Stochastic co-optimization of charging and frequency regulation by electric vehicles

Smart electrical grid infrastructure, such as advanced metering, will enable demand side participation in electrical energy and ancillary services markets. Deterministic optimization models have been proposed for minimizing the cost of charging electric vehicles (EVs) in liberalized market settings. These models include revenues that EVs could earn by providing ancillary services such as secondary frequency regulation. Optimization models currently in the literature do not account for the uncertainty in the costs and benefits of providing regulation. We propose a stochastic dynamic programming method to optimize EV charging and frequency regulation decisions under uncertainty. Expected future costs are included in decision problems as convex piecewise-linear approximations of non-convex value functions. Simulations demonstrate the benefit of charging an EV using our method over an expected value dynamic programming scheme. We also show that the proposed method gives high quality solutions.