A new pricing scheme for a multi-period pool-based electricity auction Eugeniusz Toczyłowski, Izabela Zoltowska * ,1 Warsaw University of Technology, Institute of Control and Computation Engineering, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland article info Article history: Received 1 December 2006 Accepted 11 December 2007 Available online 14 March 2008 Keywords: OR in energy Electricity market Energy pricing Thermal units Dynamic and integer programming Unit commitment abstract A new pricing scheme is proposed for determining the social welfare distribution in a centralized pool- based auction in the context of solving the unit commitment problems under competition. A significant contribution of this paper over previous publications on this subject is the inclusion of the price-respon- sive demand side for the multi-period auctions with dynamic commitment characteristics. The model allows every thermal unit and every consumer to obtain individual maximum profits, and at the same time it gives the market coordinator an adequate tool for solving the ensuing technologically constrained unit commitment problem with fair market clearing. The pricing model is in the form of a mixed linear programming model that minimizes the sum of the compensation costs. The accompanying case study illustrates the approach proposed. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Pool-type auctions are an important group of possible spot mar- ket designs that can be well suited coordination mechanisms for short-term trading on the centralized electricity markets. The pool scheduling problem can be stated as a day-ahead multi-period auc- tion. Mathematically, it can be formulated as the unit commitment optimization problem under competition, that balances production offers (sell bids) with inelastic (or elastic) demand over horizon of several periods of time. The basic goals of the pool scheduling problem can be to maximize the net social welfare through the production and consumption of electricity together with fair distri- bution of the economic surplus among the market participants. The centrally-determined pool operational schedule results from solv- ing a mixed integer linear (MILP) or nonlinear (MINP) mathemati- cal programming problem that may take into account security constraints, the generation unit capacity constraints, the produc- tion characteristics of thermal units, including up and down ramp constraints, minimum start-up and minimum shut-down commit- ment constraints, etc. The spot market rules must assure feasibility of the system operation together with efficient energy production and maximization of the social welfare objective function, see Ar- royo and Conejo (2002), Baldick et al. (2005). The appropriate rules for market pricing of energy and ancillary services are the key spot market design issues. It is now widely rec- ognized that fair market clearing and determination of welfare dis- tribution cannot be performed upon the uniform marginal prices scheme due to indivisibilities and non-convexities existing in the pool-based market models (Bouffard and Galiana, 2005; Galiana et al., 2003; Garcia-Bertrand et al., 2005; Doorman and Nygreen, 2003; Madrigal and Quintana, 2001; Motto and Galiana, 2004; Motto and Galiana, 2002; O’Neill et al., 2005). The uniform com- modity marginal prices generally associated with the electricity pool are not always able to coordinate the self-interested, profit- seeking generators to meet the demand. The centrally-determined pool operational schedule may be incompatible with self-schedule of the profit-driven independent generators. In other words, mar- ginal pricing of energy is not sufficient to assure efficient self-com- mitted schedules and to support equilibrium allocations in the auction-based markets. Therefore, a variety of market-based mech- anisms have been proposed in the literature to bridge the social welfare objectives of the pool with those of the profit-seeking mar- ket participants (Galiana et al., 2003; Garcia-Bertrand et al., 2005; Doorman and Nygreen, 2003; Madrigal and Quintana, 2001; Motto and Galiana, 2004; Motto and Galiana, 2002). In Section 2 we dis- cuss various known market clearing approaches to welfare distri- bution in the pool-based electricity markets. In this paper, a new pricing scheme is proposed for determining the fair social welfare distribution in a centralized multi-period pool-based market in the context of solving the unit commitment problems under competition. The pricing model can be considered as a separate step of the market clearing procedure, after the social welfare has been maximized by solving a unit commitment 0377-2217/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2007.12.048 * Corresponding author. Tel.: +48 22 234 7397; fax: +48 22 825 3719. E-mail addresses: E.Toczylowski@ia.pw.edu.pl (E. Toczyłowski), I.Zoltowska@ elka.pw.edu.pl (I. Zoltowska). 1 The research was supported in part by the Ministry of Science of Poland through Projects 3T11C 005 27 and PBZ-MEiN 1/2/2006. European Journal of Operational Research 197 (2009) 1051–1062 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor