Research On Joint Optimization Methods Of Speed Profile And Power Split For Hybrid Trains

Urban rail transit is considered an important way of low-carbon urban travelling,due to its salient characteristics of large passenger capacity,high energy efficiency and no greenhouse gas emissions.However,train traction energy consumption is rapidly increasing with the increase of urban rail network.It is of great practical significance to research on train energy-efficient optimization methods,which is beneficial to achieve emission peak and carbon neutrality in urban rail transit field.To fully re-use regenerative braking energy and minimize traction energy consumption,this dissertation focuses on integrated optimization and predictive control methods of speed profile and power split for a catenary-supercapacitor hybrid train,and two operational scenarios with and without time constraints from traffic lights are considered.Design-oriented optimization approaches and operation-oriented predictive control approaches are proposed.Specific contents are presented as follows:To accurately calculate operational energy consumption of a catenary-supercapacitor hybrid train,the topology of traction chain and power flow are firstly analyzed.Then,the power consumption calculation methods of on-board energy storage systems and traction power systems are presented according to equivalent circuit models,and a nonlinear power consumption model of traction drive system is established according to measured data.Finally,a coupled model of on-board energy storage-train-catenary power is formulated,which can precisely calculate dynamic power efficiency of the traction chain and energy consumption from traction substations.It is a foundation to design optimization approaches in following chapters.Part of electric braking energy cannot be fully absorbed or re-used by on-board energy storage systems while the charging power and energy limits of energy storage systems are not considered in the procedure of driving strategy optimization,since the maximum charging power of the on-board supercapacitor is less than the maximum train electric braking power.To fully re-use the electric braking energy and minimize energy consumption from traction substations,an integrated optimization model of speed profile and power split is formulated according to the coupled model.The integrated model consists of three independent state variables.To reduce the complexity of the integrated model,the integrated optimization problem is reformulated as an equivalent optimization problem with two independent state variables according to the Pontryagin maximum principle.On basis of that,a hierarchical optimization framework and a coupling optimization framework are designed to solve the problem,using dynamic programming algorithms.Simulation experiments show that the coupling method can improve the utilization rate of electric braking energy and reduce energy consumption from traction substations,compared to the results from the hierarchical method,since the coupled relationship between the power of on-board energy storage system and the power of the vehicle can be fully considered.To effectively react to dynamic speed limits and the variation of trip time in practical train operations,a predictive control model integrating speed profile and power split optimization is formulated based on a model predictive control(MPC)framework.Furthermore,to efficiently solve a nonlinear program in each MPC iteration,the nonlinear program is firstly approximated as a quadratic programming problem.Then,the quadratic program is sequentially solved with the MPC updates according to the idea of the real-time iteration framework.The algorithm only solves one single quadratic program in each MPC iteration,which has high computational efficiency and can effectively react to operational disturbances.Simulation experiments show that the proposed sequential quadratic programming algorithm can obtain results with less energy consumption compared to results from the dynamic programming.Meanwhile,the algorithm can effectively react to the variation of operational constraints.Some urban rail transit lines have semi-exclusive rights-of-way.At some intersections,train operations are constrained by traffic lights,and trains can only cross traffic lights in green time windows(GTWs).For multiple feasible GTWs of one traffic light,an integer linear model is introduced to select an optimal GTW for train crossing,where binary variables are assigned to GTWs to indicate whether the train crosses the GTW or not.To reduce the number of integer variables,a feasible time zone is constructed by integrating a min-time trajectory and a max-time trajectory.After that,only GTWs in the feasible time zone should be defined by integer variables.Then,a mixed-integer nonlinear program(MINLP)is presented to minimize trip time,which can analyze the influence of the time constraints from traffic lights on optimal speed trajectories.Furthermore,for the integrated optimization problem of speed profile and power split subject to disjunctive GTWs,an MINLP is formulated to minimize energy consumption from traction substations.Finally,a branch-and-bound algorithm is presented to solve the MINLPs.Simulation experiments show that the time constraints from traffic lights have great influence on the optimal speed trajectories.For the problem of minimizing energy consumption,compared to results from a rule-based driver model,the optimized results enable trains to smoothly cross traffic lights,and unnecessary braking modes can be avoided,which maximizes the energy efficiency of train operations.To efficiently solve the predictive control problem of speed profile and power split subjected to disjunctive green time constrains from traffic lights,a predictive control approach with multiple layers is proposed.Specifically,by limiting the maximum electric braking power of the vehicle to the maximum charging power of the energy storage system,the predictive control problem is decoupled into three subproblems,i.e.,speed profile predictive control subproblem,power coordinated control subproblem for electric drive system and energy management subproblem for energy sources.For the speed profile control subproblem,disciplined convex modelling steps including convex relaxation for binary variables and linearization for nonlinear functions are presented to reformulate the original non-convex MINLP problem into a relaxed convex program.To enable the relaxed binary variables converging to integral values,a sequential convex programming algorithm is designed to recover the solution of the original problem that can guarantee trains crossing traffic lights in GTWs.On basis of that,a dynamic power allocation algorithm is presented to optimize the output power from multiple traction units,according to the efficiency of a traction unit.By optimizing the operational number and output force of a traction unit,the efficiency of traction drive system can be improved.For the energy management subproblem,a convex program that incorporates models of energy storage system and catenary system is derived to minimize the energy consumption from traction power substations.Numerical experiments show that the sequential convex programming algorithm can efficiently solve the MINLP.Meanwhile,power coordinated control and energy management strategies can improve energy efficiency of the traction drive system and the energy system,respectively.As a result,the efficiency of the whole system can be maximized.The research of this dissertation is an important foundation to design driver assistant systems and automatic operation systems for hybrid trains,which is beneficial to reduce train operational energy consumption,improve driving skills of drivers and the intelligence level of train operations.