Electric Vehicle Charging in Smart Grid: Optimality and Valley-Filling Algorithms

Electric vehicles (EVs) offer an attractive long-term solution to reduce the dependence on fossil fuel and greenhouse gas emission. At the same time, charging a large fleet of EVs distributed across the residential area poses a challenge for the distribution network. In this paper, we formulate this problem by building on the optimal power flow (OPF) framework to model the network constraints that arises from charging EVs at different locations. To overcome the computational challenge when the control horizon is long, we study a nested optimization approach to decompose the joint OPF and EV charging problem. We characterize the optimal EV charging schedule to be a valley-filling profile, which allows us to develop an efficient offline algorithm with significantly lower computational complexity compared to centralized interior point solvers. Furthermore, we propose a decentralized online algorithm that dynamically tracks the valley-filling profile. Our algorithms are evaluated on the IEEE 14 bus system with real residential load profiles, and the simulations show that our online algorithm performs almost optimally under different settings.