PV systems are typically equipped with reactive power compensation devices when connected to the grid, and static synchronous compensator (STATCOM) devices are widely employed due to their flexible control capabilities. The increasing utilization of power electronic devices in the power grid has resulted in a shift from physical synchronization to control synchronization as the dominant mode of system operation. Analyzing static synchronization stability problem is more challenging for these systems compared to conventional power systems, as converter output characteristics are influenced by control strategies. Therefore, it is imperative to urgently address the problem of static synchronization stabilization under control strategy dominance.

First, this paper establishes the static synchronous stability analysis model of the grid-connected converter based on the control loop and circuit structure of each converter in a parallel system under the respective dq reference frame. The dq reference frame of the converter is determined by the phase information provided by the control loop in a multiple converter parallel system, thus enabling a unified coordinate system for static synchronization stability analysis. Subsequently, an equivalent small signal model is developed for analyzing multiple grid-connected converters. In comparison with existing coordinate conversion methods, Kirchhoff's current law is incorporated to enhance accuracy and reduce errors.

Then, the stability criterion for impedance analysis is enhance, and the static grid-synchronization performance indices are created. The small perturbation oscillation characteristics are measured using overshooting and regulation time, while the participation factor is employed to analyze the impact of each pole of the system. Finally, the attenuation coefficient is utilized to assess static synchronization stability performance.

The model is developed in Matlab/Simulink for simulation verification. Subsequently, an analysis is conducted on the impact of parameters such as the control loop parameters and STATCOM capacity on static synchronization stability. The main conclusions are summarized as follows:

(1) Optimizing the reactive power output of the grid-connected converter based on known control parameters can significantly enhance static synchronization stability performance, with the dominant influence of small perturbations after oscillation mode being attributed to poles generated by phase-locked loop control.

(2) The attenuation coefficient of the system exhibits a rapid increase in proximity to the critical stability region. Hence, it is imperative for the system to possess a certain margin of attenuation coefficient during operation. Based on the simulation analysis results presented in this study, static synchronous instability phenomena occur when the attenuation coefficient of the PV system exceeds 300. Conversely, when the attenuation coefficient falls below 250, the system remains in a state of static synchronous stability. These findings establish a criterion for analyzing and assessing static synchronization stability within such systems.

(3) The addition of STATCOM to the PV system primarily impacts the conductance matrix transfer function of the q-coupled channel. The phase-locked-loop coupling oscillations between the grid-connected converters do not affect the dd channel. Within the stable operating region, an increase in bandwidth for the DC voltage control loop, active current control loop, and reactive current control loop results in an amplification of both attenuation coefficient and system oscillation amplitude.

(4) When the phase-locked loop parameters of the STATCOM are the same as the PV system, the stability performance of the system is mainly affected by the grid impedance and the equivalent conductance transfer function of each grid-connected converter. And each grid-connected converter can independently connect to the grid and achieve stable operation to ensure that the system achieves static synchronous stability in this case.

(5) In cases where the active output of the PV system is low, STATCOM typically adjusts its capacitive or inductive reactive power provision to improve static synchronization stability performance. Conversely, when compensating for capacitive reactive power, utilizing STATCOM may yield superior results compared to using the PV grid-connected converter alone. Hence, allocating an optimal capacity for STATCOM can significantly enhance static synchronization stability performance.

As the penetration rate of renewable energy resources continues to increase, the traditional power system based on synchronous generators is evolving into a power system based on diversified power electronic equipment. The small disturbance stability analysis problem of multi-converter grid-connected system has attracted widespread attention. State-space model and impedance-based model are two main small disturbance stability analysis methods. Being as the white-box method, state-space model can be difficult to apply in practice because the differential equations describing the controllers of converters are not generally openly available due to commercial confidentiality. Impedance models have been popular in the field of power electronics for analysis of interactions between grid and converters. However, applying it directly to the stability analysis of multi-converter system will make the analysis process very complicated. Generally, the existing state-space and the impedance method still have room for improvement for the small disturbance stability analysis and sensitivity analysis of the oscillation mode of each converter.

Firstly, this paper proposes a single-input single-output (SISO) dq impedance stability criterion for analyzing the small disturbance stability of the multi-converter grid-connected system. Secondly, based on the formula of the stability criterion proposed, an expression for calculating the closed-loop pole of the system is derived. Because this formula is only a scalar function, the accuracy can be guaranteed for the usage of vector fitting (VF) method. Furthermore, a method for analyzing the sensitivity of oscillation modes to the impedance/admittance of each converter is proposed. This method can effectively evaluate the influence of different converters on the oscillation modes and help identify the dominant converter that causes oscillations. Finally, the accuracy of the proposed method is verified by Matlab/Simulink simulation and hardware-in-the-loop experiment.

The results are as follows: firstly, the proposed multi-converter system model can be used to represent the converter grid-connected system with any network structure and any number of grid-forming and grid-following converters. Based on the proposed method, it can be used to analyze the overall stability of the system as well as the influence of each converter on the system stability. Secondly, the proposed sensitivity analysis method can be used for evaluating which power converters are more sensitive to the close-loop poles and have a significant contribution to the harmonic instability.

The following conclusions can be drawn from the above results: (1) A recursive stability evaluation method for analyzing the stability of the multi-converter grid-connected system based on SISO dq impedance ratio is achieved, and a complete stability evaluation procedure is provided. Compared with the stability analysis method based on generalized Nyquist criterion, the stability analysis problem of a MIMO system is transformed into the stability analysis of a series of SISO systems, and the stability analysis of the whole system can be realized only by the impedance ratio of d-axis and q-axis in the stability analysis process. Because the SISO impedance ratio is used for stability analysis, the solution of the eigenvalues of the high-order return rate matrix required by the traditional method can be avoided, and the complexity of Nyquist plot analysis required for MIMO system can be effectively reduced. (2) In the proposed impedance stability criterion, dq impedance is adopted to model the VCI while dq admittance is used to describe the CCI, so the complicated procedure for obtaining the RHP open loop poles can be avoided. (3) Based on the proposed stability criterion proposed, an expression for calculating the closed-loop pole of the system is derived. Since this paper adopts dq coordinate system for modeling and derivation, compared with the sequential impedance model, the transfer function matrix elements can be guaranteed to be rational fractions, so the closed-loop poles can be obtained by VF method. (4) The sensitivity formula of the system's closed-loop poles on the dq admittance/impedance of the converter in the system is derived in this paper. Combining with the residual of the closed-loop poles obtained by the VF method, it can be used to analyze the influence of each converter on the key modes in the system. Therefore, it is helpful to identify the source that causes oscillatory instability.

Hydrogen, as a clean, efficient, and high-quality energy source, is recognized as a crucial solution for decarbonizing the energy system and mitigating climate change. The electricity and hydrogen energy system, which uses electricity and hydrogen as energy carriers, represents a key pathway for integrating power systems with hydrogen energy. It helps overcome the developmental limitations of renewable energy, fosters the interconnection and complementarity of multiple energy modes, and promotes deep integration across generation, grid, load, and storage. The electro-hydrogen coupling process, central to this system, can lower operating costs through peak shaving and valley filling. However, the efficiency of electrolyzers and fuel cell remain suboptimal, resulting in significant exergy losses alongside economic benefits during the coupling process. Striking a balance between economic viability and energy saving continues to be a challenging task. Moreover, the substantial forecasting errors caused by the uncertainty of renewable energy outputs can negatively impact the supply-demand balance and the operating conditions of electrolyzers. Therefore, the uncertainty risks associated with renewable energy must be thoroughly considered in optimal scheduling. In response to the above problems, a robust optimal scheduling model based on exergoeconomic analysis is proposed, with the uncertainty set defined by the confidence interval to reduce the conservatism of robust optimization.

Firstly, considering the dynamic efficiency characteristics of the electrolyzer, piecewise linearization was applied to handle the non-convex terms introduced by this relationship. The operation model of the electrolyzer including hydrogen production power allocation and operation models of fuel cell and energy storage equipment were constructed. Secondly, the energy quality coefficients were employed to analyze the exergy loss distribution based on the equipment operation model. A cost accounting method for exergy losses, including both internal and external factors, was proposed. Internally, the cost allocation method was used to price unit exergy losses, enabling the calculation of operational loss costs based on the distribution of exergy losses. Externally, the cost of transmission line losses and penalties of wind curtailment were calculated according to current electricity prices and relevant policies. Thirdly, taking into account constraints such as electrolyzer start-stop cycles, ramping power, and energy balance, an optimal scheduling model was developed with the goal of minimizing total exergy loss costs in the electricity and hydrogen energy system. Then, the model was reformulated into a robust optimization problem based on the uncertainty set of the confidence interval，and a dual transformation method for solving the model was proposed.

In the case simulation, four cases are set up for comparative analysis, leading to the following conclusions: (1) By setting the wind curtailment penalty coefficient appropriately, with the goal of minimizing exergy loss costs, a balance can be achieved between the economic benefits and the exergy losses associated with the electricity-hydrogen coupling process, while ensuring the efficient absorption of wind power. (2) The proposed model can further improve the overall hydrogen production efficiency of the electrolyzer array by taking advantage of the flexibility of hydrogen production power allocation. (3) The confidence interval is used as the uncertainty set of robust optimization, which can take into account the probability characteristics of random variables, and reduce the conservative degree of system operation under the premise of ensuring robustness.

Under the background of the dual carbon goals, the regional integrated energy system (RIES) can achieve interconversion between heterogeneous energy sources due to its multi-energy coupling characteristics, providing new technical support for energy-saving and efficient operation of modern energy systems. Due to the differences in the flow of heterogeneous energy sources in transmission pipelines, existing research usually adopts convex relaxation techniques or linearization methods to model and solve the RIES for multi-time-scale, and relies on high-precision source-load forecasting results and equipment mathematical modeling to improve the reliability of scheduling decisions. However, the increasingly complex internal energy coupling structure of the RIES has increased the difficulty of its refined mathematical modeling and solution, posing challenges to the real-time scheduling decisions and safe optimal operation of the RIES. therefore, this paper proposes an improved distributed bi-layer proximal policy optimization (DBLPPO) deep reinforcement learning scheduling model. This model can achieve multi-time-scale optimization management of various energy networks in the RIES and avoid the optimization difficulties caused by non-convex nonlinear model structures in scheduling solutions.

Firstly, the power output, storage, and transformation of internal energy in the RIES are constructed into a high-dimensional space Markov decision process mathematical model. Secondly, based on the improved distributed proximal policy optimization (DPPO) algorithm, a sequential decision description is made for it, and a control model of the internal bi-layer proximal policy optimization (PPO) is constructed. the local network adopts the "coupling first, then decoupling" solution approach to carry out multi-time-scale optimization decision-making for the cold-heat system and the power system. In the early stage of long time scale, the inner and outer models perform coupled solutions, and the RIES cold-heat system and power system achieve coordinated optimal operation. In the remaining short time scales, the inner and outer models perform decoupled solutions and carry out short-term flexible regulation of the power system. the inner and outer models interact with each other and fluctuating convergence towards the reward maximization direction, eventually achieving multi-time-scale optimization scheduling of the RIES cold-heat system and power system.

This paper conducts simulation experiments with a cold-heat-electric RIES as the scheduling scenario, and compares the scheduling results of the DBLPPO scheduling model with those of a single time scale scheduling model (PPO, DPPO). the results show that the DBLPPO scheduling model can flexibly regulate the system's adjustable resources in the short time scale, meet the power fluctuation requirements of electricity, heat, and cold loads in the short time scale, and has the lowest comprehensive operating cost, which is 24.47% lower than that of the DPPO scheduling model and 28.54% lower than that of the PPO scheduling model. In addition, simulation experiments are conducted with the DBLPPO scheduling model and the bi-layer PPO scheduling model in the same scenario, and the results show that the distributed structure of the DBLPPO scheduling model still has a significant advantage in improving model training efficiency, which can effectively shorten the training time, 10.01% shorter than that of the dual-layer PPO scheduling model.

Through case analysis, it is verified that the proposed scheduling model can achieve coordinated optimal management of various energy networks in the RIES at different time scales, accelerate the optimal decision-making speed of the multi-time-scale scheduling model, and by virtue of the fast adaptability of the deep reinforcement learning algorithm, efficiently solve random optimization problems in complex RIES scenarios, and improve the economic benefits of system operation. The next step of work will be to improve the model to enhance the environmental awareness ability of the inner model, so that its decision-making scheme is always the optimal scheduling decision in the long time scale.

The rapidly developing field of artificial intelligence (AI) has made significant advancements in areas such as image processing, language, decision-making, and diagnostics, providing new methods for solving complex problems. The increasing intelligence of electrical equipment, combined with the coupling of strong and weak electrical fields, has led to the emergence of multi-scale, multi-physical field coupling and nonlinear problems in electromagnetic fields. High-precision numerical modeling and optimization are increasingly challenging.

Therefore, this paper combines recent research outcomes from the author’s team to introduce deep learning methods for solving typical interdisciplinary problems, such as data-driven modeling, physics-driven PDE solving, and knowledge-embedding modeling. In particular, the paper discusses the current state of intelligent modeling for complex electromagnetic field problems driven by both data and knowledge. It also offers perspectives on the scientific challenges and important future directions in the research and engineering implementation of electromagnetic field intelligent modeling.

In the area of data-driven modeling, the paper explores its application in the performance analysis and optimization of electrical equipment. The discussion is divided into three parts: performance parameter calculation, electromagnetic thermal field prediction, and knowledge discovery modeling. By combining numerical simulation and experimental data, deep learning algorithms can mine potential knowledge from the data, enabling rapid computation of one-dimensional performance and two- and three-dimensional fields. This approach allows for real-time simulation of local performance, global performance, and micro characteristics.

Regarding physics-driven partial differential equation (PDE) solving, the paper discusses two main research directions: knowledge-embedding regularization methods and designing machine learning model structures based on physical meaning. Constructing loss functions or network structures that align with physical laws makesit possible to solve PDEs without relying on sample data. This method is beneficial when physical conditions are incomplete and sample data is scarce. Using AI to solve physical equations helps overcome traditional bottlenecks, improving computational efficiency and expanding application scope.

In the area of knowledge-embedding modeling, the paper discusses how to implicitly integrate domain knowledge, mainly through multi-fidelity models and neural network operator methods, to improve the precision and efficiency of computational models. By embedding the knowledge inherent in high-precision samples into the model, high-precision forward and inverse problem models can be built. As data accumulates, the model's accuracy and generalization ability will improve. This method fully utilizes the advantages of deep learning and integrates basic physical theories. As data grows, knowledge-embedding methods are expected to be crucial in solving more complex electromagnetic field problems and enhancing overall simulation outcomes.

In conclusion, the fusion of AI and knowledge has become a significant trend in the development of numerical simulation. Integrating data-driven, physics-driven, and knowledge-embedding methods has accelerated the advancement of electromagnetic field modeling and optimization. These methods have improved simulation accuracy and expanded the application range of numerical simulations for complex electromagnetic field problems. However, the exploration of AI in numerical simulation is still in its early stages, facing challenges such as insufficient model generalization, computational efficiency improvement, and physical constraint integration. Future research should focus on addressing these issues to promote the broader application and development of AI in the field of electromagnetic field numerical simulation.

In recent years, the rapid development of renewable energy has posed a significant challenge to the breaking capacity of DC circuit breakers in power systems. Gas-blowing arc extinguishing technology based on gassing materials can greatly enhance the breaking capacity of DC circuit breakers. However, the macroscopic and microscopic pyrolysis mechanisms of gassing materials are unclear.

Firstly, the micro-pyrolysis mechanism of typical gassing material polyamide 66 (PA66) at different pyrolysis temperatures and rates was analyzed based on the reactive force field (ReaxFF). The decomposition process of PA66 and the types and quantities of small molecule gases produced were discussed. It was found that the initial bond breaking of PA66 occurred in the C—C bond adjacent to the amide group. H₂ and H₂O were the main pyrolysis gases of PA66, and their production process was analyzed. The reaction rate of carbon-free small molecule gas at high temperatures accelerates, and the amount increases. The product amount with carbon atoms below four increases rapidly and decreases slightly after reaching a peak. The main reasons are the Diels-Alder reaction, C3/C4 reaction, and cyclization reaction in the unsaturated hydrocarbons in the product, which leads to the decrease of hydrocarbon molecules. The temperature increase aggravates the disintegration of the PA66 molecular chain and the formation of small molecular gas. The heating rate of the system affects the distribution of heat in the reaction system, thus affecting the formation of the product. The slower the heating rate of the system, the more conducive to the uniform distribution of heat in the reaction system. Additionally, the amount of carbon deposition during pyrolysis at 2 600 K was analyzed. Light tar was dominant, followed by heavy tar, with the least amount of coke.

Subsequently, pyrolysis experiments at four different heating rates were carried out. Based on the Flynn-Wall-Ozawa isoconversional model, the average activation energy of PA66 was 194.85 kJ/mol, which was very close to the activation energy of 195.015 kJ/mol obtained by molecular dynamics simulation. Additionally, the pyrolysis gas distribution of PA66 was analyzed by pyrolysis-gas chromatography/mass spectrometry (Py-GC/MS) experiments, which verified the accuracy and reliability of the pyrolysis kinetics calculation method. PA66 is suitable for the first-order reaction kinetic model, and the simulation data have high accuracy and reliability for the thermal decomposition reaction path and gas type of PA66 at the microscale.

Finally, simulation calculations and arcing experiments of three gas-producing materials, PA6, PA46, and PA66, were carried out. The gas generation rate and quantity changes during pyrolysis were observed, and the transient pressure changes during the arc-breaking experiment were analyzed. The order of transient pressure generated during the arcing process is PA6>PA46>PA66, consistent with the trend of the number of product gas molecules obtained by simulation calculation. The ReaxFF simulation results are confirmed and supplemented with the arc-breaking experiment, further verifying the reliability and accuracy of the research.

This paper offers a theoretical framework for understanding the macroscopic pyrolysis behavior and the microscopic pyrolysis mechanism of gassing materials. It contributes to a deep comprehension of material behavior under high-temperature and arc conditions, laying a methodological foundation for evaluating the performance of gassing materials in DC circuit breakers.

The low-voltage power supply and distribution system is directly connected to the user at the end of the power system. Its wide distribution, diverse applications, and complex structure make overhauling difficult and lack safety maintenance. Due to its negative resistance characteristics, the series arc can decrease line current, exhibiting high concealment of fault characteristics. It is a loophole in traditional relay protection methods. The series arc fault can produce high temperatures in a short time, which can cause a fire very quickly. The temperature characteristics of AC fault arcs have not been thoroughly studied, the development process and influencing factors of fault arc temperature are not apparent, and the mechanism of arc ignition and disaster needs to be clarified. This paper builds a real experimental platform for arc ignition, constructs a numerical simulation model of AC arc fault based on magnetohydrodynamics, verifies the temperature characteristics of arc fault through simulation and experiment, clarifies the ignition mechanism of arc fault, and puts forward suggestions for the improvement of relevant standards.

Firstly, based on the IEC 62606 standard, combined with a temperature acquisition device, an experimental platform for arc fault ignition risk is built to simulate arc faults. The current, voltage, temperature, and thermal imaging images are collected. Secondly, the physical characteristics of AC fault arc and related test standards are analyzed, and a complete set of fault arc simulation schemes is designed. Thirdly, the control equation, calculation domain, and boundary conditions of the arc fault magnetohydrodynamic simulation model are defined, the material parameters are designed, and the division of the simulation grid is refined. Finally, by analyzing the simulation model's calculation results, the fault arc's temperature characteristics are obtained, and experiments verify the simulation results.

The simulation results show that the temperature of the AC fault arc increases periodically, and the maximum temperature of the arc appears near the instantaneous peak value of the current. At this time, the influence range of arc temperature also increases significantly. The arc temperature is a cumulative process but develops rapidly in half an AC cycle. The arc current level and arc gap distance are the main factors influencing the maximum temperature of the arc, and the current level plays a decisive role in directly affecting the severity of the arc fire risk. The maximum temperature of the arc increases linearly with the current level below the 32 A current level, and the maximum temperature growth rate slows down after the 32 A current level.

The existing arc fault product standards can effectively limit the maximum temperature of arc fault and the influence range of arc temperature. However, even in the time specified in the standard, the arc center temperature can still reach more than one thousand degrees. Therefore, the standard can be improved by limiting the influence range of arc temperature to reduce the fire risk. Low current arc ignition ability cannot be ignored. The current level range covered by the relevant standards should be expanded, and the maximum removal time of 1 A and 2 A current level arc faults is recommended to be 3 s and 1.5 s, respectively. The standard action characteristic requirements should be refined to prevent arc fault hazards and reduce electrical fires comprehensively.

Recently, the bus voltage of data center power architectures has been gradually increased from the traditional 12 V to 48 V to reduce the current in the distribution lines, thus reducing distribution losses. In 48 V bus-powered architectures, the uninterruptible power supply (UPS) system is connected in parallel with the 48 V bus, which causes the bus voltage to fluctuate over a wide range (40 V to 60 V). To better manage the bus voltage and energy flow, a bidirectional DC-DC converter must be inserted between the UPS and power-using systems. The four-switch Buck-Boost converter is attractive because of its high efficiency and wide voltage regulation capability. In order to reduce the energy consumption in data centers, it becomes crucial to improve the efficiency of FSBB.

This paper analyzes the voltage gain of the FSBB converter. Then, a graphical approach compares the control strategies of the FSBB converter. The unimodal control strategy has large ripples. The bimodal control strategy system is unstable. Tri-modal solves the problems of duty cycle limitation and system stability, but the duty cycle varies greatly when the transition mode is switched. Four-mode control can add a control mode in the transition section to realize smooth conversion between different modes, and the ripple of inductor current is small. It is a control strategy with excellent performance.

Then, the minimum ripple condition of the inductor current is analyzed based on four-mode control. The inductor current ripple of the FSBB converter is minimized when the phase shift time between the Buck and Boost bridge arms is controlled to zero. The average value of the inductor current is related to the output voltage, input voltage, maximum duty cycle, and output current, and it is almost the same for all four-mode control strategies. Therefore, the control method to minimize the inductor current can be obtained by simultaneously controlling the phase shift time to zero.

Next, an accurate loss model of the FSBB converter is developed. When the voltage gain is constant, the loss of the converter increases as the load current increases. When the load is fixed, the lower the switching frequency, the lower the loss. Under the same load conditions, if the voltage gain is greater than 1, the loss decreases with the gradual increase of the gain at the same switching frequency until the loss is minimized when the voltage gain equals 1. On the contrary, if the voltage gain is less than 1, the loss gradually decreases as the gain gradually increases. Thus, this paper proposes a frequency reduction control strategy to reduce the converter loss in the transition mode and improve the conversion efficiency by reducing the switching.

Finally, an experimental platform is established to test the inverter control strategy for the FSBB converter in steady states. The minimum ripple control strategy is then validated. The results show that the transition mode’s inductor current ripple with the proposed control strategy is much smaller than the conventional four-mode control strategy. Among them, the inductor current ripple of the proposed minimum ripple control strategy is 35.2% of the conventional control strategy under the operating conditions of 51 V input voltage and 48 V output voltage. After reducing the switching frequency, the inductor current ripple of the minimum ripple control strategy is still smaller than that of the conventional control strategy. The efficiency of the proposed low ripple inverter control strategy is improved over the whole load variation range compared with the traditional fixed frequency control. Among them, the peak efficiency of the proposed inverter control strategy reaches 98.52% and full-load efficiency 98.4%, which is improved by 2.46% and 2.35% compared to the conventional scheme, respectively.

This paper analyzes the electromagnetic energy flow and coupling characteristics in wireless power transmission (WPT) systems. Addressing the complexities in accurately depicting the electromagnetic energy transformation within WPT systems, the research overcomes challenges associated with the intricate mathematical methods and the absence of models capable of characterizing spatial energy flow distribution.

A model for electromagnetic energy flow in WPT under sinusoidal excitation is established based on Poynting’s theorem. A reduced-order mathematical model is developed by analyzing common electromagnetic energy flow characteristics of basic electrical components. This model qualitatively explores the energy coupling in the transmission space. The coexistence of inductive and capacitive coupling in WPT systems is discussed, emphasizing the significance of enhancing near-field electromagnetic coupling for overall system performance. The working mode of WPT in the electromagnetic near-field region is presented from the perspective of the energy flow mechanism. An experimental platform is constructed to verify the inductive and the capacitive coupling methods.

The electromagnetic energy flow characteristics of conductors, transformers, and capacitors are analyzed, facilitating power transmission through the electromagnetic fields in their vicinity rather than by themselves. The electromagnetic energy flow characteristics of WPT systems are discussed as a combination of multiple RLC circuits. It is found that electromagnetic power is partly stored in the electromagnetic fields of individual circuits (self-energy) and partly in the fields between circuits (mutual energy). The analysis is simplified by considering a system with two RLC series circuits, revealing that WPT relies on mutual coupling between the primary and secondary sides for contactless power transfer.

The paper also discusses typical magnetic resonant WPT systems using the image method to analyze the field strength distribution in the coupling space. The symmetry between inductive and capacitive coupling characteristics is revealed, offering guidance for practical engineering design. Experiments are conducted to verify the coexistence of inductive and capacitive couplings and to analyze their frequency characteristics. Results indicate that as the operating frequency increases, the ratio of capacitive coupling to inductive coupling increases, which is significant for understanding WPT technology.

In conclusion, the paper analyzes the electromagnetic energy flow and coupling characteristics in WPT systems, offering valuable insights for the theoretical research and practical application of WPT technology. It highlights the importance of understanding the coexistence of inductive and capacitive couplings and their frequency characteristics to enhance the performance of WPT systems.

Due to the advantages of high power level, small torque ripple, and strong reliability, dual three-phase permanent magnet synchronous motors (DTP-PMSM) have been widely used in electric vehicles, ship propulsion, and aerospace power systems. The high fault-tolerant capability for open-phase faults is an important application feature of DTP-PMSM. Developing fault-tolerant control strategies is crucial for improving fault-tolerant performance. While both the minimum loss (ML) and maximum torque (MT) control strategies offer their advantages, stator copper loss and torque output capacity cannot be simultaneously considered. The full range minimum loss (FRML) control strategy comprehensively considers both ML and MT optimization objectives. The stator copper loss is effectively reduced without sacrificing the output torque range. Currently, the FRML control strategies usually add the restriction of sinusoidal current mode. However, the restriction of the sinusoidal current mode narrows the solution space of the current reference and prevents further improvement of the fault-tolerant performance. Therefore, a FRML control strategy based on harmonic current injection is proposed.

Firstly, considering the control complexity and optimization effect, third harmonics are injected into the fault-tolerant phase current to expand the solution space. By optimizing the current references, the fault-tolerant performance of ML and MT control strategies is further improved. Secondly, considering the stator copper loss and torque output capacity holistically, an allocation coefficient is introduced to combine the ML and MT strategies nonlinearly. The fault-tolerant trajectory can be smoothly switched online by adjusting the allocation coefficient under various load conditions. The proposed FRML control strategy simplifies the implementation complexity and produces a unified expression of current reference, which effectively reduces stator copper loss over the torque range. Finally, the proposed control strategy is verified on a surface-mounted DTP-PMSM platform. The quasi-proportional resonance controllers ensure accuracy in tracking the AC current reference. Both ML and MT control strategies achieve smaller stator copper loss and larger torque output capacity after the third harmonic injection than the sinusoidal current mode. When the FRML control strategy based on harmonic current injection is applied, the allocation coefficient is modified in real-time with the change of load condition. Under the rated load of 65.5%, 67.7%, and 69.7%, the stator copper loss is lowered by 6.2%, 4.91%, and 3.1%, respectively, compared to the MT control strategy. The fault-tolerant control strategy is verified.

The following conclusions can be drawn. (1) The strategies with the injection of third harmonic exhibit the superior performance of copper losses and torque output capability than that with sinusoidal current mode thanks to the more thorough current optimization. Therefore, the fault-tolerant control strategy based on third harmonic injection is more favorable for the stator copper loss optimization in the full torque range. (2) The proposed FRML control strategy based on harmonic current injection can further expand the range of torque optimization and enhance adaptability to various load conditions. (3) The proposed fault-tolerant control strategy is scalable. Future work will be focused on extending the applicability of the proposed control strategy to other polyphase motors, such as nine-phase motors.