Optimization of Driving Speed of Electric Train Using Dynamic Programming Based on Multi-Weighted Cost Function

Abstract

Trains are a large-capacity means of transportation, and they are preferred for long as well as short distances. Although trains are one of the most efficient modes of transportation for freight and passengers, they consume a significant amount of energy. Therefore, energy-efficient approaches have been studied over the years. Various optimal-control methods that integrate dynamic programming (DP) algorithms have been introduced to reduce the overall energy consumption. The purpose of optimizing the operation speed of the train according to the operating conditions using the DP algorithm is to find a speed profile that consumes minimum energy, under the condition that the target travel time is satisfied according to the given mileage. Here, a specific weight is applied to the cost function to find a velocity profile that satisfies the target travel time. In this case, the computation time increases proportionally to the number of times the weight is changed. In addition, because the weight versus the target travel time has a non-linear characteristic, various approaches have been proposed to reduce the number of iterations according to the weight change to satisfy the target travel time. This study suggests a method to quickly and effectively find the optimal solution for electric trains in a different way from previous studies. We present a DP algorithm for matrix processing, by arranging multiple weights within the applicable minimum and maximum weights and applying them to the cost function. The time taken to find the optimal solution can be reduced by half compared to the existing one, and the travel time and energy consumption corresponding to each weight can be checked at once. In addition, this result can be used as an indicator for effectively changing or establishing an electric-train operation plan. For a detailed comparison between the proposed and existing methods, the execution time results for each number of weights under the same calculation conditions are presented. In addition, to verify that there are no errors in the multi-weighting process, some of the multi-weighting coefficients were used to check whether the speed profile in the single-weighted calculation method was consistent.

Keywords

• energy optimization
• optimal control
• electric train
• speed profile
• dynamic programming
• cost function