve. D. Balancing The balancing o real power systems must accommodate demand prediction errors, system contingencies, uncertainty o non dispatchable generation and orecast errors. We simpliy the discussion by considering only wind power orecast errors, which are usually the largest demand or load ollowing in the short term in system with high wind penetration [14]. The standard economic paradigm is that these services should be charged at marginal reserve cost to those that demand them, and paid at the same value to those that produce them. Other pricing mechanisms such as penalization actors on the market prices [9], [20] can be also applied. Here, we consider a simpliied and economically standard approach where the price and the amount o balancing energy rom committed reserve result rom a perectly competitive market. The market is modeled as an optimization problem that minimizes the generation cost o balancing energy. This problem represents an auction organized by the TSO. From a modeling point o view, the result o this auction is integrated in the equilibrium through its KKT conditions. Let s k g and u k g be respectively the energy deployed rom upward and downward lexible reserve ru g and rd g in real time. Let also zl k and vl k be the energy bought or sold by wind turbines in real time to compensate the discrepancy between what had been scheduled in day head and what could be delivered in real time. The auction is modeled, or each scenario k, as the ollowing optimization problem: minimize s k g,uk g subject to: ( s k g cg g u k ) g cg g (8) z k l, (π k ) (9) s k g = l G vl k, (π k ) (10) u k g = l G s k g ru g, (η k g) (11) u k g rd g, (η k g ) (12) where the variables are s k g and u k g, and the ixed input data are the committed upward ru g and downward rd g reserve determined in real time, as well as the real time demand and supply o energy z k l and v k l by wind units. The constraints are the balancing between the energy used by wind turbines and energy provided by dispatchable generators or downward reserve (9), and upward reserve (10). Each unit can provide balancing energy only rom the capacity that has been previously committed in the reserve market (11), (12). The objective unction (8) minimizes the generation cost rom reserves using the committed generators with the minimum generation cost or upward reserve and those with the maximum cost or the downward reserve to supply the energy rom reserves. The eect o balancing on revenue and cost diers depending on whether wind realization is short or in excess. This is taken into account by the balancing cost or irm at scenario k given by the recourse unction Q k : Q k = [ ] s k g (cg g π k ) + u k g (ρ cg g π k ) + + l G [ ] (13) zl k (ρ + + π k ) + vl k (π k ρ ) where ρ is the energy price on the day ahead market and π k and π k are the energy prices rom committed upward and downward reserve respectively rom (9) and (10). In case o wind shortage, the cost incurred by wind turbine l that is short by zl k in scenario k is zl k (π k + ρ + ): The plant loses the premium or the energy committed in the day ahead market and has to substitute it by conventional energy in balancing at the equilibrium price o committed upward reserve. On the other hand, the cost o a dispatchable generator g or providing the upward reserve energy s k g is s k g (cg g π k ), which is the unitary generation cost cg g minus the price o the committed upward reserve π k. In case o wind in excess, a wind turbine can sell an amount vl k in excess on its scheduled generation (ranging rom zero to the available excess). Its revenue is vl k (ρ π k ), which involves the unitary cost o downward reserve energy π k and the revenue rom selling the energy at the equilibrium price ρ. Alternatively, the cost incurred by the dispatchable generator g in scenario k to down u k g rom its committed downward reserve to incorporate the additional wind is u k g (ρ cg g π k ). The unitary cost is the equilibrium price ρ, which was already incorporated in the day ahead revenue, rom which one subtracts the generation cost cg g, minus the non generated energy and the price o downward balancing energy π k. Summing up the balancing model uses a two-price settlement with one price or the upward energy and other price or the downward energy. The wind turbines do not lose the equilibrium price in balancing but they do not get the premium or quantities that they scheduled in day ahead and do not deliver in real time. E. Scenario tree The output o wind turbines is the only uncertainty considered in the model. It is represented by a scenario tree where each branch stands or a realization o the wind power output or one hour. We use a Beta distribution to model the wind power orecast Power output error [34], [35]. Let q = Rated power [0, 1] be the load actor or wind generation, [34] and [35] argue that this load actor its a Beta distribution: (q) = Γ(α + β) Γ(α)Γ(β) qα 1 (1 q) β 1, q [0, 1] (14) where Γ(α+β) Γ(α)Γ(β) is a scale actor such as 1 (x)dx = 1, and 0 the parameters α and β are directly related to the mean (µ) and the standard deviation (σ) o the distribution: α =µ 2 1 µ ( ) 1 σ 2 µ, β =α µ 1 (15)

6 6 The analysis o empirical data shows that σ properly its a linear unction o µ, σ = k 1 µ + k 2, [34], [35], [36] where the coeicients k 1 and k 2 mainly depend on the time horizon and the geographic dispersion o the wind turbines. Here we use the expression given in [36] or a time horizon o 24 h and large scale generation (normalized by the wind capacity installed): σ = 1 5 µ + 1 (in per unit) (16) 50 To build the scenarios, we divide the range [0, 1] or the load actor into segments and associate each scenario with a segment. Let n be the number o scenarios, k the index or scenario and z k [0, 1], then the range [0, 1] is discretized using n + 1 points, 0 = z 1 < z 2 <... z n+1 = 1. The value and the probability o scenario k are respectively: a) µ(k) = z k+1 Γ(α+β) Γ(α)Γ(β) xα (1 x) β 1 dx, which is the z k expected value on the segment that deines the scenario. b) pr(k) = z k+1 Γ(α+β) Γ(α)Γ(β) xα 1 (1 x) β 1 dx, which is the z k integral o the probability density unction o the Beta distribution on the segment associated with the scenario. The rule to select the points 0 = z 1 < z 2 <... < 1 z n+1 = 1 is to get segments o equal probability: zk+1 z k Γ(α+β) Γ(α)Γ(β) xα 1 (1 x) β 1 dx, k = 1, 2,..., n. III. MODEL EQUATIONS n = The model is cast as a complementarity problem, that consists o three groups o equations (the whole set o equations (30)-(48) is included in the appendix): 1) The global constraints (3)-(6) are the reserve constraints described in Section II-C. They represent the reserve capacity constraints o the market cleared by the TSO. Generators sell in this market at the prevailing clearing prices. These constraints are not included in the irms KKT conditions but their dual variables appear in the objective unctions o the irms. 2) The KKT conditions (34)-(39) represent the minimization o generation cost or balancing energy (8)-(12) as described in Section II-D. 3) The KKT conditions (40)-(48) or the problem o each irm, which is represented by (17)-(29) and described next. The optimization problem or each irm includes only the conditions or which the irm can make explicit decisions, taking market prices (energy, committed reserve capacity, ramping contracts and balancing energy) as given. Each irm solves a two stage stochastic program that represents the optimization o its operations between day ahead and balancing. The objective unction is a risk adjusted cash low E CV ar[p roit k ] = (1 λ ) E[P roit k ] + λ CV ar[p roit k ] that the irm wants to maximize, where E[ ] = k Prk is the expectation over the scenarios, λ [0, 1] is the level o risk aversion (λ = 0 is risk neutral) and P roit k is the net proit or irm at scenario k. P roit k = P Q k where P is the net proit o irm in the irst stage, that does not depend on the scenarios, and Q k is the value o the recourse unction (13). Taking into account the previous deinitions we can write the objective unction (17) as P (1 λ ) E[Q k ] λ CV ar[q k ]. Where CV ar[q k ] = ζ θ k Ω Prk Q k, is the application to the recourse unction o the standard deinition o the CVaR given in [37]. The net proit in the irst stage P is the sum o the income rom energy sales (ρ 0 α 0 h F d h) d, committed reserve (ru g (κ + γ) + rd g (κ + γ)), eed-in premium to wind generation l G y l ρ +, minus the cost o dispatchable generation x g cg g, all accruing in day-ahead. The optimization problem or each irm is: { max (ρ 0 α 0 d h ) d + y l ρ + d,x,y,z,rd, ru,s,u,v,ζ,q h F l G + (ru g (κ + γ) + rd g (κ + γ)) (17) x g cg g (1 λ ) Pr k Q k k ( ) } λ ζ + 1 k, Pr k Q 1 θ k Ω subject to: x g + ru g X g, (φ g ) (18) x g + s k g rd g X g, (φ k g ) (19) y l Y max l, (ψ l ) (20) y l zl k Y k l, (ψk) (21) l x g + y l = d, (ν ) (22) l G z k l Y max l Y k l, (ι k l ) (23) y l z k l Y k l, (ι k l ) (24) v k l Y k l, (ξ k l ) (25) v k l + y l z k l Y k l, (τ k l ) (26) ru g R (X g x g ), (δ g ) (27) rd g R (X g x g ), (δ g ) (28) ζ + Q k, Q k (σ k ) (29) where d, x, y, z, rd, ru, s, u, v, Q k, are positive variables. Equations (18)-(29) comprise upper and lower bounds or dispatchable plants (18), (19), wind turbines (20), (21), energy balancing in day ahead (22), upper and lower bounds or the purchases o wind turbines due to shortage o wind (23), (24), upper bound or wind generation in excess (25), energy balance or wind turbines (26), ramping constraints or the upward (27) and the downward (28) reserve, and inally the auxiliary constraint or the CVaR calculation (29). The model is implemented and solved using the sotware PATH in GAMS [38]. IV. CASE STUDY AND DISCUSSION The model is applied to a stylized version o the Spanish electricity system. It can, in principle, be used to study the impact o a number o actors present in real systems such as:

7 7 1) Premium to wind generation (policy). 2) Expected wind orecast (physical characteristic o the system). 3) Risk aversion o the irms (market characteristic). 4) Wind power orecast error distribution (physical characteristic o the system). 5) Reserve requirement set by the TSO. 6) Level o energy demand compared to the installed power capacity (market characteristic). 7) Mothballing o existing power plants (company decision subject to regulatory approval). 8) Pricing scheme or capacity o balancing reserve (market design). 9) Pricing scheme or energy rom balancing reserve (a market design). 10) Number o irms (market structure). 11) Technical capacity or ramping (technology characteristic). 12) Scheme o the balancing mechanism (market design). 13) Arbitrage between day ahead and balancing (market characteristic). We illustrate this potential by an analysis o three questions leading to a more in depth investigation o the demand or lexibility reserve. Even though the model is designed or several irms operating in the market, it is only used here with a single company to simpliy the discussion. A. Case Data The case study only considers wind and three conventional non hydro technologies: Combined Cycle Gas Turbine (CCGT), Coal and Nuclear. The conventional technologies are the only ones assumed dispatchable. Generators data are listed in Table I; capacities, number o units and year o construction are taken rom [39], generation cost and ramping capabilities come rom [40]. The system has a total installed capacity o MW o which MW (34.15%) corresponds to wind and MW to dispatchable generation. We assume that the CCGT plants with the highest cost are mothballed and that 50% o the CCGT capacity with the lower cost is also mothballed. The resulting system still have a CCGT capacity o MW with a generation cost o e/mwh. It must be noticed that CCGT are oten the marginal plants in the ollowing case studies. They then set the day ahead price at their marginal cost while making a zero margin. Bounds and weights take the ollowing values: A = 0.9, A = 1.1 (committed upward reserve in between 90% 110% o the TSO requirement), B = 0.4 (committed downward reserve at least 40% o committed upward reserve), m y = 0.15 (15 % balancing reserve actor or wind), m x = 0.02 (2% balancing reserve actor or dispatchable generation), and conidence level θ = 0.95 or CV ar θ. The parameters ρ 0 and α 0 o the inverse demand unction have been calculated by stating a price elasticity o -0.3 (data rom [41]) at a reerence point (ρ, d) where ρ = ρ 0 α 0 d. Taking ρ = e/mwh and d = MWh that correspond to hourly average or the Spanish system in 2012, one obtains ρ 0 = e/mwh and α 0 = e/(mwh) 2. TABLE I: Summary o generator data Net Capa. N. o Aver. age cg g R g = R g Technology X g (MW) units (years) (e/mwh) % o X g CCGT CCGT Nuclear Nuclear Coal Coal Coal Coal Wind Total Uncertainty is modeled through a scenario tree with 12 branches that represent the power output o wind turbines. Scenarios are constructed or a given value o the expected wind µ, according to the methodology and assumptions described in Section II-E. Four examples o scenario tree or dierent wind orecasts µ are listed in Table II. All these scenarios have the same probability ( %); this results rom the particular discretization o the original Beta distribution as discussed in II-E. Notice that this does not assume an uniorm error distribution. One shall note that the variability o wind generation is usually in the range [0.4µ, 1.6µ] except or very low values o expected wind (see Table II). TABLE II: Data o the scenario tree or wind Scenario Normalized power output (%) µ (%) σ (%) max. (base µ) min. (base µ) Given this input data, the resulting equilibrium problem has a size o 645 variables, and takes an average time o seconds to be solved with GAMS/PATH running on a laptop with an Intel CORE i7 processor and 6 GB RAM. The average computation time per case has been calculated on a sequence o 1681 runnings with hot start. Without hot start the solving time is 4 seconds or each problem. B. Problem statement The price o energy in day ahead is a particularly relevant output o markets with high wind penetration. Similarly, the expected and risk adjusted gross margins made by the conventional and wind technologies are crucial parameters in the decision to invest today in the European market. We illustrate the use o the model by concentrating on the impact o ive main actors on these elements: a) The orecast wind level: High wind power tends to 1 Calculated over the wind capacity installed.

8 8 reduce the equilibrium price. This is a direct consequence o wind replacing the most expensive dispatchable generators. It directly aects the margins made by conventional and wind plants. Table III (columns 2 and 3) reports results or average eed-in premium to wind generation and risk aversion but with dierent wind orecast µ. As expected, higher wind orecast results in higher scheduled wind and lower scheduled conventional generation. The global eect is a signiicant decrease o the equilibrium price o 17% that combines to the lower scheduled conventional generation in day ahead. At the same time, the higher scheduled wind generation also increases the capacity available or lexibility reserve, which reduces the revenue rom reserve in day ahead. The end result is a drastic loss o proits o dispatchable generators (see row 1st stage dispatchable generators in Table III) in the day ahead market. Revenue rom balancing only very partially compensate or that loss (row 2nd stage dispatchable generators in Table III). Overall, this drastic drop o revenue decreases the incentive to invest in conventional plants and increases the incentive to mothball or even dismantle existing capacities. b) The eed-in premium is analyzed subject to average wind condition and risk aversion. Columns 4 and 5 o Table III reveal that the premium does not signiicantly aect the day ahead equilibrium even i it induces a small increase o scheduled wind. The high premium tends to enhance wind scheduling in day ahead but the loss o this premium in balancing, when wind generators are short, makes the payo more risky, which has an impact on the risk adjusted proit at the second stage. Increasing the eed-in premium to wind generation obviously increases wind revenue, but this seems to take place without distorting the day ahead market. It is well known however that this eiciency result only holds where wind generation remains suiciently low compared to demand, so that the electricity price remains positive (see [7] or a study o the distortion in the short run o a market with premium and high wind penetration). c) The increased risk aversion is examined with average wind condition and eed-in premium to wind generation. One inds rom columns 6 and 7 in Table III that an increase o the level o risk aversion λ o the irms only has a low impact on the short run market. The price in the day ahead market remains at e/mwh that corresponds to the high capacity o the CCGT units with this operating cost. In contrast with the eect o a higher premium, a higher risk aversion decreases scheduled wind, albeit not by a large amount. The bad news is the decreasing margins o both types o plants. Conventional plants produce more than in the case o high wind orecast, but make the same margin due to the act that this additional generation comes rom the same CCGTs that make zero margin when they are marginal. Because o the reduction o activity in balancing resulting rom the risk aversion, these plants also see their proits reduced on that market. The conclusion o these results is that risk aversion urther reduces the incentive to invest. d) Wind induced demand or lexibility reserve. Except or column 2 with low wind and hence most ossil capacity committed or generation, none o the above cases shows any constraint on lexibility reserve in day ahead; the consequence is the lack o revenue rom the day ahead reserve market. Wind increases the demand or reserve but at the same time makes existing capacity available or that reserve. This lack o revenue rom lexibility reserve, combined with the lower price in the merit order due to wind generation, is the mechanism that eventually leads to mothballing and possibly dismantling dispatchable capacities. The ollowing analyzes this mechanism in more detail by considering two situations that dier by the demand or reserve and its impact on energy prices. We motivate the analysis by sourcing it in the error on wind orecast over dierent horizons. An alternative motivation, not discussed here, can be made by invoking ramping requirement in more detail than our equations (27) and (28). i) Suppose irst that a orecasting period o 6 hours or less is suicient or committing lexibility reserve, and assume that we can move the gate closure o the energy and reserve markets to that horizon (through some intraday market that we do not characterize otherwise). Assume that wind orecast is relatively accurate over that horizon. The residual error between the orecast and the realization can be characterized by a standard deviation σ. This deines a range or the possible wind power output values that is relatively narrow, [µ σ, µ + σ], where µ is the expected value or wind and usually σ < 1 5 µ. ii) Alternatively consider a orecasting period o 24 hours, typical o an unit commitment problem, as necessary or committing lexibility reserve. We are then in our generic day ahead/real time context and now need to work with the Beta distribution discussed in section II-E. In case o a orecast error with mean µ and standard deviation σ = 1 5 µ , (normalized values with respect to the installed wind capacity), the range o uncertain values is typically [0.4µ, 1.6µ]. This implies taking a domain o approximately ±60% over the expected value µ to cover most o the uncertainty. Depending on the amount o available reserve, the committed reserve, the expected wind and the variability o wind, a number o dierent behaviors have been observed in the model. We discuss two conigurations in this section and list other situations in the ollowing: 1) Consider irst the case where demand or lexibility reserve is suiciently small that it never constraints scheduled wind: (scheduled wind) (lowest wind scenario) (committed upward reserve). This situation occurs when the uncertainty on wind generation is small, something that occurs when one can move the gate closure close to real time. Wind orecast is then good and balancing can take advantage o a slack reserve market. The observation shows that this is the situation where the premium ρ + has little eect on the amount o scheduled wind. This is what happens in the case depicted in columns 4 and 5 o Table III. 2) Consider now the situation where the demand or lexibility reserve can constrain scheduled wind. This occurs in situations where a given value o the premium (that could be zero) leads to an amount o the scheduled wind that hits, at least the constraint (scheduled wind)

9 9 TABLE III: Simulation results or dierent conigurations m y = 0.15 (wind), m x = 0.02 (dispatch. gen.) m y = 0.60, m x = 0.02 Case 1 Case 2 Case 3 Case 4 µ (%) expected wind ρ + (e/mwh) premium λ risk aversion (0 is risk neutral) Energy demand day ahead (MWh) Scheduled wind generation (MWh) Scheduled dispatch. gen. (MWh) Equilibrium price (e/mwh) Reserve requirement (MW) Upward reserve committed (MW) Downward reserve commit. (MW) Max. available reserve (MW) INCOMES (e): Energy sales in day ahead Premium to scheduled wind Supply o upward reserve capacity Supply o down. reserve capacity COSTS (e): Cost o dispatchable generation Contribution o the β CV ar[q] Contribution o the (1 β ) E[Q] PROFIT (e) Total (wind + dispatch.) st stage wind turbines nd stage wind turbines st stage dispatchable generators nd stage dispatchable generators (lowest wind scenario) (committed upward reserve). This occurs when the uncertainty on wind generation is high, or instance because o the need to commit the reserve well in advance. This can be due to a lack o intraday market or to the impossibility to trade capacity in intraday (e.g. in a continuous intraday energy market without intermediate auction). In this case the premium ρ + to wind generation may have a strong impact on the amount o scheduled wind. We analyze this situation in columns 8 and 9 o Table III. The two cases reer to the average wind orecast (µ = 23.83%) and the average risk aversion (λ = 0.4); its characteristic is to implicitly assume a longer orecast horizon or wind implying m y = 0.6 (in contrast with m y = 0.15 otherwise), while m x remains at the value 0.02 used in cases 1 to 3. In short the demand or reserve or load ollowing due to wind is higher. We ocus on the impact o changing the eed-in premium to wind generation. In contrast with case 2, the increase o the eed-in premium to wind generation now implies a signiicant increase o the scheduled wind generation. But also in contrast with case 2, the two eed-in premium to wind generation cases lead to an increase in the price o electricity compared to those ound in all other cases (rom 1 to 3). This does not comply with the common wisdom that explicitly sees wind increase as implying a decrease o the electricity price. The justiication is to be ound in the higher demand or lexibility reserve implied by the longer horizon necessary or orecasting wind production and committing reserve (moving m y rom 0.15 to 0.6). One indeed observes higher upward and downward committed reserves in case 4 compared to all other cases, and an increase o these reserve inside case 4 when the eed-in premium to wind generation increases. The end result is a revenue rom committed reserve in the day ahead market that restores the proit accruing to dispatchable generators in day ahead to a value obtained in the case o low wind as seen by comparing the rows 1st stage dispatchable generators in columns 8 and 9 to the same inormation in column 2 (Table III). e) Other cases o high demand or reserves: The ollowing circumstances, not urther discussed here, can also lead to tight constraints on reserve that, i properly priced, could restore the proits o conventional generators and hence stop the incentive to mothball o dismantle. i) Dispatchable generators may not have enough capacity to satisy simultaneously the requirement or energy demand and reserve commitment. Firms arbitrage between using the generation capacity o dispatchable generators or reserve or or generation o energy in day ahead. This will happen at the end o a mothballing, dismantling or insuicient investment process. It will induce capacity cycles. ii) Committed reserve hits technical limits. This depends on the overall lexibility o the remaining dispatchable plants. iii) Wind incentive can have unintended eects. Consider a situation where the requirement or lexibility reserve in day ahead by the TSO is suiciently high that it does not constraint wind generation over its whole range o uncertainty (e.g. m y = m x = 0.3). Suppose also that generation capacity is tight with respect to demand (or instance as a result o mothballing). A high enough eed-in premium (or instance ρ + = 80 e/mwh) can make it proitable to supply more demand by scheduling wind even in excess o the highest scenario, at the same time as moving dispatchable generation into lexibility reserve. The incentive or this strategy has two origins.

10 10 It irst results rom the premium accruing rom total wind generation in day ahead compensating the cost o energy purchased on balancing in case o wind shortage. The second incentive results rom the higher demand or reserve lexibility by the TSO that also increases the price o energy. The strategy is only a consequence o the market design (in this case the high eed-in premium) and does not involve any exercise o market power. V. FINAL REMARKS It maybe useul to note at this stage that the above model is designed to accommodate several irms and hence cannot in principle be restated as an optimization problem. One can urther remark that the ormulation o the proit o the irm with the equilibrium prices intervening both in day ahead and balancing also diers rom a (stochastic) optimization problem even in the single irm case. Invoking a day ahead energy price in revenues occurring in balancing, (which seems common in Europe), is indeed incompatible with the backward recursive structure o stochastic optimization and requires an equilibrium ormulation. It is thus conjectured that this more general ormulation will allow or the study o various imperections o the market designs in the implementation o renewable policies that are out o reach o optimization models. The dierent case studies illustrate the common idea that the devil is in the detail. The irst case study conirms, the now well admitted idea, that wind penetration reduces the revenue o conventional plants to the point that investment is stopped and plants necessary or the system may be withdrawn rom operations because o insuicient revenue. The second and third cases suggest that this intuitive result is robust as one essentially observes the same losses o revenue or quite dierent structuring parameters (eed-in premium and risk aversion). The ourth case study suggests that the situation might be more complex: The change o a single apparently innocuous coeicient (increasing m y rom 0.15 to 0.6) can completely modiy important policy conclusions. The analysis indeed shows that conventional plants that are necessary or the operations o the system, in this case to provide lexibility reserve, will remain in the system even in case o high wind penetration i their services are economically (at marginal cost) priced. This requires that one is willing to acknowledge the demand or these services and the need to remunerate those that provide them. Reerring to current European discussions on adequacy, it is also useul to note that this pricing scheme can be embedded in energy only markets (hence without requiring a capacity market) and will not keep redundant conventional plants on line (it does not contain any element o State Aid ). From a more technical point o view, insights on how dierent actors aect the day ahead energy price can be obtained by considering the KKT conditions o the market model. Speciically one can observe that the energy price is: a) Reduced by the eed-in premium, the availability o downward reserve (the more the committed downward reserve the better), and the must-run capacity o wind turbines. This latter parameter is ixed to zero in this paper, but it could be made greater than zero or technical reasons. b) Increased by poor wind conditions with respect to the system capacity, a lack o committed downward and upward reserve, shortage o wind in real time compared to the scheduled wind generation, dispatchable generation cost, and insuicient dispatchable generation capacity. An analysis o the impact o dierent actors on plant revenue requires some other development that will be taken up in a uture paper. VI. CONCLUSION We propose a stochastic equilibrium model to investigate the impact o market design on the remuneration o conventional and wind generation plants in a market with potentially high penetration o renewable. The justiication or resorting to an equilibrium instead o an optimization approach even without market power is twoold. A irst reason is that the market is now composed o dierent irms that trade energy and services; the equilibrium ormulation is most natural or this situation. The second, possibly more compelling reason is that renewable policies are implemented through dierent market instruments that cannot necessarily be cast in an optimization orm. The proposed model is inspired by the Spanish situation but the approach is general. We try to show that the approach can embed general eatures o market design (a two settlement system), market idiosyncrasies (a somewhat detailed representation o the balancing market) and general economic characteristics o agents like risk aversion. Like stochastic programming, equilibrium models are amenable to a treatment o uncertainty. We illustrate the use o the model by ocusing on a timely European question, namely the revenue accruing to conventional plants in market with high renewable penetration. The common wisdom (and the observation o the market) is that renewable induce a decrease o energy prices together with a reduction o the activity o the conventional units, and hence an overall decrease o their revenue that put their sustainability in the market in question. We use the model to illustrate that this phenomenon indeed seems rather stable under dierent structural assumptions (same orders o magnitude in the loss o revenue or quite dierent assumptions o wind premium and risk aversion). But we also show that the phenomenon may also crucially depend on the demand or ancillary services (here requency control) induced by renewable and on their pricing by the market design. Both subjects are contentious: The incremental demand o reserve due to renewable is not well understood [14], [16], [27], [36], [42] [45] and the pricing o ancillary services is as diverse as the number o power systems in Europe. We model the demand or reserve through a coeicient and adopt an elementary, but sound, economic principle or pricing both reserve capacity and energy. The question o how the capacity payments, missing money, is determined in systems with high wind penetration (comparing regulation and deregulation) is also studied in [6], and they get similar conclusions to those summarized here. We ind that a higher demand or load ollowing reserve and

11 11 an economically sound pricing (marginal cost pricing) restore the revenue o the conventional plants. The question o the sustainability o conventional plants then boils down to the proper identiication o the demand or services (taking into account their provision by wind units themselves) and the acceptance that they be properly remunerated. Using the ramework described in this paper we plan as uture works to consider situations with several irms with a separation o wind turbines and dispatchable generators, a complete optimization problem or the TSO (not only the minimization o generation cost rom reserves), a comparison o dierent schemes or pricing and the balancing mechanism, and irms with dierent competitive behaviour (price makers, price takers). In our model the agents are price takers in both, day ahead and balancing market, a model with some points in common has been proposed in [46] with the wind turbines as price makers in balancing. APPENDIX Summary o the whole set o equations or the equilibrium problem. Let be L the Lagrangian unction or irm, L B the Lagrangian unction or the cost minimization problem or generation rom reserve, and Λ k = (1 λ ) Pr k + σ k (to reduce the length o the expressions). The whole equilibrium problem consists o three groups o equations: 1) The global constraints: A m x x g + m y B l G ru g A m x x g + m y rd g y l ru g, (κ), (30) rd g 0, (κ), (31) l G y l ru g, (γ), (32) ru g 0, (γ) (33) 2) The KKT conditions or the minimization o generation cost rom reserves: L B s k g L B u k g L B π k L B π k L B η k g L B η k g = cg g π k + η k g 0, s k g 0 (34) = cg g π k + η k g 0, uk g 0 (35) = zl k s k g = 0, π k ree (36) l G = vl k u k g = 0, π k ree (37) l G = s k g ru g 0, η k g 0 (38) = u k g rd g 0, η k g 0 (39) 3) The KKT conditions or each irm (here only or primal variables): d rd g ru k g v k l x g y l z k l Q k, ζ = (ρ 0 α 0 d h ) ν 0 d 0 (40) h F = κ γ + k Ω φ k g + δ g 0 rd g 0 (41) = (κ + γ) + φ g + δ g 0 ru g 0 (42) = Λ k (π k ρ ) + ξ k l + τ k l 0 v k l 0 (43) = cg g + φ g φ k + ν g k Ω + R δ g + R δ g 0 x g 0 (44) = ρ + + ψ l + (τl k + ι k l ψ k ) l k Ω + ν 0 y l 0 (45) = Λ k (π k + ρ + ) + ψ k l + + ι k l ι k l τ k l 0 z k l 0 (46) = λ 1 θ Pr k σ k 0 Q k, 0 (47) = λ k Ω σ k = 0; ζ ree (48) REFERENCES [1] National Round Table on the Environment and the Economy (Canada). Economic Instruments or Long-term Reductions in Energy-based Carbon Emissions [2] G. Cornelis van Kooten and G. R. Timilsina. Wind Power Development. Economics and Policies. Policy Research Working Paper WPS4686, The World Bank Development Research Group Environment and Energy Team, Washington, DC, March [3] F. Borggree and K. Neuho. Balancing and Intraday Market Design: Options or Wind Integration. Discussion paper 1162, DIW Berlin, German Institute or Economic Research, [4] International Renewable Energy Agency (IRENA). 30 Years o Policies or Wind Energy. Lessons rom 12 Wind Energy Markets. Tech report, IRENA and Global Wind Energy Council (GWEC), C67 Oice Building, Khalidiyah Street, P. O. Box 236, Abu Dhabi, United Arab Emirates, [5] B.F. Hobbs. -$300 Bid Floor Due to Renewable Subsidies?, Fix the Real Problem: Production-Based Incentives. CAISO Market Surveillance Committee Meeting, 18 March [6] T. D. Mount, S. Maneevitjit, A. J. Lamadrid, R. D. Zimmerman, and R. J. Thomas. The Hidden System Costs o Wind Generation in a Deregulated Electricity Market. The Energy Journal, 33(1): , January [7] R. Baldick. Wind and Energy Markets: A Case Study o Texas. Systems Journal, IEEE, 6(1):27 34, [8] B.F. Hobbs. Transmission planning and pricing or renewables: Lessons rom elsewhere. In Power and Energy Society General Meeting, 2012 IEEE, pages 1 5, [9] D. Newbery. Contracting or wind generation. Technical Report EPRG Working Paper 1120, Electricity Policy Research Group, Unversity o Cambridge, Austin Robinson Building, Sidgwick Avenue, Cambridge CB3 9DE, UK, July [10] A.J. Conejo, J.M. Morales, and J.A. Martinez. Tools or the Analysis and Design o Distributed Resources - Part III: Market Studies. Power Delivery, IEEE Transactions on, 26(3): , july 2011.

12 12 [11] J. Cox. Impact o Intermittency: How Wind Variability Could Change the Shape o the British and Irish Electricity Markets. Technical report, Pöyry Energy Consulting, King Charles House, Park End Street, Oxord OX1 1JD, UK, July [12] G. Giebel, R. Brownsword, G. Kariniotakis, M. Denhard, and C. Draxl. The State o the Art in Short-Term Prediction o Wind Power. Technical Report aplus deliverable D1.2 STP-SOTA v1.0.docx, ANEMOS.plus and SaeWind projects, Frederiksborgvej 399, 4000 Roskilde, Denmark, 28 January [13] S. Martin. Stochastic-Based Models or Electricity Market Analysis with High Wind Energy Penetration. Phd dissertation, Universidad de Málaga, [14] R. Doherty and M. O Malley. A new approach to quantiy reserve demand in systems with signiicant installed wind capacity. Power Systems, IEEE Transactions on, 20(2): , [15] J.M. Morales, A.J. Conejo, and J. Perez-Ruiz. Economic Valuation o Reserves in Power Systems With High Penetration o Wind Power. Power Systems, IEEE Transactions on, 24(2): , [16] A. Papavasiliou, S.S. Oren, and R.P. O Neill. Reserve Requirements or Wind Power Integration: A Scenario-Based Stochastic Programming Framework. Power Systems, IEEE Transactions on, 26(4): , [17] F. Bouard and M. Ortega-Vazquez. The value o operational lexibility in power systems with signiicant wind power generation. In Power and Energy Society General Meeting, 2011 IEEE, pages 1 5, july [18] F. Bouard and F.D. Galiana. Stochastic Security or Operations Planning With Signiicant Wind Power Generation. Power Systems, IEEE Transactions on, 23(2): , may [19] C. Hiroux and M. Saguan. Large-scale wind power in European electricity markets: Time or revisiting support schemes and market designs? Energy Policy, 38(7): , [20] L. Vandezande, L. Meeus, R. Belmans, M. Saguan, and J. M. Glachant. Well-unctioning balancing markets: A prerequisite or wind power integration. Energy Policy, 38(7): , [21] J.M. Morales, A.J. Conejo, and J. Perez-Ruiz. Short-Term Trading or a Wind Power Producer. Power Systems, IEEE Transactions on, 25(1): , eb [22] M. Carrión, A.J. Conejo, and J.M. Arroyo. Forward Contracting and Selling Price Determination or a Retailer. Power Systems, IEEE Transactions on, 22(4): , [23] M. Rahimiyan, J. M. Morales, and A. J. Conejo. Evaluating alternative oering strategies or wind producers in a pool. Applied Energy, 88(12): , [24] J. M. Morales, A. J. Conejo, K. Liu, and J. Zhong. Pricing Electricity in Pools With Wind Producers. Power Systems, IEEE Transactions on, PP(99):1 11, [25] J. P. S. Catalão, H. M. I. Pousinho, and V. M. F. Mendes. Optimal Oering Strategies or Wind Power Producers Considering Uncertainty and Risk. Systems Journal, IEEE, 6(2): , June [26] R.A. Jabr. Robust sel-scheduling under price uncertainty using conditional value-at-risk. Power Systems, IEEE Transactions on, 20(4): , [27] A. Tuohy, P. Meibom, E. Denny, and M. O Malley. Unit Commitment or Systems With Signiicant Wind Penetration. Power Systems, IEEE Transactions on, 24(2): , [28] Directive 2009/28/EC o the European Parliament and o the Council o 23 April 2009 on the promotion o the use o energy rom renewable sources and amending and subsequently repealing Directives 2001/77/EC and 2003/30/EC. [29] E.Y. Bitar, R. Rajagopal, P.P. Khargonekar, K. Poolla, and P. Varaiya. Bringing Wind Energy to Market. Power Systems, IEEE Transactions on, 27(3): , [30] J. Rivier. Electricity market participation o wind arms: the success story o the Spanish pragmatism. Energy Policy, 38(7): , [31] Y.G. Rebours, D.S. Kirschen, M. Trotignon, and S. Rossignol. A Survey o Frequency and Voltage Control Ancillary Services Part I: Technical Features. Power Systems, IEEE Transactions on, 22(1): , [32] UCTE - Union or the Coordination o the Transmission o Electricity (2009, Marth, 19th). Operation Handbook - Policy 1: Load- Frequency Control and Perormance (V3.0 rev 15) [Online]. Available: [33] S. Spiecker and C. Weber. Integration o luctuating renewable energy; A German case study. In Power and Energy Society General Meeting, 2011 IEEE, July [34] S. Boinger, A. Luig, and H. G. Beyer. Qualiication o wind power orecasts. In Global Wind Power Conerence, Paris, France, Apr [35] A. Fabbri, T.G.S. Román, J.R. Abbad, and V.H.M. Quezada. Assessment o the Cost Associated With Wind Generation Prediction Errors in a Liberalized Electricity Market. Power Systems, IEEE Transactions on, 20(3): , [36] M.A. Ortega-Vazquez and D.S. Kirschen. Estimating the Spinning Reserve Requirements in Systems With Signiicant Wind Power Generation Penetration. Power Systems, IEEE Transactions on, 24(1): , [37] R.T. Rockaellar and S. Uryasev. Optimization o conditional value-atrisk. Journal o Risk, (2):21 41, [38] GAMS Development Corporation. GAMS Base Module (LEX LEG x86 64/Linux) Potomac Street, NW, Washington, DC 20007, USA, 4 July [39] Spanish Ministry o Industry, Energy and Tourism. Register o generators in the Spanish power system, Consulted on September [Online]. Available: [40] J. Bertsch, C. Growitsch, S. Lorenczik, and S. Nagl. Flexibility in Europe s power sector -an additional requirement or an automatic complement? EWI Working Paper No 13/10, Institute o Energy Economics at the University o Cologne (EWI), June [41] M. G. Lijesen. The real-time price elasticity o electricity. Energy Economics, 29(2): , [42] J.C. Smith, M.R. Milligan, E.A. DeMeo, and B. Parsons. Utility Wind Integration and Operating Impact State o the Art. Power Systems, IEEE Transactions on, 22(3): , [43] M. Milligan, P. Donohoo, D. Lew, E. Ela, B. Kirby, H. Holttinen, E. Lannoye, D. Flynn, M. O Malley, N. Miller, P. B. Eriksen, A. Gottig, B. Rawn, M. Gibescu, E. Gómez, A. Robitaille, and I. Kamwa. Operating Reserve and Wind Power Integration: An International Comparison. In The 9th Annual International Workshop on Large-Scale Integration o Wind Power into Power Systems as well as on Transmission Networks or Oshore Wind Power Plants Conerence, Québec, Canada, number NREL/CP National Renewable Energy Laboratory (NREL), October [44] P. Meibom, R. Barth, B. Hasche, H. Brand, C. Weber, and M. O Malley. Stochastic Optimization Model to Study the Operational Impacts o High Wind Penetrations in Ireland. Power Systems, IEEE Transactions on, 26(3): , [45] Agora Energiewende. 12 Insights on Germany s Energiewende. Discussion paper 010/ /EN, Agora Energiewende, Rosenstrasse 2, Berlin, Germany, February [46] M. Zugno, J.M. Morales, P. Pinson, and H. Madsen. Pool strategy o a price-maker wind power producer. Power Systems, IEEE Transactions on, 28(3): , Aug Sebastián Martín (S 08) was born in Málaga, Spain, in He graduated rom University o Granada, Spain, as Civil Engineer in 2003, and rom University o Málaga, Spain, as Industrial Engineer in He is currently pursuing the Ph. D. degree at the University o Málaga, Spain. He is currently a Lecturer at the University o Málaga. His research interests include optimization theory, operation and economics o electric energy systems, and teaching methodologies. Yves Smeers Yves Smeers received the M.S. and Ph.D. degrees rom Carnegie Mellon University, Pittsburgh, PA, in 1971 and 1972, respectively. He is currently a Proessor Emeritus and a member o the Center or Operations Research and Econometrics, at Université Catholique de Louvain, Louvainla-Neuve, Belgium. José Antonio Aguado (M01) received the Ingeniero Eléctrico and Ph.D. degrees rom the University o Málaga, Málaga, Spain, in 1997 and 2001, respectively. Currently, he is an Associate Proessor and Head o the Department o Electrical Engineering at the University o Málaga. His research interests include operation, planning, and deregulation o electric energy systems and numerical optimization techniques.