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 problem in a practical scenario where the non-causal information about future PEV arrivals is not known in advance, but its statistical distribution can be estimated. This leads to an "online" charging scheduling problem that is  formulated as a multistage stochastic programming (MSP) problem in this paper. Instead of solving the MSP using the standard approaches such as sample average approximation (SAA), we show that solving a deterministic counterpart of the stochastic problem yields significant complexity reduction with negligible performance loss. Compared with the SAA approach, the computational complexity of the proposed algorithm is drastically reduced from O(\epsilon^T) to O( T^3) per time stage , where T is the total number of the time stagesand \epsilon is a constant related to the accuracy of the solution. More importantly, we show that the proposed algorithm can be made scalable when the random process describing the arrival of charging demands is first-order periodic . That is , the complexity of obtaining the charging schedule at each time stage is O(1) and 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\\%DIF < in most cases. As such, the proposed online algorithm is very appealing for practical implementation due to its scalable computational complexity and close to optimal performance.abstract %DIF > in most cases.
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\\%DIF < in most cases. As such, the proposed online algorithm is very appealing for practical implementation due to its scalable computational complexity and close to optimal performance.abstract %DIF > in most cases.
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