The complex energy coupling and numerous adjustable parameters in urban rail traction power supply systems equipped with both energy storage systems (ESS) and energy feedback systems (EFS) make optimal energysaving control a significant challenge. To address this issue, this paper proposes a novel day-ahead optimization design method based on causal inference. First, a comprehensive five-layer energy flow model of the integrated traction power supply system is established. Then, the Reciprocal Information Entropy Causal Inference (RIECI) method is introduced to analyze and quantify the causal relationships between different regenerative energy utilization paths and the total system energy consumption. The parameter domain restriction rules are formulated to guide the optimization process. Finally, the modified Salp Swarm Algorithm (MSSA) is applied to solve for the optimal voltage control parameters for the EFS and ESS under different train headways. Case studies based on a real-world subway line demonstrate that the proposed method can effectively identify true causal links within the system. The results indicate that the optimal control strategy adapts to varying headways, confirming the effectiveness and necessity of the proposed causal-guided optimization framework for enhancing energy efficiency in urban rail transit.

A rail-to-earth insulation diagnostic method is proposed for subway systems, leveraging a computationally efficient improved field-circuit coupling model (IFCM) combined with an improved Minkowski distance (IMD) metric. The model innovatively excludes rail electric field effects and relocates leakage sources to the stray current collection network (SCCN), achieving dynamic rail-to-earth resistance simulations with deviations below 5.47% compared to experimental measurements. A multisignal fusion approach combines rail potential and SCCN polarization potential, employing time-varying filtered empirical mode decomposition denoising and IMD-based feature extraction to quantify insulation degradation. In dynamic simulations, high computational efficiency is maintained by the IFCM, which shows a relative error of 8.09% compared to current distribution, electromagnetic fields, grounding, and soil structure analysis (CDEGS) results. Validation using 5000 defect samples demonstrates 98.09% classification accuracy, with diagnostic thresholds optimized via the Youden index. Bootstrapping confirms robustness, while sensitivity analyses validate performance under noise interference, with energy feedback system in operation, and localized insulation variations.

The growing demand for energy-efficient urban rail transit has led to the increasing deployment of reversible substations (RS) in traction power supply systems. These substations, equipped with bidirectional converter devices (BCDs), involve high initial costs and complex parameter optimization challenges. This paper presents a coordinated optimization method for BCD-equipped RS using a two-layer model. In the upper layer, the model determines the siting of RS and the capacity of BCD to minimize life-cycle cost (LCC). In the lower layer, it adjusts the control parameters of BCDs to reduce annual operating cost. An improved salp swarm algorithm (ISSA), incorporating Tent chaotic mapping and Levy flight, is developed to solve the model. A case study based on an 18.2 km subway line shows that the optimized configuration reduces overall cost by 5.12% and electricity cost by 10.53% compared with a conventional rectifier system. Moreover, it achieves a 1.19% reduction in electricity cost over a system with fixed control parameters, while maintaining rail potential and catenary voltage within safe limits. These findings demonstrate that the proposed method strikes an effective balance between initial investment and long-term operational benefits, contributing to improved energy efficiency and economic performance.

The integration of renewable energy into traction power networks has emerged as a major trend in rail transit, while the mismatch between photovoltaic generation and traction demand in urban rail systems often causes curtailment and wasted energy. This paper proposes a two-stage energy management scheme that couples network reconfiguration with converter control to increase local PV utilization. In Stage 1, ring switching re-partitions the traction supply to enlarge the PV-fed area. A fast feasibility check verifies that the new topology meets limits on capacity, voltage, and equipment loading, thereby ensuring that the expanded PV-supplied area remains operationally secure before converter-level control is applied. In Stage 2, with the verified topology fixed, reversible traction substations are coordinated to shift PV power along the line toward traction sections, reducing grid imports and curtailment. The control problem is formulated as a Markov decision process (MDP), and a deep deterministic policy gradient (DDPG) agent with safety aware reward shaping is trained offline to handle PV variability, converter operating limits, and abnormal high-voltage conditions that may arise during strong PV generation periods. For a typical metro line with a track-side or station-area photovoltaic installation at the MW level, a case study framework is outlined to evaluate the method’s effectiveness. The results indicate that combining ring reconfiguration with coordinated converter control can effectively expand the local PV absorption range, reduce photovoltaic curtailment, and decrease utility-grid energy imports, thereby improving the energy performance of PV-integrated urban rail traction power systems.

Corrosion poses a substantial threat to the structural integrity of railway tracks. The microzones formed in welded joints of rails exhibit different microstructures and stress distributions, which affect the corrosion performance. The corrosion behaviours of the weld microzones have a significant impact on the overall rail performance. To protect the rail joints from corrosion and enhance the service life of high-speed rails, we evaluated the corrosion properties of different microzones of U75V welded joints in 3.5 wt.

ObjectiveThe application scheme of reinforced insulating coating for rails is investigated to address the stray current issues and optimize the scope of above coating. Based on stray current control indicators, the implementation range of the reinforced insulating coating for rails centered on traction substations, is optimized. MethodA field-circuit coupling model based on the boundary element method is used to calculate the rail leakage current and the earth potential gradient around the railway line. Centered on traction substations, an iterative search algorithm is employed to determine the implementation distance of the reinforced insulating coating for rails. Using stray current control indicators as the evaluation criterion and traction substations as the center for applying the reinforced insulating coating, the above-mentioned implementation distance is calculated through the iterative search algorithm. Result & Conclusion The case analysis shows that with the proposed optimization algorithm, when the rail transition resistance is increased to 30 Ω·km, the average positive leakage current of the entire line is less than 2.5 mA/m, and the earth potential gradient at 50 m from the line is less than 2.5 mV/m. Compared to applying the reinforced insulating coating to the entire line, this approach reduces the scope of the mentioned coating by 63.8%.

ObjectiveIn the DC traction power supply system of urban rail transit equipped with inverter feedback devices, electrical loops can be formed between the inverter feedback devices and rectifier devices in the substation or between adjacent substations via AC/DC buses. This can easily induce inter-substation circulating currents, leading to ineffective power circulation, increased equipment losses, and reduced overall efficiency. Therefore, it is necessary to conduct an in-depth investigation into the formation mechanism, influencing factors and occurrence patterns of inter-substation circulating currents from the perspective of traction power supply system design. MethodAn AC/DC integrated equivalent circuit model is established covering traction substations, inverter feedback devices, trains and the traction network, to analyze the generation paths and power balance relationships of inter-substation circulating currents under typical operation scenarios. The circulating current probability is proposed as a quantitative index to evaluate the occurrence likelihood of circulating currents. In the case study of an actual metro line, a simulation model is built by combining its power supply topology, train operation parameters and equipment characteristics to validate the accuracy of the above-mentioned circuit model. Result & Conclusion The formation of inter-substation circulating currents depends on the matching relationship between the capacity of inverter feedback devices and the adjacent AC load, and is closely related to the real-time distribution of traction power and braking power of the trains on the line. From the perspective of operation organization, the probability of inter-substation circulating currents generally first increases and then decreases as the train headway grows. For a given headway, the duration and occurrence probability of circulating currents are significantly affected by the departure time difference between up-bound and down-bound trains.

This article presents a hierarchical formation control method for heterogeneous unmanned surface vehicles (USVs). Firstly, the USVs are organized into groups, each comprising one leader and multiple followers. Secondly, the cooperative path tracking problem for leaders along a parameterized path is addressed, wherein multiple leaders form a serpentine configuration. Then, a control methodology is then proposed to enable each group of followers to track their respective leader while maintaining a predefined formation geometry. The hierarchical framework generates the requisite speed and heading commands for formation control, which are transmitted to each USV for tracking. Corresponding software and hardware implementations have been developed and deployed on the USV prototypes. Finally, simulation studies demonstrate the performance of the proposed formation control algorithm, while lake experiments further validate the effectiveness and practical applicability of the proposed strategy.

Efficiently utilizing the energy-saving potential of reversible converter (RC) has received significant attention in urban rail transit with reversible substations. However, energy management is considerably challenged by the highly dynamic and stochastic nature of train operations when relying on traditional methods. Therefore, a real-time energy management model based on deep reinforcement learning (DRL) is proposed in this paper. The model aims to minimize energy consumption through real-time decision-making, in which an agent dynamically optimizes RC control parameters using continuous state feedback from trains, traction substations (TSs), and main substations (MSs). A novel reward function is designed to incorporate both safety constraints and a day-ahead optimization benchmark, thereby effectively coordinating operational safety with energy efficiency. Moreover, stochastic timetable disturbances are introduced during training to enhance the model's robustness. Simulations based on Qingdao Metro Line 3 demonstrate that the proposed approach significantly improves regenerative braking energy (RBE) utilization and reduces reverse power at the MSs, achieving a daily energy saving of 8.30%. Sensitivity analysis further quantifies the impact of key parameters, including RC capacity, step-down loads, and system scale, on overall performance. Finally, hardware-in-the-loop (HIL) experiments confirm the model's practical effectiveness and robustness against communication delays, demonstrating its strong potential for real-world applications.

Traditional urban rail traction substations have drawbacks such as short power supply distance and poor insulation performance. The traction converters they use also have contradictions between economic efficiency and the utilization rate of regenerative braking energy. Moreover, traditional traction converters are difficult to meet the requirements of higher-level voltages in terms of insulation and reliability. In response to the above problems, this paper proposes a new type of flexible traction power supply system for urban rail transit. Medium-voltage alternating current (AC33kV/35kV) is rectified into 35kV direct current by the modular multilevel converter (MMC) in the traction substations of this system, and then reduced to 1500V/750V direct current through a bidirectional DC-DC converter to supply the traction network. This flexible traction power supply system has the advantages of large power supply radius, low line loss, high insulation performance and high utilization rate of regenerative braking energy. To meet the requirements of high-voltage direct current transmission, this paper also proposes a multi-level cross-shaped sub-module MLCSSM suitable for MMC in the above-mentioned system. Under non-locking and locking operation conditions, this sub-module can rapidly clear DC faults while simplifying the system cascaded structure at the same voltage level. This paper also studies the control strategy of MLCSSM, and builds a simulation model using Matlab/Simulink to verify the correctness and effectiveness of the sub-module topology structure proposed in this paper.

Integrating photovoltaic (PV) energy into urban rail transit faces challenges due to PV variability and fluctuating train loads, often leading to low PV utilization. This paper proposes a deep reinforcement learning (DRL)-based energy management strategy that dynamically coordinates reversible converters to intelligently redistribute surplus PV energy across multiple power supply sections. The approach incorporates stochastic PV generation and train operation uncertainties into the training process within a Markov decision framework, and leverages day-ahead optimization results to design a time-varying reward mechanism that guides real-time control at per second time. Simulation studies on Qingdao Metro Line 2 show that the proposed method achieves a 4.15% reduction in annual energy consumption, corresponding to 1.7 GWh, and outperforms recent optimization-based methods. To further verify real-time feasibility and control effectiveness, a hardware-in-the-loop (HIL) platform using a reduced-scale metro line is developed, on which the trained DRL agent is deployed and shown to achieve energy saving in real-time tests. These results highlight the method’s ability to improve energy efficiency and facilitate greater integration of PV energy under dynamic and uncertain conditions in urban rail transit.

[Objective]To ensure the safety of traction trans-formers in dual current power supply lines and prevent issues such as transformer vibration and winding temperature increase caused by excessive DC bias current,which can lead to severe distortion of excitation current,it is essential to study the de-gree of DC bias in transformers of dual current power supply lines.[Method]The DC bias problem in transformers of dual current power supply lines is introduced.By dividing the line into smaller sections,with trains in the DC segment modeled as power sources,and trains in the AC segment and traction transformers modeled as resistances,a chain-circuit model for the dual current power supply system is established.Using con-tinuous linear load flow calculation method,the DC bias cur-rent of transformers in the AC segment of a dual current power supply line is computed.The calculated results are compared with field-measured data to verify the validity and accuracy of the proposed method.[Result & Conclusion]The DC bias current in transformers significantly exceeds the standard at cer-tain times.The proposed calculation method,characterized by minimal admittance matrix order and fast computation speed,is suitable for dynamic calculations of DC bias currents in trans-formers of dual current power supply lines.

As urban rail transit grows, stray current seriously threatens the safety of power systems and oil/gas pipelines. Rail-to-earth insulation the key to control stray current. Aiming at the problem that it is difficult to detect and locate the rail insulation defects of DC traction power supply system, a novel rail insulation defect detection method based on the FFC-Swin-Transformer is proposed. By establishing a four-layer "catenary-rail-SCCN-earth" equivalent circuit model and integrating multi-train operation conditions, a rail potential dataset is efficiently generated via parallel computing. Time-domain signals of rail potential are converted to frequency-domain features using Fourier transform, and the fused time-frequency information is fed into an improved FFC-Swin-Transformer network to achieve accurate detection of rail insulation states. Experimental results show that after training on 22496 sample groups, the model achieves a test accuracy of 82.95%, effectively identifying section insulation defects and exhibiting promising engineering application potential.

The system efficiency of reversible substations (RSSs) in urban rail transit power supply systems has garnered significant attention. In particular, reverse power flow from the main substation (MS) has been observed in the real world, adversely impacting system efficiency. This article proposes a novel power supply structure for RSSs that effectively reduces reverse power flow. To further enhance system efficiency, an optimal model is established by leveraging the control characteristics of RSSs. Then, a system efficiency energy regulation and control framework considering complex scenarios is presented, with the lowest system losses as the optimization objective. The modified Cheetah Optimizer algorithm is adopted to optimize the control parameters of reversible converters (RCs). Simulations of actual engineering cases are conducted, and the results demonstrate the effectiveness of the proposed power supply solution and energy regulation control in various scenarios. The proposed method can improve energy efficiency by up to 3.25% and 2% compared with nonoptimized and existing offline optimized methods, and this value varies depending on the scenario. Additionally, performance analysis and evaluation highlight the fundamentals of energy regulation in enhancing system efficiency, including balancing bus load, appropriately increasing catenary voltage, and adjusting the proportion of regenerative braking energy (RBE) between the ac and dc sides based on different situations.

In a traction power supply system, the design of traction substations significantly influences both the system’s operational stability and investment costs, while the energy management strategy of the flexible substations affects the overall operational expenses. This study proposes a novel two-stage system optimization design method that addresses both the configuration of the system and the control parameters of traction substations. The first stage of the optimization focuses on the system configuration, including the optimal location and capacity of traction substations. In the second stage, the control parameters of the traction substations, particularly the droop rate of reversible converters, are optimized to improve regenerative braking energy utilization by applying a fuzzy logic-based adjustment strategy. The optimization process aims to minimize the total annual system cost, incorporating traction network parameters, power supply equipment costs, and electricity expenses. The parallel cheetah algorithm is employed to solve this complex optimization problem. Simulation results for Metro Line 9 show that the proposed method reduces the total annual project costs by 5.8%, demonstrating its effectiveness in both energy efficiency and cost reduction.

In urban rail flexible traction power supply system (FTPSS), conventional energy-saving strategies for reversible converter (RC) predominantly rely on offline optimization with fixed parameters. However, inherent uncertainties in train operations, such as timetable deviations and stochastic load fluctuations, result in energy consumption volatility, rendering traditional approaches suboptimal. To address this, we propose a multi-timescale model predictive control (MPC) framework that integrates day-ahead scheduling and intraday rolling optimization. Second, we propose a novel data processing method for neural network training in the intraday to construct a neural network-based load prediction model, which is used as the model prediction control (MPC) input for rolling optimization. Validated on Qingdao Metro Line 11 datasets, the prediction model achieves a correlation coefficient (R2) value of 95.2%, and the mean squared error (MSE) is 0.078, outperforming conventional prediction methods. By integrating MPC-based rolling optimization with day-ahead scheduling, the proposed strategy improves the energy-saving rate by 2.00% over traditional offline optimization methods. Demonstrating robustness against timetable perturbations and load uncertainties.

In response to global carbon neutrality goals and the growing emphasis on sustainable urban development, enhancing the energy efficiency of urban rail systems has emerged as a critical focus in sustainable transportation planning. In this context, effective operation requires optimization that captures key operational factors. Passenger load varies over time, which changes train mass and traction demand. With reversible substations, part of regenerative braking energy can be absorbed on the AC side by station auxiliaries or returned to the grid. These mechanisms motivate an integrated formulation that accounts for both effects. To leverage these effects, this paper proposes an energy-efficient multi-train scheduling strategy that adjusts train dwell times and inter-train departure intervals. An integrated operation model captures the interaction between train mass dynamics and power flow on the traction network, and the resulting nonlinear problem is solved with the Adaptive Leader Salp Swarm Algorithm (ALSSA). On Xuzhou Metro Line 2, incorporating dynamic mass alone reduces external energy supply by 4.28 %, and the proposed co-optimization delivers a further 5.62 %, for a total saving of 9.67 %. The results indicate that jointly modelling passenger-mass dynamics and substation-side use of regenerative energy significantly improves energy efficiency.

The problem of dc interference caused by stray currents in dc traction power supply system (DPS) is becoming increasingly serious. In order to study the interference degree of stray currents, a unified model of DPS and stray current dissipation based on the direct boundary element method (UBEM) has been established. The stray current collection network (SCCN) polarization potential is an important index to evaluate the leakage level of stray current. In this article, the relationship between SCCN polarization potential and rail-to-earth resistance (RE), train headways and longitudinal resistance of SCCN is investigated. It provides a partial theoretical basis and calculation method for stray current protection and system optimization. Field tests and CDEGS software simulations prove that UBEM is effective. The results show that UBEM is within 6.07% of the CDEGS simulation results and within 11.45% of the field test results. Taking the actual metro project in China as an example, SCCN polarization potential is only affected by local stray current. When RE>7.35 Omegakm, The average value of the SCCN polarization potential drops below 0.5 V.

In a dual-traction power supply system (DTPSS), an improper value of onboard grounding resistance could result in a larger current distribution, axle end potential, and surge overvoltage (SOV) of the vehicle body (VB) because of the interaction between the ac and dc traction power supply system and the train crossing the neutral sections. Therefore, it is important to carefully select the appropriate value of the resistance and position of the grounding points. This research article proposed the steady-state model of DTPSS to evaluate the current distribution and axle-end potential, and the transient state model of DTPSS to calculate the SOV of the VB of vehicle grounding systems (VGSs). To obtain the best optimal solution, particle swarm optimization (PSO) and the technique for order of preference by similarity to ideal solution (TOPSIS) multiobjective optimization techniques have been implemented. The accuracy and efficiency of the VB current distribution are verified by observing the experimental and simulation results. The proposed VGS optimization technique demonstrates that the VB current distribution has achieved a significant improvement of 24.8% of the total current in the dc section and 21.1% of the total current in the ac section. By observing experimental, simulation, and optimal solutions of transient models in DTPSS, the SOV value was reduced to 33.4% of the total voltage.

Compensation with a power flow controller (PFC) is crucial for enhancing power quality and power supply capability of the long-distance co-phase cable traction power supply system (TPSS). The integration of PFC introduces new demands on the power flow calculation methods, operation strategies, and analysis. Firstly, a compensation scheme with stronger power supply capability is proposed, and a multi-objective unified model for various schemes is developed based on the port connection angle. Secondly, a power flow calculation method based on network transformation and unified iteration is proposed, enabling efficient power flow calculation for asymmetric networks with PFC. Then, an operation strategy based on mathematical analysis to minimize PFC capacity is proposed, aiming to achieve the economic operation of TPSS. Finally, the accuracy of the compensation scheme and models is verified, and the different operation characteristics of the TPSS with PFC are demonstrated based on the Xining to Golmud Plateau Railway in China. The research shows that the voltage compensation capability of the proposed scheme is eight times that of the existing scheme with the same capacity. In contrast to the 45 ∼ 104 iterations needed for the alternating iteration method, the proposed method converges in merely 5 ∼ 7 iterations, achieving the same accuracy.