Energy-Efficient Speed Profile Approximation: An Optimal Switching Region-Based Approach with Adaptive Resolution

Abstract

Speed profile optimization plays an important role in optimal train control. Considering the characteristics of an electrical locomotive with regenerative braking, this paper proposes a new algorithm for target speed profile approximation. This paper makes the following three contributions: First, it proves that under a certain calculation precision, there is an optimal coast-brake switching region-not just a point where the train should be switched from coasting mode to braking mode. This is very useful in engineering applications. Second, the paper analyzes the influence of regenerative braking on the optimal coast-brake switching region and proposes an approximate linear relationship between the optimal switching region and the regeneration efficiency. Third, the paper presents an average speed equivalent algorithm for local speed profile optimization in steep sections. In addition, this paper simplifies the proof of the optimality of smooth running on a non-steep track in two steps. The effects on energy consumption from two important factors (optimal coast and running time) are systematically analyzed. Extensive simulations verify these points of view and demonstrate that the proposed approximation approach is computationally efficient and achieves sufficient engineering accuracy.

SmartDrive: Traction Energy Optimization and Applications in Rail Systems

“…The running time with minimum cruising speed should fulfil the longest running time constraint. Therefore, _ is given by (10).…”

“…The GA performed quite poorly and failed to converge to a good solution in some certain circumstances. The speed profile optimization, which is a complex global optimization problem, is transformed into a simple local optimization problem in [10]. An adjusted algorithm is proposed to search for an optimal coast-brake switching region rather than just one point.…”

The Energy-Efficient Operation Problem of a Freight Train Considering Long-Distance Steep Downhill Sections

“…Further study is proposed to solve the problem with the speed constraint. According to Equation (15) and Theorem 1, two complementary slackness factors (M(x) and T(x)) are introduced [14,38]:…”

Energy — Efficient Operation in Subway Systems: Tracking Optimal Speed Profile with on Board Supercapacitor Energy Storage System

“…Iannuzzi et al (5) using onboard SCESS integrated with traction drive system saves energy to 38%, reducing peak power up to 50% in accelerating regime, stabilizing voltage on DC bus to 1%, increasing power supply distance among traction substations ; Dominguez et al released a study of energy consumption reduction to 24% in the Metro de Madrid (7) ; Michael Steiner et al (8) shows Bombardier installed Mitrac energy saver being able to reduce the consumption of the traction energy to 30% and line current peak and voltage drop by 50% ; Diego Iannuzzi, Flavio Ciccarelli, Davide Lauria (12) use stationary ultra-capacitor storage device for improving energy saving and voltage profile of light transportation networks; reversible substations (17,18) ; maximizing the regenerative energy exchange between trains by synchronizing their accelerating and braking phases as much as possible (19)(20)(21) , Fathy Ahmed et al (22) applied parasitism-predation algorithm (PPA) in the energy management strategy for hybrid photovoltaic/fuel cell/battery/supercapacitor to minimize the hydrogen consumption of fuel cell; Jamadar Najimudin et al (23) developed regenerative braking system (RBS) and braking energy management techniques, considering different driving situations and road conditions which employed in addition to mechanical braking for increasing the braking efficiency of the electric vehicle system. Additionally, another energy saving approach which has also attracted more attention from experts is to find optimal speed profile by two methods: the Mathematical and Optimal theory (Maximum principle, Dynamic programming, Linear programming); the other one is the Computational Intelligence (Fuzzy neural networks, Genetic Algorithm, Predictive control, Colony Optimization Algorithm) (24)(25)(26) . A group of scientists at the University of South Australia Howlett et al (27,28) , Vu (29) , and Albrecht et al (30,31) systematically have researched optimal strategies using mathematical approaches and optimal theory to propose control laws to detect optimal switching points, then finding the optimal speed profile, and others, Khmelnitsky (32) attempted to solve the problem of optimal control by applying the Pontryagin's maximum principle and adjoint variables, which consider regenerative braking, Liu et al (33) uses the maximum principle for finding a set of optimal controls, the control switching graphs, and complementary conditions of optimality.…”