Optimizing Electric Rail Energy Consumption Using the Lagrange Multiplier Technique

Abstract

In the railway sector, one of the sensitive issues to be borne very much in mind is the cost brought about by the energy consumption required to meet schedules, be they local trains, metropolitan systems, or long-distance trains. To reduce energy consumption, considering restrictions like traveling time or speed limits, it is necessary to find a solution for a complex problem in the domain of optimal control theory (OCT). The analytical solution for those problems is not easily carried out. A simpler alternative to that approach is presented in this paper, using a semianalytical solution that leads to a discretization and to the application of the Langrage multipliers method to solve the optimization of n-tuples of speed. With the solution introduced in this work, is possible to include all the details about train operation, such as timetable restrictions or braking types. In the full paper, the detailed solution is presented as well as some real cases to illustrate the method results.