A novel method for determining fixed running time in operating electric train tracking optimal speed profile

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<span lang="EN-US">Tracking the optimal speed profile in electric train operation has been proposed as a potential solution for reducing energy consumption in electric train operation, at no cost to improve infrastructure of existing Metro lines as well. However, the optimal speed profile needs to meet fixed running time. Therefore, this paper focuses on a new method for determining the fixed running time complied with the scheduled timetable when trains track the optimal speed profile. The novel method to ensure the fixed running time is the numerical-analytical one. Calculating accelerating time ta, coasting time tc, braking time tb via values of holding speed vh, braking speed vb of optimal speed profile with the constraint condition: the running time equal to the demand time. The other hands, vh and vb are determined by solving nonlinear equations with constraint conditions. Additionally, changing running time suit for each operation stage of metro lines or lines starting to conduct schedules by the numerical-analytical method is quite easy. Simulation results obtained for two scenarios with data collected from electrified trains of Cat Linh-Ha Dong metro line, Vietnam show that running time complied with scheduled timetables, energy saving by tracking optimal speed profile for the entire route is up to 8.7%, if the running time is one second longer than original time, energy saving is about 11.96%.</span>