Cooperative eco-driving of multi-train combined with dc railway system can achieve energy saving at the substation level for the metro system. This article presents an integrated optimization method for eco-driving by combining energy-efficient train control and dc traction power supply system (TPSS) model, to minimize the substation energy consumption. The coupled time-varying TPSS models for single train and multi-train are established, and a novel power flow calculation (PFC) method is proposed, to directly obtain the precise power flow distribution without iterations. Then, customized dynamic programming (DP) algorithms for specific TPSS models are developed, and optimal speed profiles of the tracking train and the preceding train can be respectively obtained by the multi-phase DP method. The former maximizes the utilization of a distributed regenerative braking energy (RBE), and the latter actively generates RBE to be fully utilized. Finally, the performance of the proposed method is analyzed by implementing the numerical experiments with field data from Guangzhou Metro Line 8, and the effectiveness is verified by comparing it with a previous study-based heuristic algorithm (HA). The simulation result indicates that the proposed method can also effectively reduce the lost energy on the catenary, suppress catenary voltage fluctuations, and precise match power during the RBE transmission phase.

Eco-driving for trains has traditionally focused on minimizing mechanical energy consumption at wheels, while completely ignoring traction chain losses that are rather significant. This paper presents a computationally efficient approach to minimize the total electrical energy consumption from traction substations (TS). After a nonlinear and non-convex program is formulated in time domain, a nonlinear and non-convex program is formulated in space domain to overcome the drawbacks of the model in time domain. By convex modeling steps, the non-convex program in space domain is reformulated as a convex program that can be efficiently solved. To further reduce computational effort, a real-time iteration sequential quadratic programming (SQP) algorithm is proposed to solve the convex program in a model predictive control framework. Numerical results indicate that the proposed SQP method yields a near-optimal solution with high computational efficiency. Compared to a traditional mechanical energy consumption model, a TS-to-traction energy efficiency can be improved.

The Carbon Neutralization is a grand strategy to deal with global climate change. As a major energy consumer, urban rail transit (URT) system should contribute corresponding solutions. This paper proposes an energy-efficient train control and schedule integrated optimization method under DC traction power supply system (TPSS) with reversible substation (RSS). The dynamic coupling mechanism between the train movement process and the RSS working mode is analyzed and modeled. Aiming to minimize the total RSS energy consumption for the train traveling over multi-interstation with a given total trip time, the train trajectory and schedule optimization problem is integrated in the same level, and is formulated as a multi-phase optimal control problem (MOCP) to be solved by a pseudo-spectral method (PSM). As a supplement, a customized dynamic programming (DP) method for the problem is introduced to verify the validity of the proposed solution framework. Simulation results under the models of the RSS energy together with conventional rectifier substation energy and vehicle mechanical energy are presented and compared, indicating that the proposed methodology has great energy saving performance for the new-type DC railway system.

Aiming to minimize the total electricity usage in realistic operation of urban rail transit (URT) trains, this paper establishes the coupled model for the train-line-electric network-timetable (TLET) comprehensive system, and proposes a multi-train cooperative eco-driving method to achieve the system energy optimal. The dynamic power flow within the DC railway system with multiple trains is analyzed by modeling the traction power supply system (TPSS), and an improved power flow calculation (PFC) method is proposed to calculate the dynamic power flow distribution. To achieve the total substation energy minimization, a space-time-speed (STS) three-dimensional network is presented to transform continuous train motion process into discrete states on space-speed plane, and a multiple individuals dynamic programming (MIDP) algorithm is throughly developed to cooperatively optimize the multi-train trajectories along the time horizon, with which the optimal speed profiles and timetables of each train can be obtained simultaneously. Moreover, a computationally efficient heuristic algorithm together with a train-to-train (T2T) communication policy are developed as a comparative study. Numerical experiment with field data from Guangzhou Metro Line 8 is implemented, to illustrate the energy-saving performance of the proposed methods.

The Multi-train comprehensive optimization (MTCO) combined with the AC traction power supply system (TPSS) can achieve energy savings of traction substations. However, traditional energy-saving optimization methods can cause continuous voltage fluctuations in the power grid, which may endenger train security. To address this issue, this paper proposes a comprehensive optimization method for energy-saving and voltage-stability in multiple trains. Firstly, this paper establishes the Train-Track-Power grid (TTP) comprehensive optimization model for freight trains, which is composed of Train dynamics model, traction drive model, and TPSS. Considering the dynamic complex power and network power loss, a multi-objective function for train energy saving and voltage offset is constructed. Due to the strong coupling and complexity of the nonlinear TTP model, it is difficult to optimize algorithm solution and convergence accuracy is low, as well as the deficiencies in the distribution of non-dominated solution set during iterations, an adaptive multi-strategy multi-objective particle swarm optimization algorithm (amMOPSO) is proposed. Then, the effectiveness of the TTP model is validated through the measured data from the Shuohuang Railway in China. Finally, several classical and state-of-the-art algorithms are employed for experimental comparisons. Experimental results show that amMOPSO outperforms the other algorithms. And the feasibility of the freight multi-train MTCO method is verified through three comparative experiments. The energy consumption of the trains is reduced by 53.97%, the total voltage offset is reduced by 66.96%, and the utilization efficiency of RBE (Regenerative Braking Energy) is increased by 75.3% as demonstrated through the comprehensive optimization experiments involving three trains.

Nowadays, most metro vehicles are equipped with an automatic train operation (ATO) system, and the speed control method, combining cruise speed planning and proportional-integral-derivative (PID) control, is widely used. The automation is achieved, and the energy-efficient can be improved. This paper presents an improved artificial bee colony algorithm for speed profile optimization with coast mode and an adaptive terminal sliding mode method for speed tracking. Specifically, a multi-objective optimization model is established, which considers energy consumption, comfortableness, and punctuality. Then, a novel artificial bee colony algorithm named regional reinforcement artificial bee colony (RR-ABC) is designed, to search the optimal speed profile with coast mode, in which some improvements are made to speed up convergence and to avoid local optimal solutions. For speed-tracking control, the adaptive terminal sliding mode controller (ATSMC) is used to improve the speed error, robustness, and energy saving. In addition, a disturbance observer (DOB) is designed to improve the anti-interference ability of the system and further improve the robustness and anti-disturbance, which are also conducive to speed error and energy saving. Finally, the line and train data of the Qingdao Metro Line 6 are used for simulation, which proves the effectiveness of the study. Specific to the energy saving rate, and compared with normal algorithms, RR-ABC with coast mode is approximately 9.55%, and ATSMC+DOB is 7.58%.