A Game Theoretic Approach to Phase Balancing by Plug-In Electric Vehicles in the Smart Grid

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. 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.