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.

Network partitioning is a popular research topic. Not all available partitioning methods are equally suitable for power grids. Community detection is a critical issue in complex network theory, and power grid is a typical type of complex network. This paper proposes a functional community structure based on an extended weighted network model. An extended adjacency matrix is used to represent an extended weighted complex network model based on coupling strength rather than the conventional adjacency matrix. Meanwhile, we upgraded the Newman fast algorithm of community detection for establishing a novel power grid partitioning algorithm. The electrical coupling strength (ECS) is defined to better reflect electrical characteristics between any two nodes in power grid. Modularity is also redefined as electrical modularity based on ECS. The Newman fast algorithm is upgraded with electrical modularity maximization as the objective to detect functional communities in power grids. A case study on IEEE test systems with 30, 39, 118, 300 buses and one Italian power network demonstrates the rationality of the extended weighted network model and partitioning algorithm.

Nowadays, the infrastructure and technologies in conventional distribution networks (CDNs) limit its further development to smart distribution networks. One way to overcome this is to develop CDNs using interconnected virtual microgrids (VMs); however, there is no consensus for an explicit definition of VMs. Therefore, in this paper, a comprehensive discussion on VMs is conducted, and a general framework for developing VMs is proposed. The core issue for developing VMs is to identify boundaries of VMs, and most of the suggested methods are based on analyzing operating states. In this paper, a different partitioning method, which is based on the analysis of structural characteristics, is proposed. The electrical coupling strength is defined as a composite weight coefficient for the analysis of electrical connection, and the electrical modularity is used to assess the quality of the partition so as to identify boundaries of VMs. This partitioning method is applied to the IEEE 33-bus distribution network and the PG&E 69-bus distribution network, and it can quickly evaluate the partitioning quality and effectively identify the boundaries of VMs.

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.