Carbon reduction policies and the increasing trend toward transportation electrification have spurred the rapid development of electric vehicles (EVs). However, the uncertainties of charging demands and facility failures, resulting from factors such as power disruptions, equipment damage, and inefficient operation, pose challenges in balancing the economic efficiency and service reliability of electric vehicle charging stations (EVCSs). This paper proposes a robust planning model in the coupled traffic-power network, aiming to minimize the investment costs of EVCSs and the operation costs, including detour costs for EV users, penalty costs for unmet demands, and generation costs while maintaining a controllable risk level. To solve the model, we employ the column-and-constraint generation algorithm along with the alternative directions method (C&CG-AD). Furthermore, a second-order cone programming (SOCP)-based branch flow model (BFR) is incorporated to repair the duality gap of BFR and ensure the convergence of the C&CG-AD algorithm. A comprehensive case study is conducted to validate the effectiveness of the proposed model and solution methods. The findings demonstrate that the robust solution considering both uncertainties offers superior cost-effectiveness, operational reliability, and resilience against various failures compared to strategies that either average out uncertainties or overlook facility failures.

The permanent magnet synchronous motor (PMSM) has recently garnered significant interest due to its high efficiency, lightweight, and low life cycle cost, positioning it as a strong candidate for the next-generation traction system in railway applications. By comparing the widely used induction motor (IM) with the PMSM, this paper integrates the dynamic motor efficiency map, which plays a crucial role in energy saving, into the energy-efficient train control (EETC) problem. The paper adopts auxiliary variables and utilizes data transformation to perform double surface-fitting for highly nonlinear and non-convex dynamic efficiency. This transformation naturally distinguishes the train traction and braking operating states, further enhancing the solution accuracy of the EETC model. Results reveal that the proposed model, while maintaining high computational accuracy, can achieve millisecond-scale computation time, and the results are closer to the actual distribution of train operating points. Based on a real case analysis of Qingdao Metro Line, it was found that replacing the IM with PMSM as a traction motor does not require adjustments to the train operation control strategy, and the PMSM can save at least 1.01 kWh/km, achieving an energy-saving rate of 12.96%.

To improve the energy-efficiency of transport systems, it is necessary to investigate electric trains with on-board hybrid energy storage devices (HESDs), which are applied to assist the traction and recover the regenerative energy. In this paper, a time-based mixed-integer linear programming (MILP) model is proposed to obtain the energy-saving operation for electric trains with different constraints of on-board HESDs, such as their capacity, initial state of charge (SOC), and level of degradation. The proposed integrated power flow model based on the train longitudinal dynamics, power split of on-board HESDs, and line impedance is discretized and linearized, aiming to minimize the net energy consumption (NEC). The results reveal that on-board HESDs with a higher capacity does not necessarily lead to a higher energy-saving rate; a lower or excessive initial SOC could undermine the energy-saving potential; considering the long-term train operation, the degradation of the Li-ion battery will influence the energy-saving operation for electric trains, as well as result in an energy-saving rate that ranges from 41.57% to 31.90%. The practical data from Guangzhou Metro Line 7 were applied in the simulations, which enhanced the practicality and effectiveness of the proposed method.

With the increasing concerns about railway energy efficiency, researchers have developed various approaches to optimize train trajectories for energy savings. However, these methods often rely on different models, and most studies validate their effectiveness on a single type of railway system, making it challenging for readers to compare them effectively. To address this, our paper introduces a novel comparative framework that evaluates three distinct optimization methods: nondominated sorting genetic algorithm (NSGA-II), convex optimization (CO), and mixed integer linear programming (MILP). We develop a continuous train trajectory optimization model, tailored to each method. Comprehensive asymptotic analyses of the computational complexity for NSGA-II and CO are performed, along with an in-depth examination of MILP’s NP-hard problem complexity. Additionally, we analyze the distinct characteristics of metro and high-speed railways to assess the applicability and performance of these methods under varied operational conditions. Our comparative analysis reveals that while all methods effectively achieve significant energy savings, they display distinct profiles in terms of computational demand and operational stability. These differences are crucial for practitioners when selecting the most appropriate method for specific railway research and operational needs.