Grid Connection of Shared Electric Vehicles

The paper examines the decision of whether to connect electric vehicles, for grid-balancing purposes, to an electric power grid, in addition to renting them out on a car-sharing market. Because grid connection tends to degrade a battery over and above its expected loss of recharge capacity due to normal rental use, an operator needs to make state-contingent dynamic decisions about making the battery-electric fleet available to a power grid. An optimal policy needs to implement the best tradeoff between the additional degradation of the battery from grid sharing and the expected additional revenue. We formulate a continuous-time optimal control problem to identify the fleet operator’s profit-maximizing grid-connection policy. Closed-form solutions are obtained are obtained via dynamic optimisation using optimal control theory. We characterise the optimal grid-connection policy for different parameter configurations, showing that there can be three potentially optimal operating regimes: no grid sharing, permanent grid sharing, or partial grid sharing. We find that permanent grid sharing dominates no grid sharing if and only if the expected feed-in revenue exceeds the difference in the rental revenues due to the shorter battery life induced by connecting to the grid. Furthermore, it is best to connect vehicles with relatively new batteries to the grid and as the battery state declines to take them off the grid, specializing the vehicle car-sharing. A closed-form solution is obtained for the optimal switching time. And, the battery lifetime is determined endogenously.