A Stackelberg game model for Plug-in Electric Vehicles in a Smart Grid

In this paper, we consider and analyze a Stackelberg game model for Plug-in Electric Vehicles (followers) charging from a Smart Grid (leader). Our model attempts to account for the time-of-use pricing of the Smart Energy Meter using an indirect penalty approach. We show that a unique Stackelberg Equilibrium exists for the game under realistic conditions. To better understand the evolution of the game, we solve a monopolistic version of the game and then we solve the game for the general case. The solution we obtain is in closed form and tractable, yet reveals several important aspects of the game arising from the interplay between the vehicles and the grid. The results can be applied to both individual vehicles and vehicle groups. We show that, if the battery capacity of a particular vehicle model falls below the threshold battery capacity of the game, that model will be out of the market in the long run. We discuss the relation between the monopolistic game and the general game.