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 fast development of energy storage technology, more applications of Energy Storage Devices (ESDs) have been found in rail transportation in recent years. This paper aims to address the optimal sizing problem of on-board Hybrid Energy Storage Devices (HESDs) which are installed to assist train traction and recover the regenerative braking energy. On-board HESDs combining Li-ion battery and supercapacitor can further enhance the capacity and instant power rating. In this paper, a mixed integer linear programming (MILP) model is proposed to minimize the economic cost in terms of energy consumption and installation, and the degradation cost of on-board HESDs considering the long-term train operation constrained by the initial investment of on-board HESDs. Train operation is found to be highly related to characteristics of on-board HESDs including the maximum power, capacity, and state of health (SOH). By changing the investment ratio between Li-ion battery and supercapacitor, the energy-saving rate and economic cost for various investment ratios have been obtained. Compared with the results of train optimal control with Li-ion battery only, supercapacitor only and no on-board HESDs, the results indicate an energy-saving rate up to 25.59%, from the perspective of the long-term train operation. When the allowable capital cost is relaxed from 20 k $\$ $ to 60 k $\$ $ , the cost per kilometer is reduced from 0.55 USD/km to 0.53 USD/km, showing higher capital cost is closely linked to higher cost reduction in the long-term train operation.

The optimization of the train speed trajectory and the traction power supply system (TPSS) with hybrid energy storage devices (HESDs) has significant potential to reduce electrical energy consumption (EEC). However, some existing studies have focused predominantly on optimizing these components independently and have ignored the goal of achieving systematic optimality from the standpoint of both electric systems and train control. This paper aims to establish a comprehensive coupled model integrating the train control, DC traction power supply, and stationary HESDs to reach the minimum EEC within the integrated system. The original non-convex and time-varying model is initially relaxed and reformulated as a convex program that can be solved quickly. On this basis, a model predictive control (MPC) framework is proposed to derive specifications in the space-domain-based model and overcome the drawbacks of the time-domain-based model. The designed controller solves the optimization problem for the remaining journey through time sampling, guaranteeing real-time and closed-loop performance. The numerical experiments present five case studies based on the real-world scenario i.e. Guangzhou Metro Line No.7. The results demonstrate that the proposed integrated convex model without stationary HESDs can reduce the accumulated EEC by up to 27.99% compared to the existing field test results. In addition, compared to mixed integer linear programming (MILP) method, the convex program proposed in this work obtains the highest energy savings rate (48. 71%) and significant computational efficiency, ranging from milliseconds (0.03 s) to seconds (4.20 s) in the TPSS with stationary HESDs. Additionally, the convex model features satisfactory modeling accuracy by invoking the nonlinear solver to simulate the power flow of the integrated system and recalculate the EEC.

Considering the unknown compound interference in manufacturing systems, the finite-time tracking and synchronization performance of the multi-motor system significantly affects the production safety, reliability, and quality, which can be considered a multi-agent system with unmeasured speed and uncertainty. In recent years, the synchronous control schemes of the multi-motor system have grown to maturity, but the research on the speed sensorless finite-time consensus tracking control remains to be extended. This paper proposes an observer-based leader–follower consensus tracking control for the synchronous coordination control of the multi-motor system. The speed and position of all motors can be tracked by consensus in a finite time when only some motors realize partial interaction. First, a finite-time observer is designed to estimate the unknown composite disturbance and unmeasurable speed variable of each motor. Second, the distributed finite-time consensus tracking control protocol is designed using the observed value and local information interaction. The stability of the overall closed-loop system is theoretically analyzed based on Lyapunov theory and graph theory, which shows that the consensus tracking error converges to an arbitrary small neighborhood of zero, and all signals are globally bounded in finite time. Finally, simulation results are provided to illustrate the effectiveness of the proposed control method.

In high frequency AC (HFAC) distribution system, the resonant inverter is used to improve power quality and keep the stability of the output AC voltage. Aiming at the problems of poor output power quality and slow transient performance caused by unreasonable filter parameter design and load change during inverter operation, a single-phase H-bridge LCLC resonant inverter based on analog circuit controller implement is introduced in this paper for HFAC power distribution system (PDS). In this study, to design harmonic compensator and analyze the responsiveness of the inverter, it is necessary to analyze the output voltage total harmonic distortion (THD) of LCLC resonant inverter and the performance of the open loop system in detail. On the one hand, a proportional-integral-resonant (PIR) controller is designed to maintain the zero static error of the voltage output and suppress the output voltage THD of LCLC resonant inverter. On the other hand, an integral controller combines with phase-shift modulation (PSM) method is presented to effectively improve the transient performance of resonant inverter and provide the fixed frequency of the output voltage. On the basis of the above, the experimental prototype is implemented with the output AC voltage root mean square of 28 V, and the output voltage frequency for resonant inverter is equal to switching frequency. A rated output power of 130 W experimental platform is built to verify the effectiveness of the theoretical analysis, control strategy, and modulation method.