纯电动公交车以其低排放、低噪声等优点在公交系统中得到越来越广泛的应用。然而相对较短的车辆续航里程和较长的充电时间使其在运营中需要频繁充电，从而衍生出新的充电计划问题。合理的充电方案对于节省充电设施建设成本和缩减充电成本等方面均有重要意义。目前电动公交充电计划优化的研究通常将充电时长与充电量设定为线性关系，且较少考虑充电计划与充电桩作业流程的综合优化，导致充电场景还原性差和资源浪费等问题。为此，在给定车次安排的前提下进一步优化电动公交充电计划，构建了以最小化系统总成本为目标的混合整数规划模型，对充电事件的发生时段、充电开始与结束时间以及充电桩作业流程进行同步优化，且充分考虑了分时电价政策、不完全充电策略和电池的非线性充电特性。在问题求解方面，首先通过线性近似的方式将电池的非线性充电曲线改写为分段线性函数，进而利用商业求解器 Gurobi 得到最优方案；之后基于最小费用最大流理论与逆差函数设计了一套专门的优化算法；最后，以北京市5条公交线路为例设计多组实验，并分别应用 Gurobi 与本文设计的算法进行优化求解。优化结果验证了所提出算法的准确性与高效性，可使当前充电系统总成本降低28.34%~56.1%。

Battery electric buses are increasingly applied and promoted in public transportation systems due to their advantages, such as low emissions and low noise levels. However, their limited driving range and long charging time necessitate frequent charging during daily operations, thus leading to a new charging scheduling problem. A reasonable charging schedule is of great significance in reducing the construction cost of charging facilities and charging costs. However, current research on optimizing electric bus charging schedules typically assumes a linear relationship between charging time and state of charge (SOC), and often neglects the comprehensive optimization of charging schedules and charging station operations, resulting in poor scenario reproduction and resource inefficiencies. Therefore, this paper further studied the optimization of charging schedules based on a predefined set of bus trip schedules. A mixed-integer programming model was developed to minimize the total system cost by optimizing the occurrence periods, the start and end times of charging, and the schedules of the charging piles synchronously. The model also fully considers time-of-use electricity pricing policy, partial charging strategies, and the nonlinear characteristics of battery charging. To solve the problem, this paper first linearized the nonlinear charging function of the battery into a piecewise linear one and then used the commercial solver Gurobi to obtain the optimal solution. Additionally, a tailored algorithm was designed based on the minimum-cost-maximum-flow theory and the deficit function. Multiple sets of experiments were conducted to validate the effectiveness of the proposed algorithm based on five bus routes in Beijing. The results, obtained through both Gurobi and the proposed optimized algorithm, demonstrate that the proposed algorithm can achieve a significant reduction in total system costs, ranging from 28.34% to 56.1% across various scenarios. These findings confirm the efficiency of the algorithm and its potential to optimize charging schedules effectively.