# Modelling bilevel games in electricity

1 May 2003
14:00
Dr Danny Ralph
Abstract
Electricity markets facilitate pricing and delivery of wholesale power. Generators submit bids to an Independent System Operator (ISO) to indicate how much power they can produce depending on price. The ISO takes these bids with demand forecasts and minimizes the total cost of power production subject to feasibility of distribution in the electrical network. \\ \\ Each generator can optimise its bid using a bilevel program or mathematical program with equilibrium (or complementarity) constraints, by taking the ISOs problem, which contains all generators bid information, at the lower level. This leads immediately to a game between generators, where a Nash equilibrium - at which each generator's bid maximises its profit provided that none of the other generators changes its bid - is sought. \\ \\ In particular, we examine the idealised model of Berry et al (Utility Policy 8, 1999), which gives a bilevel game that can be modelled as an "equilibrium problem with complementarity constraints" or EPCC. Unfortunately, like bilevel games, EPCCs on networks may not have Nash equilibria in the (common) case when one or more of links of the network is saturated (at maximum capacity). Nevertheless we explore some theory and algorithms for this problem, and discuss the economic implications of numerical examples where equilibria are found for small electricity networks.
• Computational Mathematics and Applications Seminar