A Game-Theoretic Approach for Electric Vehicle Aggregators Participating in Phase Balancing Considering Network Topology

With the increasing popularity of electric vehicles (EVs), uncontrolled charging of single-phase plug-in EVs will result in severe three-phase unbalance problem in distribution networks. To solve the problem, a phase balancing (PB) scheme performed by EV aggregators (EVAs) based on the linear multiphase power flow model is proposed in this paper. In the scheme, the PB compensations are provided to encourage EVAs to help the distribution system operator reduce the phase unbalance of the entire grid. Considering all EVAs are selfish and rational, the PB scheme is formulated as a game problem, in which each EVA competes with other EVAs to determine its charging strategy to minimize the charging cost minus the PB compensation. The consideration of coupling voltage constraints leads this game model to a challenging generalized Nash equilibrium problem (GNEP). By employing the theory of variational inequality, the properties of solutions for the GNEP are investigated. Furthermore, a two-level distributed algorithm is designed to find the unique variational solution, a fair and stable solution. Finally, comprehensive case studies are conducted on the IEEE-13 and IEEE-123 test systems to corroborate that the proposed PB game model can effectively mitigate voltage unbalance and cut EV users' costs.