Risk trading in capacity equilibrium models

We present a set of power investment models, the class of risky capacity equilibrium problems, reflecting different assumptions of perfect and imperfect markets. The models are structured in a unified stochastic Nash game framework. Each model is the concatenation of a model of the short-term market operations (perfect competition or Cournot), with a long-term model of investment behavior (risk neutral and risk averse behavior under different assumptions of risk trading). The models can all be formulated as complementarity problems, some of them having an optimization equivalent. We prove existence of solutions and report numerical results to illustrate the relevance of market imperfections on welfare and investment behavior. The models are constructed and discussed as two stage problems but we show that the extension to multistage is achieved by a change of notation and a standard assumption on multistage risk functions. We also treat a large multistage industrial model to illustrate the computational feasibility of the approach

Rational Actors in Balancing Markets: a Game-Theoretic Model and Results

Guided by game theory we develop a model to explain behavioral equilibria under uncertainty and interaction with the spot market on balancing markets. We offer some insights for the general model and derive explicit solutions for a specific model in which the error distributions and pricing function are given. The most interesting conclusions are the unique existence of an equilibrium and that no participant acts contrary to the aggregate market (either all market participants buy or sell power) and all strategies are, normalized properly, equal (which is rather counterintuitive). Furthermore the aggregate behavior is a stochastic process varying around its own variance.game theory, nash equilibrium, regulated energy market, balancing power

Using EPECs to model bilevel games in restructured electricity markets with locational prices

CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context

Electricity Liberalisation in Britain: the quest for a satisfactory wholesale market design

Britain was the exemplar of electricity market reform, demonstrating the importance of ownership unbundling and workable competition in generation and supply. Privatisation created de facto duopolies that supported increasing price-cost margins and induced excessive (English) entry. Concentration was ended by trading horizontal for vertical integration in subsequent mergers. Competition arrived just as the Pool was replaced by New Electricity Trading Arrangements (NETA) intended to address its claimed shortcomings. NETA cost over £700 million, and had ambiguous market impacts. Prices fell dramatically as a result of (pre-NETA) competition, generating companies withdrew plant, causing fears about security of supply and a subsequent widening of price-cost margins.electricity, liberalisation, market design, market power

An exact solution method for binary equilibrium problems with compensation and the power market uplift problem

We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first order conditions of a linearization, or relaxation of integrality conditions. The reformulation offers a new approach to obtain and interpret dual variables to binary constraints using the benefit or loss from deviation rather than marginal relaxations. The method endogenizes the trade-off between overall (societal) efficiency and compensation payments necessary to align incentives of individual players. We provide existence results and conditions under which this problem can be solved as a mixed-binary linear program. We apply the solution approach to a stylized nodal power-market equilibrium problem with binary on-off decisions. This illustrative example shows that our approach yields an exact solution to the binary Nash game with compensation. We compare different implementations of actual market rules within our model, in particular constraints ensuring non-negative profits (no-loss rule) and restrictions on the compensation payments to non-dispatched generators. We discuss the resulting equilibria in terms of overall welfare, efficiency, and allocational equity