Game Theory Application for Finding Optimal Operating Point of Multi-production System Under Fluctuations of Renewable and Various Load Levels

Abstract

In order to implement sustainable and efficient energy supply, precise mathematical tools are needed to determine an appropriate strategy at different levels of planning and operation. To this end, oligopoly equilibrium models, such as Cournot models, Bertrand models, and supply function equilibrium (SFE) models, draw the attention in the analysis of power system recently. The decision variables in SFE models are the parameters of supply functions rather than quantity and price as in the Cournot and Bertrand models. In this chapter, we first study different game theory models and their applications in power system. Then, an appropriate model is selected to formulate the optimization problem for finding the optimal operating point of the multi-production system. The study includes fluctuations of renewable energy resources, various load levels, and the market environment. Two game models based on deterministic and stochastic approaches are proposed, formulated, and investigated. Finally, the results and numerical study are presented to verify the efficiency of game models.