Abstract
The significant energy consumption for railway electric transportation operation poses a great challenge in outlining saving energy solutions. Speed profile optimization based on optimal control theory is one of the most common methods to improve energy efficiency without the railway infrastructure investment costs. The paper proposes an optimization method based on Pontryagin's Maximum Principle (PMP), not only to find optimal switching points in three operation phases: accelerating, coasting, braking, and from these switching points being able to determine the optimal speed profile, but also to ensure fixed-trip time. In order to determine trip time abiding by the scheduled timetables by applying nonlinear programming puts the Lagrange multiplier λ in the objective function regarded as a time constraint condition. The correctness and energy effectiveness of this method have been verified by the simulation results with data collected from the electrified trains of the Cat Linh-Ha Dong metro line in Vietnam. The saving energy levels are compared in three scenarios: electrified train operation tracking the original speed profile (energy consumption of the route: 144.64kWh), train operation tracking the optimal speed profile without fixed-trip time (energy consumption of the route: 129.18kWh), and train operation tracking the optimal speed profile and fixed trip time (energy consumption of the route: 132.99kWh) in an effort to give some useful choices for operating metro lines.
Highlights
With the worldwide booming of urbanization, people face the increased carbon emission problem and the traffic congestion to affect their quality of live
The simulations are based on the data of Cat Linh-Ha Dong metro line
Assessing the levels of energy savings follow 3 scenarios: energy consumption with original speed profile with fixed trip time, energy consumption with optimal speed profile with fixed trip time, and energy consumption with optimal speed profile but with trip time which is less by 1s in each station
Summary
With the worldwide booming of urbanization, people face the increased carbon emission problem and the traffic congestion to affect their quality of live. Authors in [5,6,7,8,9] systematically researched optimal strategies using mathematical approaches and the Optimal theory to propose control laws to detect the optimal switching points and to find the optimal speed profile whereas authors in [10] attempted to solve the problem of optimal control by applying the Pontryagin's Maximum Principle (PMP). Authors in [14] designed the speed profile giving guarantees of running time and saving energy consumption. Authors in [19] dealt with speed profile optimization using Pontryagin's Maximum Principle (PMP) and achieved energy-saving but did not guarantee fixed running time in the Cat Linh - Ha Dong metro line in Vietnam. The simulation results with three diffirent seniories showed the effectiveness of PMP optimal control method in saving energy of train operation without any changes of infrustructure or facilities
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