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A Model Predictive Control Approach for Low-Complexity Electric Vehicle Charging Scheduling: Optimality and Scalability

With the increasing adoption of plug-in electric vehicles (PEVs), it is critical to develop efficient charging coordination mechanisms that minimize the cost and impact of PEV integration to the power grid. In this paper, we consider the optimal PEV charging scheduling, where the non-causal information about future PEV arrivals is not known in advance, but its statistical information can be estimated. This leads to an "online" charging scheduling problem that is naturally formulated as a finite-horizon dynamic programming with continuous state space and action space. To avoid the prohibitively high complexity of solving such a dynamic programming problem, we provide a Model Predictive Control (MPC) based algorithm with computational complexity $O(T^3)$, where $T$ is the total number of time stages. We rigorously analyze the performance gap between the near-optimal solution of the MPC-based approach and the optimal solution for any distributions of exogenous random variables. Furthermore, our rigorous analysis shows that when the random process describing the arrival of charging demands is first-order periodic, the complexity of proposed algorithm can be reduced to $O(1)$, which is independent of $T$. Extensive simulations show that the proposed online algorithm performs very closely to the optimal online algorithm. The performance gap is smaller than $0.4\%$ in most cases.