Power System Optimization Problems: Game Theory Applications

We look at the conflict situation in power system problems from an optimization perspective and use Game Theory (GT) concepts for modelling and solving the problem. In order to model the conflicts effectively, we first identify the players, the optimizing quantity and the optimizing platform. This paper details two power system problems and present a case study. We also identify two more areas where the same principles may be applied. Though our work focuses on Cooperative Game Theory (CGT), an extension to the NonCooperative Game Theory (NGT) platform is possible. Since GT is more relevant to a market structure, we use market engineering principles including multilateral trades, differential pricing, inverse elasticity rule, graph theoretical allocation, etc. as tools for organizing the optimization process. A useful addition for inducing stability in the decision making process is the concept of 'Power Vectors' borrowed from sports and game parlance for ceding players. Results are encouraging, with a transmission loss reduction of more than 70% in a five bus and 40% in a 24 bus system. We conclude that both versions of GT, the CGT and NGT are powerful tools for optimization in a practical scenario with conflicts and contradictory incentives.