1 Introduction2 The model2.1 Modeling approach2.2 Model notations2.3 The Formulation3 The 24-bus System4 Concluding RemarksAcknowledgementReferencesCournot Equilibria in Two-Settlement Electricity Markets withSystem ContingenciesJian Yao, Shmuel S. Oren, Ilan AdlerDepartment of Industrial Engineering and Operations ResearchUniversity of California at Berkeley, Berkeley CA 94720{jyao, oren, adler}@ieor.berkeley.eduAbstract: We study Nash equilibrium in two-settlement competitive electricity marketswith horizontal market power, flow congestion, demand uncertainties and probabilistic systemcontingencies. The equilibrium is formulated as a stochastic Equilibrium Problem withEquilibrium Constraints (EPEC) in which each firm solves a stochastic Mathematical Programwith Equilibrium Constraints (MPEC). We assume a no-arbitrage relationship between theforward prices and the spot prices. We find that, with two settlements, the generation firms haveincentives to commit forward contracts, which increases social surplus and decreases spot energyprices. Furthermore, these effects are amplified when the markets become less concentrated. Keywords: Two Settlements, Cournot, Equilibrium Problem with EquilibriumConstraints.1 IntroductionThe last decade has witnessed a fundamental transformation of the electric power industryaround the world from one dominated by regulated vertically integrated monopolies to anindustry where electricity is produced and traded as a commodity through competitive markets. Inthe US, this transformation was pioneered in the late 1990s by California and the northeasternpower pools including Pennsylvania-New Jersey-Maryland (PJM) Interchange, New York andNew England. A recent arrival is the ERCOT market in Texas.While there are significant differences among the many implemented and proposed marketdesigns that vary in terms of ownership structure, level of centralization and the authority of thesystem operator, the primary rationale for electricity restructuring in most markets has been toreap welfare gains by supplanting regulation with competition. Both theory and experience fromother formerly regulated industries suggest that these gains will include increased efficiency ofshort-run production, of resource allocation and of dynamic investment.A potentially significant obstacle to these welfare gains is market power. Market powerexercised by suppliers typically entails the withholding of output and an upward distortion in themarket price. Market power is generally associated with various forms of economic inefficiency.Among the many proposed and implemented economic tools for mitigating market power is amultiple settlement approach wherein forward transactions, day-ahead transactions, and real timebalancing transactions are settled at different prices. The crisis in California in 2001 has drawnmore attention to the role of forward market in mitigating market power and in managing pricerisk in the electricity supply chain.Theoretical analysis [1, 2, 12] and empirical evidences [7, 9, 14,16] suggest that forwardcontracting and multi-settlement systems reduce the incentives of sellers to manipulate spotmarket prices since under a multi-settlement approach, the volume of trading that can be affectedby an increase in spot prices is reduced substantially. Thus, forward trading is viewed as aneffective way of mitigating market power at real time. Allaz [1] assumes a two-period market anddemonstrates that, if all producers have access to a forward market, it leads to a prisoners'dilemma type of game among them. Allaz and Vila [2] show that, as the number of forwardtrading periods increases, producers lose their ability to raise energy prices above their marginalcost. Kamat and Oren [12] analyze two-settlement markets over two- or three-node networks, andextend Allaz's results to a system with uncertain transmission capacities in the spot market. It isalso argued that setting prices at commitment time provides incentives for accurate forecastingand provides ex-ante price discovery that facilitates trading. Accurate forecasting and advancedscheduling of generation and load also improves system operation and reliability while reducingthe cost of reserves to handle unexpected deviations from schedule.While intuitively the above arguments in favor of forward trading and multi-settlementsystems are compelling, this studies typically ignores network effects, flow congestion, generatoroutages, and other system contingencies. When flow congestion, system contingencies, anddemand uncertainties are all present in the spot market, it is not clear to what extent producers arewilling to engage in forward transactions, or how their incentives will be thus affected.Furthermore, it is not well understood whether forward trading may in fact help producersexercise market power in the spot market to lock in or even increase their Oligopoly rents. Ifindeed forward trading can be used to mitigate the exercise of market power but generators havelittle incentive to engage in such trading, then a natural public policy question is whether forwardcontracting should be imposed as a regulatory requirement and the market be designed tominimize spot transactions. As a matter of fact, the current market rules in California and in Texasare designed to limit the scope of the real-time balancing markets through penalties or addedcharges.In this paper, we formulate the two-settlement competitive electricity markets as a two-period game, and its equilibrium as a subgame-perfect Nash equilibrium (see [8]) expressed as anEquilibrium Problem with Equilibrium Constraints (EPEC), in which each firm faces aMathematical Program with Equilibrium Constraints (MPEC, see [13])) parametric on otherfirms' forward commitments. We apply the model to an IEEE 24-bus test network. With thespecific data and simplifying assumptions of the example, it is shown that in equilibrium, firmscommit certain quantities in forward transactions and adjust their positions in the spot marketresponding to contingencies and demand realization. While this paper covers much of the sameground and employs the same modeling framework as [21], it extends the preliminary workreported in [21] in both content