For improving the energy efficiency of railway systems, on-board energy storage devices (OESDs) have been applied to assist the traction and recover the regenerative energy. This paper aims to address the optimal sizing problem of OESDs to minimize the catenary energy consumption for practical train operations. By employing a mixed integer linear programming (MILP) model based on energy flow and the law of conservation of energy, three types of widely used OESD: supercapacitors, Li-ion batteries and flywheels have been studied in a real-world case of Beijing Changping line. Results show that without the constraints of capital cost and volume, the supercapacitor, Li-ion battery and flywheel with optimized capacity can save the catenary energy consumption by 23.6%, 22.9% and 23.7% compared to the cases without OESDs respectively. The minimum catenary energy consumption for each type of OESD has also been found with the constraints of capital cost and volume. The study shows that with a volume constraint less than 0.6 m3 and a higher allowed capital cost more than 20 k$, flywheel tends to achieve the least catenary energy consumption. When the volume is relaxed to go beyond 0.6 m3, supercapacitors always achieve the minimum catenary energy consumption disregarding the constraint of capital cost.

Rail transportation is used extensively in urban areas to reduce CO₂ emission and increase road capacity. As a result, the energy efficiency of rail transportation is becoming a popular research topic. Energy-efficient train operation involves four types of control: maximal traction, cruising, coasting, and maximal braking. With the rapid development of energy storage devices (ESDs), this paper aims to develop an integrated optimization model to obtain the speed trajectory with the constraint of on-board ESD properties such as capacity, initial state of energy (SOE), and the degradation of the on-board ESD. Mixed integer linear programming is implemented on the discretized distance-based model to find the solution. In addition to the optimal speed trajectory, the on-board ESD discharge/charge operation strategy will be obtained. Results show that with high on-board ESD capacity, a train tends to apply more braking to recover more energy by using ESD; high initial SOE leads to more traction operation but undermines the energy-recovering process; degradation of on-board ESD influences the train operation and net energy consumption by affecting discharge/charge frequency. Additionally, in the case with on-board ESD, more than 11.6% of net energy consumption can be reduced compared with the one without on-board ESD. This paper indicates that the proposed method is an effective and robust way to study how on-board ESD influences optimal train operation as well as to achieve optimal train speed trajectory with on-board ESD.

This article proposes a novel two-step approach to concurrently optimize the train operation, timetable, and energy management strategy of the onboard energy storage device (OESD) to minimize the net energy consumption for a whole urban railway line. In Step 1, approximating functions representing the minimum net energy consumption of each specific interstation operation is obtained by data fitting based on the previous research outcomes. In Step 2, the optimal running time, initial state of energy (ISOE) of OESD, train speed profiles, discharge/charge management of the OESD during each interstation journey and at each station are obtained by applying convex optimization formulated by approximating functions gained in Step 1. The method is first tested with several general train cases to show its robustness and adaptability. Then, a real-world case based on Beijing metro Yizhuang line is studied and the optimal solution is found to reduce the net energy consumption 1.04%, 2.09%, and 23.77% for a service cycle of a single train when compared to other operation scenarios, i.e., fully charged, no management, and no OESD scenario, respectively. The approach is also computationally efficient with a computational time less than 1 min, namely 38.86 s for the upline and 48.38 s for the downline, spent on finding the optimal solution.

With the rapid progress in railway electrification and energy storage technologies, onboard energy storage devices (OESDs) have been widely utilized in modern railway systems to reduce energy consumption. This article aims to develop the optimal driving strategy of electric trains with three popular types of energy storage devices, namely supercapacitors, flywheels, and Li-ion batteries, as the OESD to minimize the net energy consumption. With the given OESD investment cost, the dynamic power limits of different types of OESDs are fully considered to optimize the dynamic discharge/charge behavior of the OESD in the train operation. The case studies investigate the train operation on fully electrified railways, discontinuously electrified railways, and catenary-free railways, showing that the optimal eco-driving strategy of the train and discharge/charge behavior of the OESD is significantly different for a different type of OESDs. The obtained train speed, OESDs' state of energy (SOE), power profiles, and energy-saving potential for each type of OESDs under various scenarios are compared comprehensively, and the results also reveal that the flywheel has the best performance for its energy-saving rate ranging from 0.15 %/k $\$ $ to 0.86 %/k $\$ $ , while a Li-ion battery is observed with the weakest performance with the energy-saving rate being only 0.01 %/k $\$ $ -0.26 %/k $\$ $ . The error rate analysis also confirms a satisfactory modeling accuracy of the proposed method.

With the rapid development of energy storage technology, onboard energy storage systems(OESS) have been applied in modern railway systems to help reduce energy consumption. In addition, regenerative braking energy utilization is becoming increasingly important to avoid energy waste in the railway systems, undermining the sustainability of urban railway transportation. However, the intelligent energy management of the trains equipped with OESSs considering regenerative braking energy utilization is still rare in the field. This paper considers the stochastic characteristics of the regenerative braking power distributed in railway power networks. It concurrently optimizes the train trajectory with OESS and regenerative braking energy utilization. The expected regenerative braking power distribution can be obtained based on the Monte-Carlo simulation of the train timetable. Then, the integrated optimization using mixed integer linear programming (MILP) can be conducted and combined with the expected available regenerative braking energy. A generic four-station railway system powered by one traction substation is modeled and simulated for the study. The results show that by applying the proposed method, 68.8% of the expected regenerative braking energy in the environment will be further utilized. The expected amount of energy from the traction substation is reduced by 22.0% using the proposed train control method to recover more regenerative braking energy from improved energy interactions between trains and OESSs.

Train speed trajectory optimization has been proposed as an efficient and feasible method for energy-efficient train operation without many further requirements to upgrade the current railway system. This paper focuses on an adaptive partial train speed trajectory optimization problem between two arbitrary speed points with a given traveling time and distance, in comparison with full speed trajectory with zero initial and end speeds between two stations. This optimization problem is of interest in dynamic applications where scenarios keep changing due to signaling and multi-train interactions. We present a detailed optimality analysis based on Pontryagin’s maximum principle (PMP) which is later used to design the optimization methods. We propose two optimization methods, one based on the PMP and another based on mixed-integer linear programming (MILP), to solve the problem. Both methods are designed using heuristics obtained from the developed optimality analysis based on the PMP. We develop an intuitive numerical algorithm to achieve the optimal speed trajectory in four typical case scenarios; meanwhile, we propose a new distance-based MILP approach to optimize the partial speed trajectory in the same scenarios with high modeling precision and computation efficiency. The MILP method is later used in a real engineering speed trajectory optimization to demonstrate its high computational efficiency, robustness, and adaptivity. This paper concludes with a comparison of both methods in addition to the widely applied pseudospectral method and propose the future work of this paper.