Energy-efficient speed profile: an optimal approach with fixed running time

Abstract

Tracking the optimal speed profile in electric train operation has been proposed as an efficient and feasible solution for not only reducing energy consumption, but also no at costs to upgrading the existing railway systems. This paper focuses on finding the optimal speed profile based on Pontryagin’s maximum principle (PMP) while ensuring the fixed running time, and comparing energy saving levels in the cases of applying or not applying PMP. The way to determine the fixed running time also differs from works published is to calculate the total trip time equal to scheduled timetable exactly. Calculating accelerating time t_a, coasting time t_c, braking time t_b via values of maximum speed v_h, braking speed v_bof optimal speed profile. The other hands, v_h and v_bare determined by solving nonlinear equations with constraint condition: the running time equal to the demand time. Simulation results with data collected from electrified trains of Cat Linh-Ha Dong metro line, Vietnam show that energy reduction for the entire route when PMP utilization is up to 8.7% and running time complied with scheduled timetables.