A Game Theoretic Approach to Phase in Matlab

Abstract:

With the increasing penetration of renewable energy resources and plug-in electric vehicles (PEV) in the smart grid, the problem of phase imbalance in a three-phase distribution system becomes more challenging. In this paper, we propose a phase balancing (PB) scheme performed by PEVs. With PB remunerations introduced as financial incentives, PEV owners are encouraged to assist the distribution system operator in reducing the phase imbalance. Minimizing the phase imbalance problem, achieving system reliability and effective power flow to customers is essential. Genetic algorithm technique has been proved to be an efficient tool for solution of optimization problems. Formulation of an optimization problem for minimizing the phase imbalance in smart grid is proposed. An attempt is made to apply Genetic algorithm for finding an optimal solution for the phase imbalance problem arising in Smart grid due to the PEVs and DERs in smart grids. This is achieved by exploiting the charging flexibility of PEV batteries. We formulate this problem into a non-smooth non-cooperative game, where each PEV owner autonomously minimizes his/her charging cost minus the PB remuneration, considering decisions of other PEV owners. Through transforming this game into a smooth extended one, we are able to solve this challenging problem. Specifically, existence of its Nash equilibrium (NE) is demonstrated, and a distributed algorithm is developed to achieve the NE. Convergence proof of this algorithm is also provided. Simulation results validate our proposed scheme, and illustrate that both PEV owners and the distribution system operator will benefit financially. Moreover, the power quality and system reliability of the distribution network can also be improved.