Energy-efficient Train Operation Optimization Based On Control Variable Parameterization

Reducing energy consumption is the eternal theme in the field of rail transit.In this dissertation,to minimize traction energy consumption,the optimization algorithm for energy-efficient single train operation is researched based on the control parameterization scheme,then,the theories and methods of running time supplement allocation among multiple stations and collaborative utilization of regenerated energy of multiple trains are studied.The main contents and contributions of the dissertation are as follows:(1)Based on the control parameterization scheme,the numerical method for solving position-based optimal train control problem is studied.Since the train speed constraint is an infinite dimensional constraint,the approximate parameters are hard to choose and can even affect the convergence of the algorithm when handling this kind of constraint by using conventional algorithms.To address this issue,an alternative method is proposed to transform the position-based infinite dimensional constraints into finite dimensional interior-point constraints.In addition,to deal with the bound constraint of traction force,which is a non-smooth function of train speed,a smooth function is first given to approximate the bound function,and then the bound constraint is transformed into an integral inequality constraint.Based on the above work,the energy-efficient train control problem is converted into a nonlinear programming problem,then,the energy-efficient traction/braking force sequences and speed profile are obtained by numerical simulation,and thus the effectiveness of the proposed methods is verified.(2)Since the position-based train state differential equations cannot be solved numerically at the initial point,the numerical method for solving time-based energy-efficient train control problem is studied.Based on the control parameterization scheme with piecewise-constant approximation and the time-scaling transformation,the analytical solutions to the time-based train state differential equations are given,and the time-based infinite dimensional speed constraints are equivalently converted into finite dimensional interior-point constraints.In addition,the theoretical proof of the equivalence is given.Then,the bound constraints of traction and braking forces are transformed into a series of integral inequality constraints.Based on the above work,the energy-efficient train control problem is transformed into a nonlinear programming problem.Furthermore,on the basis of the analytical solutions of the state sensitivity functions,the gradient formulas of the objective and constraint functions of the transformed problem are given.Finally,with Yizhuang subway line as the application background,the traction and braking force sequences and speed profile of energy-efficient train control,which satisfy all constraints,are obtained by numerical simulation,and thus the effectiveness of the proposed algorithms is verified.(3)To minimize train's total traction energy consumption of the whole line,the optimization algorithm for allocating running time supplements among multiple stations is studied.Taking the line gradients,speed limits and traction/braking force constraints into account,the optimal control model and numerical algorithm for obtaining the minimum technical running time between stations are proposed,and the mathematical model for describing the relationship between traction consumption and running time is established.On this basis,the nonlinear optimization model for allocating running time supplements among multiple stations is proposed,and thus the optimal running times between multiple stations with fixed total running time are obtained.Finally,the effectiveness of the proposed models and algorithms is verified by numerical simulation using real data of a subway line.(4)Based on the utilization of regenerated energy,the collaborative optimization problem for energy-efficient operations of multiple trains is studied.By using the energy-efficient control strategy for a single train,a calculation model for collaboratively utilizing the regenerated energy of multiple trains is established and thus the optimal departure headway is obtained.On this basis,an optimal control model and its numerical algorithm for adjusting operation stages of nearby trains are proposed,which further increase the utilization of regenerated energy.Simulation results using data of the Yizhuang line show that the proposed algorithms can significantly reduce the total traction energy consumption of the whole line.