Models for Optimal Design of Capacity and Electricity Market

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OPTIMA - 2013

Alexander Vasin, Polina Kartunova Lomonosov Moscow State University Moscow, Russian Federation

Gerhard-Wilhelm Weber Middle East Technical University Ankara, Turkey

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Introduction.

What market architecture can provide an efficient capacity structure? Russia (and PJM): two-stage market, 1)Competitive Selection of Capacities (CSC) 2)Electricity Market (DAM). The CSC aims to choose a capacity structure that can satisfy the demand with minimal costs.

Determination of the optimal capacity structure under centralized planning is an optimization problem. Stoft (2002) and Davidson et al. (2010) consider some variants of this problem. We study a general setting of the problem with account of fixed and variable costs. We provide two algorithms that determine the optimal capacity structure with account of fixed and variable costs. The first one relates to the case where there are several capacity types, and for each type the capacity constraint is not binding. The second algorithm is applicable when electricity is produced by standard small generators with the same capacity and different costs. Then we study two typical architectures of the market and examine their Nash equilibria. We consider a uniform price supply function auction in the electricity market. For pay-as-bid and uniform price versions of the capacity market design, we compare the equilibrium outcomes with the optimal capacity structure. The paper shows that the market equilibrium corresponds to the optimal capacity structure under conditions of pure competition, full rationality, and completely informed agents in the market. However, under more realistic assumptions, selection of the optimal structure is unlikely. Finally we provide the auction design that realizes such selection of capacities and does not require any additional information of each producer besides his own production costs. We establish sufficient conditions for perfect competition in the market.

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Determination of optimal capacity structure.

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Determination of optimal capacity structure.

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Determination of optimal capacity structure.

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Determination of optimal capacity structure.

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Determination of optimal capacity structure with limited capacities.

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Determination of optimal capacity structure with limited capacities.

Uniform price auction at the CSC and DAM.

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Uniform price auction at the CSC and DAM.

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Optimal auction design.

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Conditions for perfect competition.

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References.

Vasin A., Kartunova P., Weber G.-W. (2013) “Models for Capacity and Electricity Market Design” // Central European Journal of Operations Research. Vol. 21, Issue 3, pp. 651-661 M. R. Davidson, Yu. V. Dogadushkina, E. M. Kreines, N. M. Novikova, Yu. A. Udaltsov, L. V. Shiryaeva (2004) “Mathematical Model of the Competitive Wholesale Power Market in Russia.” Izv. Ross. Akad. Nauk, Teor. Sist. Upr. No. 3, pp. 72–83 M. R. Davidson, Yu. V. Dogadushkina, E. M. Kreines, N. M. Novikova, A. V. Seleznev, Yu. A. Udaltsov, L. V. Shiryaeva (2009) “Mathematical Model of Power System Management in Conditions of Competitive Wholesale Power(Capacity).” Izv. Ross. Akad. Nauk, Teor. Sist. Upr. No 2, pp. 84–94 Myerson R. (1981) Optimal auction design // Mathematics of Operations Research. Vol. 6, № 1. pp. 58–73. Projected Balance for the electricity industry for 2008-2015 (2008) (The main provisions). JSC «Angecy for electric power balance forecasts» (ZAO "APBE") Russian Federation Government Resolution No 476, June 28 (2008) On Amendments to Certain Decrees of the Government of the Russian Federation on the Issues of Generating Capacity Competitive Trade on the Wholesale Electricity and Capacity Market Russian Federation Government Resolution No 1172, December 27 (2010) On the Amendments to Some Acts of the Government of the Russian Federation on the Issues of Organisation of Functioning of the Wholesale Market of Electric Energy and Power Ralph D., Smeers Y. (2011) “Pricing Risk Under Risk Measures: An Introduction to Stochastic-Endogenous Equlibria.” Published at SSRN: http://ssrn.com/abstract=1903897. Accessed 9 February 2012 Stoft S. (2002) “Power System Economics. Designing Markets for Electricity.” John Wiley & Sons Nash J.F. “Non-cooperative Games” // Annals of mathematics – 1951 - №54 –p.286-295 Vasin A.A, Vasina P.A.. “Auctions of a homogeneous good”. Proceedings of MTE, Hitachinaka, Ibaraki, Japan. 2006 Klemperer, P.D. (1999) “The economic theory of auctions: A guide to the Literature” // Journal of economic surveys, 13, 227-286