Unlike refueling an internal combustion engine vehicle, charging electric vehicles is time-consuming and results in higher energy consumption. Hence, charging stations will face several challenges in providing high-quality charging services when the adoption of electric vehicles increases. These charging infrastructures must satisfy charging demands without overloading the power grid. In this work, we investigate the problem of scheduling the charging of electric vehicles to reduce the maximum peak power while satisfying all charging demands. We consider a charging station where the installed chargers deliver a preemptive constant charging power. These chargers can either be identical or non-identical. For both cases, we address two optimization problems. First, we study the problem of finding the minimum number of chargers needed to plug a set of electric vehicles giving different arrival and departure times and required energies. We prove that this problem belongs to the complexity class P, and we provide polynomial-time algorithms. Then, we study the problem of minimizing the power grid capacity. For identical chargers, we prove that the problem is polynomial, whereas it is NP-hard in the case of non-identical chargers. We formulate these problems as a mixed-integer linear programming model for both cases. To obtain near-optimal solutions for the NP-hard problem, we propose a heuristic and an iterated local search metaheuristic. Through computational results, we demonstrate the effectiveness of the proposed approaches in terms of reducing the grid capacity.

与内燃机汽车加油不同，电动汽车充电非常耗时且能耗更高。因此，随着电动汽车普及率的提高，充电站在提供高质量充电服务方面将面临多项挑战。这些充电基础设施必须满足充电需求而不会使电网过载。在这项工作中，我们研究了调度电动汽车充电的问题，以降低最大峰值功率，同时满足所有充电需求。我们考虑一个充电站，其中安装的充电器提供先发制人的恒定充电功率。这些充电器可以相同，也可以不同。对于这两种情况，我们解决两个优化问题。第一的，我们研究的问题是，在不同的到达和出发时间以及所需能量的情况下，找到为一组电动汽车充电所需的最少充电器数量。我们证明这个问题属于复杂度类P，并且我们提供了多项式时间算法。然后，我们研究了电网容量最小化问题。对于相同的充电器，我们证明该问题是多项式的，而对于不同充电器的情况是 NP 困难的。对于这两种情况，我们将这些问题表述为混合整数线性规划模型。为了获得 NP 难问题的近乎最优解，我们提出了启发式和迭代局部搜索元启发式。通过计算结果，我们证明了所提出的方法在减少电网容量方面的有效性。