Energy-efficient Train Operation Optimization Using Control Parameterization Method

An optimal control model for energy-efficient train operation was established, with the objective to minimize the train tractive energy consumption subjected to fixed travel time, variable track slope, arbitrary speed restriction, tractive and braking forces bounds, as well as driving comfort of the train. Using the control parameterization method, the optimal train control problem was transformed into a nonlinear programming(NLP) problem, which took the constant train control forces on each subsection as its optimal parameters. In order to overcome the problem that the conventional method can not effectively deal with the step-type speed limit, a discretization method was presented to simplify the infinite dimension constraint into finite dimension inequality constraints. Considering that the upper bound of the traction force was a non-smooth function of train speed, a quadratic function was employed to smooth the train traction characteristic curve firstly, with the upper bound constraint being converted into an inequality constraint as the next step. The finally transformed NLP problem can be solved readily by sequential quadratic programming(SQP) algorithm. Simulation results indicated that, using the proposed scheme, the optimal train control forces and the corresponding reference speed profile can be obtained efficiently with all the constraint conditions being precisely satisfied. © 2017, Editorial Office of Journal of the China Railway Society. All right reserved.