Optimizing the Energy Delivery via V2G Systems Based on Stochastic Inventory Theory

In this paper, we study the optimal energy delivery problem from viewpoints of both the vehicle owner and aggregator, in load shaving services of a vehicle-to-grid (V2G) system. We formulate the optimization problem based on a general plug-in hybrid electric vehicle (PHEV) model, taking into account the randomness in vehicle mobility, time-of-use electricity pricing, and realistic battery modeling. Stochastic inventory theory is applied to analyze the problem. We mathematically prove that a state-dependent $(S,S^{\prime})$ policy is optimal for the daily energy cost minimization of each vehicle, and develop an estimation algorithm to calculate the parameters of the optimal policy for practical applications. Furthermore, we investigate the multi-vehicle aggregator design problem by considering the power system constraints. A policy adjustment scheme is proposed to adjust the values of $S$ and $S^{\prime}$ with respect to the optimal policy adopted by each PHEV, such that the aggregated recharging and discharging power constraints of the power system can be satisfied, while minimizing the incremental cost (or revenue loss) of PHEV owners. Based on characteristics of the state-dependent $(S,S^{\prime})$ policy and our proposed policy adjustment scheme, the optimal aggregator operation problem is transformed into a convex optimization one which can be readily solved by existing algorithms. The performance of our proposed schemes is evaluated via simulations based on real data collected from Canadian utilities, households, and commuters.