LLC converters are widely used in the power stage of battery energy storage converters due to their excellent soft switching performance and low output impedance. Under low voltage and high current conditions, matrix transformers are often used on the secondary side of LLC to reduce current stress. In practical circuits, the volume of matrix transformers accounts for about 25% of the total main power, which seriously restricts the improvement of device power density. This paper proposes an integrated optimization design of LLC four-element-matrix planar transformer considering loss and parasitic parameters. Decoupling the influence of various structural parameters of transformers on parasitic parameters this method achieves efficient operation of transformers and controllable parasitic parameters. Voltage drop and oscillation are effectively suppressed.

Firstly, establish an accurate transformer loss model based on the proposed distributed magnetic core loss calculation method. Select the key parameters of the magnetic core that meet the efficiency and volume requirements: the radius of the magnetic core's central pillar r and the total width of the winding c. Afterward, select the winding layer structure. Establish a leakage inductance model based on transformer leakage magnetic field energy, determine the feasibility of leakage inductance integration through PCB thickness constraints, and design leakage inductance values.

The experiment shows that the secondary-side V_ds voltage oscillation is significantly reduced after integration optimization, reducing the parasitic capacitance value. By matching the resonant inductance to ensure that LLC operates in critical continuous mode at 300 kHz, the magnitude of the transformer's primary leakage inductance before and after integration can be calculated. The resonant inductance before integration is 1.8 μH, indicating the original edge leakage is 0.7 μH. After integrated optimization, the resonant inductance is 2.3 μH, indicating the original edge leakage is 0.2 μH. When operating in reverse, with the same input voltage of 3.2 V, the LLC output voltage rises from 34 V to 35 V. This means that the secondary edge leakage has decreased after integration. After resonance point matching, the secondary leakage inductance can be reduced from 33 nH to 12 nH. The secondary side V_ds oscillation caused by parasitic capacitance is close and small, which verifies the control effect of parasitic parameters.

This method can achieve the following effects. (1) The proposed distributed magnetic core loss calculation method for planar transformers based on P-B curves eliminates the influence of uneven magnetic density distribution on the accuracy of the magnetic core loss model, achieving accurate modeling of integrated transformer losses. (2) This method provides a judgment method for the feasibility of leakage inductance integration. (3) The prototype parasitic parameters can be controlled by accurately modeling the leakage inductance and parasitic inductance. This method provides theoretical support for designing and optimizing energy storage converters in LLC low-voltage and high-current scenarios.

In non-destructive testing (NDT), there is a growing demand for simulation tools that can predict magnetic characteristics, enhance understanding, and avoid harsh and uncertain experimental expectations. Due to the high sensitivity and non-destructive nature, the measurement and simulation of magnetic barkhausen noise (MBN) have become important in NDT.

This paper measured the MBN signals of soft magnetic materials under different stress conditions at a magnetic frequency of 10 Hz. The experimental results revealed the significant impact of tensile and compressive stresses on the MBN signals. Specifically, as tensile stress increases, the spacing between magnetic domain walls decreases, reducing energy loss in the movement of domain walls. The migration rate of the domain walls is accordingly increased, which in turn causes the MBN signals to rise. At the same time, due to the presence of additional domains in oriented silicon steel, the MBN signals exhibit a double-peak structure. As tensile stress increases, these additional domains are suppressed. Hence, peak-to-peak values one and two increase, and the increase in peak value two is significant. When a magnetic field and compressive stress are applied along the rolling direction, the compressive stress increases the energy of the magnetic domain walls, reducing their migration rate and weakening the MBN signals. Ithelpsto better understand the changes in the magnetic properties of soft magnetic materials under different stress conditions.

Existing MBN models can not accurately simulate the MBN signals of different soft magnetic materials under stress. This paper proposes a mathematical model based on the improved S-J-A hysteresis model. This model simulates MBN signals by considering the irreversible motion of magnetic domain walls in soft magnetic materials, thereby increasing the accuracy of the simulation. Specifically, the improved S-J-A hysteresis modelsimulates the irreversible hysteresis loops of soft magnetic materials, considering the relationship between magnetic anisotropy, model parameters, and stress. Then, these irreversible hysteresis loops are linked with the MBN envelope line to establish a mathematical model for the MBN envelope curve. Next, the MBN signals are simulated by modulating white noise in the 1~50 kHz range with this envelope curve. Finally, three different soft magnetic materials are selected: oriented electrical steel sheet (30QG120), non-oriented silicon steel (35WW230), and amorphous alloy (1K101). The proposed MBN model simulates MBN signals under different mechanical stress conditions.

The proposed MBN model accurately simulates the MBN signals of the oriented electrical steel sheet (30QG120), non-oriented silicon steel (35WW230), and amorphous alloy (1K101) under stress. A comparison of MBN signals between oriented silicon steel, non-oriented silicon steel, and amorphous alloy is conducted, revealing that the double-peak structure exhibited by oriented silicon steel under tensile stress is related to its anisotropy. Microscopic analysis gains a deep understanding of the stress effects on the magnetism of soft magnetic materials and the generation mechanism of MBN. The proposed MBN model provides a reliable tool in material characterization and non-destructive testing (NDT) applications, laying the foundation for further engineering applications.

In distributed power supply and distributed energy storage technologies, a bidirectional AC-DC converter is an important energy conversion device connecting AC-DC hybrid microgrids, and its performance index directly affects the overall performance and effect of hybrid microgrids. Compared with the two-stage topology, the single-stage dual active bridge (DAB) AC-DC converter removes the intermediate DC bus capacitance with a large capacitance value, reduces the conversion link, and has apparent power density and cost advantages. The traditional DAB AC-DC converter mainly adopts the modulation strategy of phase shift, which has the problems of high current stress and narrow soft-switching range. In addition, only adopting the phase shift control leads to the nonlinear relationship between the system input current and the shift ratio, increasing the control complexity. Therefore, this paper proposes a linearization-based minimum current stress control strategy for the converter to address the problems of modulation nonlinearity and high current stress in a single-stage dual active bridge AC-DC converter. This control strategy reduces the converter’s control complexity and current stress, ensuring a wide zero voltage switch (ZVS) range of the switching tubes.

Firstly, the switching characteristics of the extended phase-shift (EPS) modulation strategy are analyzed. For the nonlinearity between the input current and the shift ratio, the input current i_ac and the shift ratio D₁ are linearly related by introducing the phase shift index k and the maximum switching frequency f_smax. The expressions of the shift ratio D₁ and the switching frequency f_s are obtained combined with power factor correction. The switching characteristics of the EPS modulation strategy are analyzed. The trajectory of the phase-shift index k under the minimum current stress is obtained by the differential polarity method. Then, the expression of the shift ratio D₂ is obtained. Finally, the soft-switching ranges are analyzed for switch tubes S₂, S₅, and S₈. Except for the DC-side switch tube S₅, which is difficult to realize soft-switching in the small range under extreme light-load conditions, the other two switch tubes can realize ZVS in the wide range in other cases.

This paper verifies the proposed control strategy by combining simulation and experiment. Firstly, regarding simulations, the proposed control strategy can achieve the linearization between the input current and the shift ratio, effectively reducing the converter current stress. An experimental prototype is constructed with an AC 50 V input, DC 12 V output, and 100 W output power. The current stress is compared before and after optimization under different input voltages and the soft-switching realization under different load conditions. The control strategy effectively reduces the current stress of the converter while ensuring that the switching tubes have a wide ZVS turn-on range.

The magnetic lift control rod drive mechanism (CRDM) is a critical electromagnetic actuator for regulating nuclear reaction rates. Its dynamic process is complex to predict due to the cross-coupling among current response, magnetic circuit saturation, and motion state. The latest equivalent magnetic network (EMN) model exhibits inaccuracies and relies on flux distribution during modeling, lacking generality. In multi-field coupling analysis, researchers often employ multi-software collaborative or semi-simulation methods, which incur significant time and hardware costs. This paper proposes a dynamic equivalent magnetic network (DEMN) model and a multi-physics field coupling calculation method considering transient current changes and saturation.

Firstly, the structure of the magnetic lift CRDM is introduced, and its lift solenoid valve is selected to analyze the electromagnetism-mechanics coupling during dynamic processes. Then, the mechanism is partitioned using orthogonal grid lines, and mesh units of multiple media are consolidated into a single medium to unify the reluctance calculation formula. During dynamic changes, only the grid size or position in the motion region is altered, thereby eliminating redundant modeling and reducing computational errors caused by mesh discrepancies. A connection relationship and calculation method for branch reluctance are established to address the misalignment between fixed and moving mesh units, facilitating continuous armature movement. A multi-physics field coupling calculation method is proposed by combining circuit models and kinematic formulas, which consider transient current changes and saturation. Finally, Compared with 3D finite element analysis (FEA) and experiments, the DEMN model and the proposed multi-field coupling calculation method are verified.

3D FEA results show that the magnetic density distribution, inductance, and electromagnetic force are highly consistent with the DEMN results, where the maximum error of inductance is 5.7%, and the maximum error of electromagnetic force is 3.4%. The experiments show that linear and saturated inductance variations are similar. The calculation accuracy of the release and suction currents under various loads exceeds 91%. Additionally, the dynamic results closely align with experimental results, with motion time calculation errors at 28 A and 40 A currents of 0.99% and 2.99%, respectively.

The conclusion is as follows. (1) By using orthogonal grid lines, the unified calculation of reluctance is achieved, accelerating the modeling speed. (2) By changing the grid size or position of local areas, the dynamic changes of the EMN model are achieved, avoiding the problem of repeated modeling in the multi-field coupling calculation process and reducing the calculation errors caused by differences in mesh partitioning. (3) Compared with FEA, the proposed DEMN model requires less computational resources and shorter computation time while ensuring accuracy. Compared with the experimental results, the effectiveness and accuracy of the DEMN model and multi-field coupling calculation method are verified. It can be extended to EMN modeling, performance analysis, and rapid optimization design of the entire CRDM.

Traditional control parameter design methods of grid-connected converters (GCCs) are usually carried out under rated operation conditions. The stability margin is generally characterized by the magnitude margin (GM) and phase margin (PM). The bandwidth of the phase-locked loop (PLL) needs to be sacrificed for enough system stability margin, which ensures that the system can operate safely under non-rated working conditions. Therefore, traditional parameter design methods make it difficult to achieve a compromise between the stability and rapidity of GCC. Furthermore, the relationship between the stability margin and the output limit of the system is difficult to obtain, which relies on simulations or experiments. To address this issue, this paper proposes a control parameter design method based on the system stable operation domain, which com- prehensively considers the variable working conditions and different stability requirements.

Firstly, the complex vector open-loop transfer function G_s(s) is derived, which can analyze the stability of the system in a wide operating range or under different parameters. Secondly, varying the values of the PLL and current loop control parameters, the feasible domain of control parameters can be obtained by numerical analysis. PLL and current loop are coupled to each other due to the grid impedance. Therefore, the phase-locked loop parameter has a stable parameter boundary. Thirdly, based on the upper limit of the obtained PLL parameter, the three-dimensional diagram between the PLL parameter and the output current of the dq-axis is plotted, which shows the stable operation boundaries of GCC under different PLL parameters. Finally, taking the operation margin as the stability margin, the PLL parameter can be flexibly designed to realize the balance between the stability margin and the dynamic performance. Theoretical analysis results show that the control parameter design method based on the stable domain can ensure the safe and reliable operation of the system. Compared with traditional parameter design methods, determining the value of control parameter based on operation margin can improve the dynamic performance of PLL. At the same time, the corresponding relationship between different stability margin and the output current limit of the system can be obtained. Finally, the simulation and experiment results verify the correctness of the theoretical analysis and the effectiveness of the proposed design method.

The following conclusions can be drawn from the theoretical analyses: (1) The derived open-loop complex transfer function can be used to plot the control parameter feasible domain and the stable operation domain of GCC. The PLL control parameter satisfying the operation margin can be obtained quickly without repeated trial and error in the parameter design. (2) The analysis results show that the grid strength is positively correlated with the parameter feasible domain and the PLL cutoff frequency is negatively correlated with the stable operation domain. The cutoff frequency value of PLL is limited by the current loop parameter. The smaller the operating current in the parameter design, the wider the range of PLL cutoff frequency, and the better the dynamic performance of the PLL. (3) The control parameter design method based on the stable operation domain can directly quantify the influence of stability margin on the limit of the output current, which can be used for obtaining the stable boundaries under different stability margin. At the same time, the control parameters of PLL can be flexibly designed according to the actual needs of rapidity.

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.

As China advances its dual carbon strategy, integrating new energy sources into power grids has grown significantly, making power system operations more complex and dynamic. For deep learning-based models used in transient stability assessment to be reliable, the training data and the data encountered in real-world applications must be independent and identically distributed. However, because power systems are time-varying and uncertain, models trained offline may not perform well in new operational scenarios. This paper proposes a transient stability assessment-discriminative domain adaptive (TSA-DDA) framework to address variations in operating scenarios.

Firstly, an inter-domain dual distribution adaptation method was proposed. While aligning the marginal probability distributions of the source and target domains, this method also used Bayes' theorem to align the conditional probability distributions, achieving optimal domain adaptation. Secondly, both mean and variance differences between the source and target domains were comprehensively considered in the domain adaptation process. A new transfer regularization term was constructed to measure the inter-domain distribution differences, improving the model's domain adaptation capability. Finally, a discriminant Softmax function with adjustable parameters was developed to make intra-class sample features more compact while keeping inter-class sample features away by adjusting the parameters. This improvement can enhance the applicability of the assessment model to power grids.

In the case studies, the TSA-DDA framework's ability to address variations in operational scenarios was first validated on the New England 10-machine 39-bus system. Subsequently, four alternative TSA-DDA frameworks, each with specific modules removed, were established to evaluate the effectiveness of individual components. The prediction accuracy of the target and source domain test sets was compared using a fine-tuning algorithm and the TSA-DDA. The TSA-DDA’s capacity for continual learning is confirmed. The TSA-DDA was then benchmarked against mainstream transferred learning approaches to verify its effectiveness in scenarios with limited new data. Finally, to assess the generalization capability of the proposed scheme, experiments were conducted on a larger and more complex provincial power grid in Southwest China. The experimental simulations utilized the PSD Power Tools and Dynamic Simulation Program to offer high-fidelity power system simulation data for model training and testing.

The conclusions of this paper are given as follows. (1) The inter-domain dual distribution adaptation method comprehensively measures differences in marginal and conditional probability distributions between domains from both mean and variance perspectives. It constantly forces the feature extractor to narrow these differences, ensuring effective feature alignment across domains and enhancing the model’s adaptability. (2) The discriminant Softmax function improves the model’s learning of discriminative features by compacting intra-class features and separating inter-class features, which enhances the performance of the domain adaptation framework in transient stability assessment tasks. (3) Using voltage trajectory clusters with clustering and convergence properties as model inputs, the proposed framework ensures effective transferability across systems with varying structures and scales.

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.

The dynamic transformer rating (DTR) and thermal life loss of oil-immersed transformers under on-site variable load operation conditions are closely related to the transient temperature rise of the equipment. However, as an implicit solution method, the traditional finite element analysis and finite volume method need to be iteratively solved in each sub-step of transient thermal analysis, which has many computational resources and is time consuming. It is challenging to meet the requirements of fast calculation. The rapid and accurate solution of the temperature field (especially the hot spot temperature rise) of the oil-immersed transformer in field operation is the premise to realize the digital operation and maintenance of the transformer and the DTR evaluation. Therefore, this paper proposes a lattice Boltzmann (LBM) physical in the loop simulation model for coupled electrical networks. The real time evaluation of DTR under electrical network constraints is realized through the rapid solution of the transformer temperature field.

Firstly, the D2Q9 model is used to solve the fluid flow and thermal lattice Boltzmann equations (LBEs) to capture the transient oil flow and temperature rise process inside the transformer. In the Simulink environment, the equivalent current source model is used to construct the electrical network constraints of multi-level load scenarios, and the established transformer LBM model is used as a component for numerical encapsulation to complete the construction of the physical-in-the-loop simulation model. Secondly, to verify the effectiveness of the proposed method, the finite volume method (FVM) is used to simulate the same oil-immersed transformer model. The grid independence test determines the optimal number of grids. The number of grids is 1 250×420 for LBM modeling and simulation, and the number of units is 43 654 for FVM meshing. Compared with the constructed LBM-Simulink model with the FVM model, LBM still has the advantages of speed and memory occupation when the number of lattices is higher than the number of FVM units. If commercial software is used, this advantage will be further expanded. Thirdly, the steady state solution results of the hot spot temperature rise of the established LBM model are compared with the FVM solution, and the error is 2.60%. According to the load curve given in the transformer guidelines, it is used as input to solve the transient temperature rise of the established LBM and FVM simulation models. Finally, the results show that the LBM and FVM calculations are better than the transformer guide calculation. The maximum error between the hot spot temperature calculated by LBM and FVM is 6.44%. Moreover, the hot spot temperature rise trend of LBM is consistent with the transformer load guidelines, which verifies the effectiveness of the proposed method.

Based on the constructed LBM model, the load capacity of oil-immersed transformers under constant 25℃ and typical ambient temperature changes in summer and winter are evaluated at 6~18 hours during the day. The results show that under the premise that the relative insulation life loss of oil-immersed transformers is less than 1. The maximum load capacity coefficients are 1.20, 1.10, and 1.60 under the constant ambient temperature of 25℃, typical temperature changes in summer, and typical temperature changes in winter. The simulation model based on the proposed LBM provides an effective method for real-time monitoring of temperature rise, load capacity evaluation, and dynamic capacity increase of oil-immersed transformers.

The maximum torque per ampere (MTPA) control strategy can fully use the reluctance torque to output the maximum torque per unit stator current and improve the operating efficiency of interior permanent magnet synchronous motors (IPMSMs). Still, the traditional formula method or the high-frequency signal injection method requires the installation of at least two phase-current sensors to obtain the current information of the motor. Once the current sensor fails, the closed-loop control of the system will fail and cause unpredictable damage. The paper proposes an MTPA control strategy for IPMSM without current sensors. The strategy can accurately realize the MTPA control of the permanent magnet synchronous motor by calculating the optimal voltage control instruction only from the rotational speed information and the mathematical model of the system.

Firstly, the relationship between the control voltage command and the rotational speed is calculated using the formula method according to the mathematical model of the IPMSM and the conditions of the MTPA control. Secondly, inverter nonlinearity can cause the inverter output voltage to deviate from the commanded voltage, resulting in the motor deviating from the MTPA operating point. Therefore, the mean value compensation method is proposed to compensate the command voltage for the nonlinearity. Thirdly, the effect of current estimation error on the calculated voltage compensation value is analyzed. The analysis shows that even if the current estimation error exists, the average error of the voltage compensation value based on the estimated current is still 0. Finally, the effect of parameter deviation on the control strategy is analyzed, and the influence of parameter deviation on the optimal voltage command amplitude and the response current is given.

The experimental results for steady-state conditions show that the A-phase current fundamental wave amplitude of the motor with the proposed strategy is smaller than that with the traditional strategy. The effectiveness of the proposed method is verified. The experimental results at the same load torque under different speeds show that the current vector amplitude error of the MTPA control with the proposed method is small. Its maximum error does not exceeding 0.5%, while the traditional method is 14%~30%. The experimental results at the same speed with different load torques show that the current vector magnitude error of MTPA control with the proposed method is small, with the maximum error not exceeding 1%. In contrast, the traditional method’s maximum error is in the range of 2%~37%. The experimental results of dynamic operation and loaded starting conditions show that the proposed control strategy is robust to parameter deviations and has good dynamic performance.

The following conclusions can be drawn. (1) The proposed method can realize MTPA control of IPMSM without current sensors, which is of great significance to the fault-tolerant control capability of current sensor failures in the IPMSM drive system. (2) The proposed method has good dynamic performance and is robust in the variation of motor parameters. (3) The proposed MTPA control strategy considers the effect of VSI nonlinearity, and the control voltages are compensated, effectively improving the running accuracy in MTPA.