Energy-efficient train reference speed profile optimization using control parameterization method

Abstract

With the expansion of high-speed railway network, the issue of train energy consumption becomes more serious and attracts much greater concerns. One of the important ways of saving energy is to find the energy-efficient train reference profile, which actually is a problem of optimal control. In this paper, the control parameterization method, a general and efficient numerical approach, is employed to solve the optimal train control problem. The objective function is to minimize the train energy consumption with a penalty on the control variation subjected to fixed travel time, traction and braking forces restriction and safety speed limit. Using the control parameterization technique, the train control force is approximated by a piecewise-constant function and the original train control problem is transformed into a nonlinear programming problem which can be solved efficiently. The numerical results indicate that the proposed method can obtain the optimal train reference profile which guarantees minimum energy consumption. Moreover, by increasing the penalty factor against control variation, the smoothness of train reference profile is significantly improved while the train energy consumption is almost unchanged.