考虑客流空间分布的地铁列车节能时刻表优化方法

客流变化引起的列车质量变化是影响地铁列车能耗与节能运行的重要因素之一. 本文考虑地铁线路客流空间分布差异，研究耗散型再生制动能利用方式下的列车节能时刻表优化方法. 结合各区间载荷差异和列车运动方程，建立以净能耗最小为目标的时刻表优化模型，通过适度优化计划停站时间、区间运行时间和折返时间协同多列车牵引、巡航、惰行和制动过程的时空分布，设计二分法和粒子群算法对模型求解. 以北京地铁某线路进行实例研究，结果表明，优化模型能有效协同多列车的节能运行，考虑客流空间分布差异比假定列车载荷为常数能进一步提升节能效果.

An Energy-efficient Timetable Optimization Method for Metro Operation Considering Spatial Distribution of Passenger Flow

Section passenger variation is a key factor to change the weight of metro trains which can affect their energy consumption and energy-efficient operation. An energy-efficient timetable optimization method incorporated with an unbalance spatial distribution of passenger flow is proposed for metro train operation under the dissipative regenerative braking mode. Based on the load variation and train motion equation, a timetable optimization model aiming at minimizing the net energy consumption is established to coordinate the temporal and spatial distribution of traction, cruising, coasting, and braking trains by adjusting their planned running times, dwell times, and turnaround times in a modest range. The dichotomy and particle swarm optimization algorithms are designed to solve the proposed model. The results from a case study based on one metro lines in Beijing show that the proposed method could effectively coordinate the energy-efficient operation of multiple trains. Besides, by considering the variation of section passenger flow, the timetable optimization model can further improve the energy-saving performance compared with the scheme that assumes the train load is constant.