Bayesian Nash Equilibrium in Electricity Spot Markets: An Affine-Plane Approximation Approach

This article proposes a system of stochastic mixed complementarity problems (MCP) for calculating the Bayesian Nash equilibrium (BNE) in an electricity spot market. The generators submit strategic multilevel price-offer functions under incomplete information about their rivals' marginal cost. This strategic multilevel price offering of each generator is modeled as a standard stochastic bilevel program which is then reformulated as its equivalent MCP. The merger concept is employed and formulated to model multilevel price-offer functions. We then propose the BNE-MCP model which solves the stochastic MCP models of all generators together. A scenario reduction technique is also developed to accurately model the wind and demand uncertainty in the proposed BNE-MCP model. The proposed BNE-MCP model is carefully studied on two illustrative examples. The modified IEEE 14-, 30-, and 57-node systems are also examined in our article.