On an equilibrium problem with complementarity constraints formulation of pay-as-clear electricity market with demand elasticity

We consider a model of pay-as-clear electricity market based on a Equilibrium Problem with Complementarity Constraints approach where the producers are playing a noncooperative game parameterized by the decisions of regulator of the market (ISO). In the proposed approach the bids are assumed to be convex quadratic functions of the production quantity. The demand is endogenously determined. The ISO problem aims to maximize the total welfare of the market. The demand being elastic, this total welfare take into account at the same time the willingness to pay of the aggregated consumer, as well as the cost of transactions. The market clearing will determine the market price in a pay-as-clear way. An explicit formula for the optimal solution of the ISO problem is obtained and the optimal price is proved to be unique. We also state some conditions for the existence of equilibria for this electricity market with elastic demand. Some numerical experiments on a simplified market model are also provided.

[1]  Alejandro Jofré,et al.  Monopolistic competition in electricity networks with resistance losses , 2010 .

[2]  Francisco Facchinei,et al.  Generalized Nash equilibrium problems , 2007, 4OR.

[3]  Didier Aussel,et al.  Electricity spot market with transmission losses , 2013 .

[4]  Daniel Ralph,et al.  Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices , 2007, Oper. Res..

[5]  Jirí V. Outrata,et al.  A Generalized Mathematical Program with Equilibrium Constraints , 2000, SIAM J. Control. Optim..

[6]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[7]  Masao Fukushima,et al.  Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games , 2009, Comput. Manag. Sci..

[8]  Didier Aussel,et al.  Nash equilibrium in a pay-as-bid electricity market: Part 1 – existence and characterization , 2017 .

[9]  P. Bendotti,et al.  Nash equilibrium in a pay-as-bid electricity market Part 2 - best response of a producer , 2017 .

[10]  René Henrion,et al.  ANALYSIS OF M-STATIONARY POINTS TO AN EPEC MODELING OLIGOPOLISTIC COMPETITION IN AN ELECTRICITY SPOT MARKET ∗ , 2012 .

[11]  Sven Leyffer,et al.  Solving multi-leader–common-follower games , 2010, Optim. Methods Softw..

[12]  P. Klemperer,et al.  Supply Function Equilibria in Oligopoly under Uncertainty , 1989 .

[13]  B. Hobbs,et al.  Complementarity Modeling in Energy Markets , 2012 .

[14]  Didier Aussel,et al.  Deregulated electricity markets with thermal losses and production bounds: models and optimality conditions , 2016, RAIRO Oper. Res..

[15]  Andreas Fischer,et al.  On generalized Nash games and variational inequalities , 2007, Oper. Res. Lett..

[16]  Jirí V. Outrata,et al.  A note on a class of equilibrium problems with equilibrium constraints , 2004, Kybernetika.

[17]  Masao Fukushima,et al.  Variational Inequality Formulation of a Class of Multi-Leader-Follower Games , 2011, J. Optim. Theory Appl..