5. Conclusion
This paper proposes a multi-objective formulation for the optimal charging schedule of EVs with N − 1 security constraints. An EV aggregator representing a cluster of controllable EVs is modeled for determining the optimal charging schedule based on a trilevel hierarchy. On the top level, the grid control center determines the EV charging strategy from the proposed formulation, where bus voltage fluctuations, network power losses, and EV charging adjustments are considered as multi-objective functions. To reduce the computational burden, Lagrangian Relaxation (LR) is introduced to handle time- coupled constraints, and Benders Decomposition is introduced to decompose the EVs charging formulation into one master problem that solves the basecase charging schedule and a set of slave problems that check the feasibility of the obtained charging schedule against the security constraints under individual contingencies. Case studies have been conducted to demonstrate the effectiveness of the proposed formulation and solution method. The results show that the proposed charging strategy can solve the potential security problems of the system, and the portfolio optimization can preferentially select the optimal schedule to improve the system voltage profile, reduce the system power losses, and improve the user satisfactions. In this paper, unit commitment is set in advance. A better strategy could be obtained by the co-optimization of the EV charging with unit commitment. In addition, we only discuss the optimization strategy of the control center. Future works can be done to the optimization strategy of the EVs aggregator, which may provide more exact limits of charging power of EV aggregators to the control center.
