This document summarizes models for optimal design of capacity and electricity markets. It discusses determining the optimal capacity structure under centralized planning as an optimization problem. It provides two algorithms for determining the optimal capacity structure while accounting for fixed and variable costs. One algorithm applies when there are several capacity types and capacity constraints are not binding, and the other applies when electricity is produced by standard small generators with the same capacity and different costs. It also examines Nash equilibria for two market architectures and compares equilibrium outcomes to the optimal capacity structure. Finally, it provides an auction design that can select the optimal capacity structure without requiring additional information from producers beyond their own production costs.

1. Models for Optimal Design of
Capacity and Electricity Market
1
OPTIMA - 2013
Alexander Vasin, Polina Kartunova
Lomonosov Moscow State University
Moscow, Russian Federation
Gerhard-Wilhelm Weber
Middle East Technical University
Ankara, Turkey

2. 2
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.

3. 3
Determination of optimal capacity structure.

4. 4
Determination of optimal capacity structure.

5. 5
Determination of optimal capacity structure.

6. 6
Determination of optimal capacity structure.

7. 7
Determination of optimal capacity structure with
limited capacities.

8. 8
Determination of optimal capacity structure with
limited capacities.

9. Uniform price auction at the CSC and DAM.

10. 10
Uniform price auction at the CSC and DAM.

11. 11
Optimal auction design.

12. 12
Conditions for perfect competition.
…

13. 13
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