A potential game framework for charging PHEVs in smart grid

Due to the proliferation of plug-in hybrid electric vehicles (PHEVs), the peak load in the power grid is expected to increase in future. The peak load can be reduced by implementing appropriate load scheduling schemes using advanced metering infrastructure (AMI) and smart chargers. In this paper, we formulate the charging problem of PHEVs as a potential game to jointly optimize the cost of the utility company and payoff of the customers. The potential game approach enables us to study the existence and uniqueness of the pure strategy Nash equilibrium and to design a polynomial time distributed algorithm to achieve that equilibrium. It also enables us to define a Lyapunov function to show that the Nash equilibrium is globally asymptotically stable, i.e., the proposed distributed algorithm converges to the Nash equilibrium from any arbitrary initial conditions. To evaluate the efficiency of our proposed algorithm, we compare its running time with an algorithm based on the customers´ best response.