Gaming Strategy for Electric Power With Random Demand

Recent work has shown that the profit maximizing problem for a generator in a competitive electricity market can be written as a mathematical program with equilibrium constraints (MPECs). In this paper, the problem of optimal generator bidding when there is a single demand is considered. The simplifications to the MPEC afforded by the assumption on the demand are shown. When the demand is stochastic and assumed to be normally distributed, the optimization that each player undertakes is written as a chance constrained program. It is shown that the solution to this stochastic problem can be found by solving a deterministic MPEC. The problem is considered with and without supply capacity constraints. By considering each of these cases as a game theory problem, the existence and uniqueness of Nash points are analyzed. These properties of the Nash point are then inferred onto the stochastic problem.