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  • Zongbin Ye, Chenxiao Gao, Xu Liu
    Transactions of China Electrotechnical Society. 2025, 40(12): 3770-3786.

    With the increase of power and frequency of wireless power transmission systems, requirements for the control performance of power transmission and real-time high-frequency data interaction between the power transmitter and receiver continue to increase. This paper proposes an implementation method for low-cost and highly robust wireless power and signal transfer (SWPDT). Based on the traditional magnetically coupled wireless power transfer (WPT) system structure, the two metal-shielded pole plates on the outside of the magnetically coupled coil provide an independent capacitive channel for data transmission, and the magnetically coupled mutual inductance coil provides an independent inductive channel for power transmission, which achieves decouples energy transmission and signal transmission. The six-plate capacitive coupling is constructed under the coil parasitic capacitance. The mathematical and physical models of six-plate capacitive coupling are constructed, and the fourth-order resonant network is built to achieve full-duplex communication through four blocking networks and compensation structures. The overall cost and size of the WPT system are significantly reduced. The crosstalk of power transmission on signal transmission is reduced without changing the power transmission capability, and the power transmission frequency no longer restricts the transmission frequency. Finally, a 50 W power transmission prototype is constructed. The power transmission efficiency reaches 80% under the 17 cm coil distance condition. The full-duplex parallel transmission of power and signals is achieved within a serial communication bit rate range from 240 to 800 kbit/s. The BERs can be maintained at a low level, and the effects of the pole plate offset on the signal and power transmission are verified. The transverse drift ratio reaches 87.5.0%. In the case of the pole plate offset with an 87.72% lateral drift ratio, the signal transmission efficiency of the system is only 22.66%. Under the magnetic shielding function of the metal pole plate, the signal transmission is robust under extreme working conditions, improving the reliability of the power transmission process. The shielding pole plate reduces the power transmission efficiency but has a significant shielding effect on electromagnetic leakage. Compared with the existing wireless energy and data synchronous transmission technology in transmission efficiency, transmission distance, signal rate, and BER, the correctness and feasibility of the proposed method are verified.

  • Sirui Wang, Dongyuan Qiu, Bo Zhang, Yanfeng Chen, Fan Xie
    Transactions of China Electrotechnical Society. 2025, 40(12): 3787-3802.

    Magnetically coupled resonant wireless power transfer (MCR-WPT) technology has received significant attention due to its ability to realize mid-range power transfer. However, the transmission characteristics of MCR-WPT systems are susceptible to variations in coupling coefficients and loads. Parity-time (PT) symmetry has been introduced into the WPT system (PT-WPT) to achieve constant power and high-efficiency transmission over medium distances. This paper provides a comprehensive review of the PT-WPT technology.

    First, the paper introduces the PT-WPT system’s basic structure and operating mechanism. It analyzes how the system balances energy gain and loss through the nonlinear saturated negative resistor, allowing it to maintain stable power transmission under varying coupling conditions. Coupled-mode and circuit models are used to construct the PT-WPT system. The two models’ similarities and differences in the energy transmission mechanism, PT symmetry conditions, and system characteristics are described. In addition, PT-WPT can be considered a novel wireless power transfer technology.

    Next, the paper discusses the construction methods of nonlinear saturated negative resistors, which can be divided into two categories based on the components used: operational amplifiers and power converters. While operational amplifiers provide a simple and low-cost solution, they are limited in power output. In contrast, power converters, such as half-bridge, full-bridge, and class E inverters, enable higher power output and efficiency but require more complex control strategies. Then, the advantages and disadvantages of these methods are discussed, and directions for improving the design of negative resistors are given.

    This paper introduces the different types of coupling mechanisms and the implementation of charging functions. Among the topologies of PT-WPT systems, single-transmitter-single-receiver is the most basic structure; high-order compensation networks and the introduction of relay coils are commonly used to extend the transmission distance of the PT-WPT system. Multi-transmitter/multi-receiver can also improve the system’s reliability and realize stable power transmission in multi-load systems. Furthermore, the charging control strategies are investigated to realize the constant power and constant current/voltage functions independent of the coupling coefficient and load variation, further promoting the practicalization of PT-WPT systems.

    Finally, this paper summarizes the existing research on PT-WPT systems and future research issues. PT-WPT technology is expected to find broader applications in the future and promote the development of wireless charging technology.

  • Dele Kong, Jinbin Zhao, Ling Mao, Yifan Yin, Junwei Zhang
    Transactions of China Electrotechnical Society. 2025, 40(12): 3803-3814.

    The rapid development of power electronics technology and wireless power transmission (WPT) has broadened application prospects in consumer electronics and traditional fields like electric vehicles, implantable medical devices, and autonomous underwater vehicles. The unique nature of wireless charging scenarios often results in significant variations in transmission distance, causing rapid drops in coupling coefficient and transmission efficiency. Therefore, coil compensation is an important research area of WPT. This paper proposes a segmented coil compensation method using inter-turn capacitance to solve increased internal voltage gradients in coils caused by traditional external capacitor compensation methods. By closely fitting the adjacent turns of the receiving coil, the capacitance of the closely fitting section is increased, thereby achieving coil compensation. The coil is divided into several segments, with inter-turn capacitance to compensate for each segment.

    First, the advantages of segmented coil compensation are derived using rigorous circuit theory. Next, equivalent modeling and calculation of the Litz wire wound coil are performed to analyze the factors influencing the size of the inter-turn capacitance. Finally, the overall coil with inter-turn capacitance segmented compensation is modeled, and the port impedance of the entire coil is calculated. The inter-turn capacitance of the closely fitting coil segments increases significantly, effectively replacing the external capacitors for compensation. Compared to external capacitor compensation topologies, the proposed segmented compensation topology can reduce the internal voltage gradient of the coil, voltage loss, and energy dissipation. Accordingly, the energy reception efficiency of the coil is improved. Additionally, this structure is compact, with a small size and cost.

    An experimental coil is compared with a coil using external capacitor compensation. Under the same input and load conditions, the receiving power of the coil with the proposed segmented compensation is increased by 54.3%, and efficiency is improved by 27.6%, which verifies the proposed method.

    The following conclusions can be drawn. (1) The tight alignment length of the turns and the dielectric constant of the wire insulation layer influence the inter-turn capacitance. When Litz wire is used for equivalent analysis, the inter-turn capacitance increases significantly with the tight alignment length and shows a linear growth trend. The capacitance also increases significantly as the equivalent dielectric constant of the insulation layer increases, effectively compensating the coil. (2) Inter-turn capacitance compensation provides adequate compensation. Compared to traditional concentrated compensation methods, the proposed segmented compensation reduces the internal voltage gradient of the coil, decreases voltage losses and energy dissipation, and enhances the energy reception efficiency of the coil.

  • Xuwei Xiong, Song Xu, Pengqiang Nie, Miao Wang, Wei Jiang
    Transactions of China Electrotechnical Society. 2025, 40(12): 3815-3827.

    Renewable energy systems have gained continuous attention for achieving “carbon peak” and “carbon neutrality”, especially DC conversion technologies for renewable energy conversions. Multi-port converter (MPC) has been widely applied in renewable energy systems and electric vehicles due to the characteristics of low cost, high efficiency, and high power density. The non-isolated MPC suffers poor stability due to insufficient electrical isolation between ports. In contrast, isolated converters are often more complex and less flexible. Wireless power transfer (WPT) technology offers convenience, safety, flexibility, and the ability to charge multiple devices, effectively achieving electrical isolation between input and load ports. Thus, combined with WPT and MPC technologies, this paper proposes a three-port DC-DC converter with integrated wireless power transfer capability. The proposed topology facilitates DC power transfer between multiple DC sources with the same or different voltage levels. It enables wireless power transfer between DC sources and load by introducing WPT coupling technologies. The system achieves non-contact hot plug & play between DC loads and the power grid side, which indirectly isolates the impact of the load on the power grid.

    The system employs a hybrid power flow control method, with dual half-bridge micro-inverters providing the dual input ports. The load port is wirelessly coupled through an LCL-LCL-type resonant coupling network connected to a full-bridge rectifier. This three-port topology is simple and highly flexible, allowing free power transmission between dual input sources, with the two sources sharing one LCL resonant tank for power transmission to the load without any additional circuit components. System control strategies can be divided into two phases: Phase1: pulse width modulation (PWM) controls the power flow between two DC sources by controlling the average DC offset current in the LCL resonant tank, enabling bidirectional power transmission; Phase 2: phase shift modulation (PSM) control method adjusts the wireless output power for DC load. These two control loops can operate independently or be combined for comprehensive control. The absence of coupling between these methods enhances the stability and effectiveness of each control function. Additionally, the system allows for dual input ports with unbalanced voltage levels.

    Firstly, a dual-sided LCL resonant coupling network model is established based on the AC impedance method to analyze its frequency limitations under constant voltage and constant current output characteristics. Secondly, the system topology’s various operating states are analyzed based on switching modes. The overall system model is developed using time-domain analysis, and a small-signal model of the resonant coupling network is established to determine the primary-side PWM control and secondary-side PSM control strategies. Thirdly, a simulation model is built in PSIM to verify the system’s functionality. Matlab/Simulink is used to optimize the parameters of the compensation network. Finally, an experimental platform is set up in a microgrid and energy storage interconnected system to evaluate the system's dynamic characteristics under different voltage levels and load conditions, efficiency variations, steady-state control performance of the closed-loop controller, and dynamic response characteristics.

    Experimental results show that under dual inputs of DC 36 V with only wireless output, the system achieves a peak efficiency of 93.6% and load-independent constant current output performance. The system effectively controls the power flow direction and magnitude between the primary-side energy ports, and the designed controller maintains stable load power even under sudden changes in load resistance and voltage levels at the dual half-bridge energy ports. The controller also demonstrates good robustness and dynamic response performance.

  • Xu Liu, Yupeng Cao, Chenyang Xia, Longyue Yang
    Transactions of China Electrotechnical Society. 2025, 40(12): 3828-3841.

    For the wireless charging systems for electric vehicles (EVs), the misalignment phenomenon due to inaccurate parking is the most significant issue, which causes non-negligible negative impacts on the power efficiency and amount. That is because the positional misalignment between coils leads to significant changes in parameters such as mutual inductance, which in turn causes dramatic fluctuations in the system’s output voltage and efficiency. It potentially prevents the system from functioning correctly or even damages it. Therefore, research on the anti-misalignment capability of EV wireless charging systems is crucial. Current research focuses on high-frequency inverter control, coupling mechanism design, and compensation topology design. However, these methods fail to maintain a constant output voltage when both coil misalignment and large variations in load occur. This paper proposes a novel hybrid compensation topology based on the QRQP coil.

    This paper uses finite element simulation software to investigate a QRQP coil and its misalignment and coupling characteristics. To reduce output voltage fluctuations caused by coil misalignment and large variations in load, a novel hybrid topology is introduced based on the QRQP coil. This topology leverages the principle of opposing output characteristics between S-LCC, LCC-S, LCC-LCC, and SS topologies. Detailed design guidelines for the parameters and optimization strategies are proposed. Meanwhile, the system’s anti- misalignment capability under different parameter selections is analyzed. Finally, optimal system parameters are selected and analyzed. The optimized system can maintain a constant output voltage under various misalignment angles and load variations within a specific range. When the receiving coil is removed, the primary-side current can be effectively limited, which ensures the system's safety.

    The proposed topology has been validated through a 1 kW laboratory prototype. Experimental results show that when the load resistance varies from 20 Ω to 100 Ω, the system maintains output voltage fluctuations of less than 5% under X-axis misalignment from -140 mm to +140 mm, Y-axis misalignment from -105 mm to +105 mm, and diagonal misalignment along the XY-axis from -200 mm to +200 mm. When the load resistance varies from 20 Ω to 100 Ω and the coils’ vertical distance changes from -35 mm to 70 mm, the output voltage fluctuation can be kept within 8%. Furthermore, since the system exhibits capacitive behavior after misalignment and has no compensating inductance, it can operate with high efficiency. Analysis under extreme conditions shows that when the receiving coil is removed, the optimized hybrid topology effectively limits the primary-side current surge, preventing system damage.

    The following conclusions can be drawn. (1) The proposed optimization theory for the novel hybrid topology is consistent with the experimental results. (2) The optimized hybrid compensation topology based on the QRQP coil can effectively reduce output voltage fluctuations when coil misalignment and large variations in load occur simultaneously. (3) When removing the receiving coil, the optimized hybrid topology effectively limits the primary-side current surge, preventing system damage.

  • Liangdeng Hu, Cheng Guo, Xiaosong Xu, Xiangyu Luo
    Transactions of China Electrotechnical Society. 2025, 40(12): 3842-3856.

    The multi-phase open-winding induction motor and its adaptive H-bridge multi-phase inverter system have received extensive attention due to their advantages of small torque ripple, strong fault tolerance, and easy power capacity expansion. This paper analyzes the modeling of the multi-phase open-winding motor system and speed sensorless control technology to achieve high degrees of freedom control and low switching frequency characteristics in a twelve-phase, large-capacity, open-winding motor system. The simulation and experimental verification are conducted to enhance the operating performance of the low-switching-frequency multi-phase open-winding motor system.

    The twelve-phase open-winding induction motor system and its equivalent three-phase simplified model are established. The equivalent three-phase full-order observer model and its speed estimation method are presented. The full-order observer used in speed sensorless control has the advantages of low control bandwidth requirements and a wide range of observation speeds. However, the switching frequency of the H-bridge large-capacity inverter supporting the ship’s multi-phase open-winding induction motor is low, which inevitably increases the digital discretization error of the full-order observer. This paper derives the full-order flux observer models based on the forward Euler method, the simplified second-order discretization method, and the proposed Adams fourth-order discretization method. Then, the steady-state error and observer stability are compared using the F-norm and pole diagram. Theoretical analysis reveals that the full-order observer, based on Adams' fourth-order discretization method, achieves the best discrete accuracy and stability of the observation system while minimizing the computational complexity of the digital control system.

    A simulation model and a test platform for a twelve-phase, 25 kW open-winding induction motor with speed sensorless control have been developed. The results show that, compared with the forward Euler method and the simplified second-order discretization method, the observation results for speed, current, and flux based on the Adams fourth-order discretization method are almost consistent with the actual values. Through the speed sensorless closed-loop speed regulation test and load mutation test, it is further verified that the full-order observer based on Adams' fourth-order discretization method exhibits good speed regulation and load-carrying capacity, which can achieve better dynamic and steady-state performance under both extremely low and high-speed conditions. The full-order observer discretization method can provide technical support for applying speed sensorless control technology to low switching frequency multi-phase open-winding motor systems.

  • Mengmeng Ai, Xingyu Song, Wenhui Liu, Tao Shen
    Transactions of China Electrotechnical Society. 2025, 40(12): 3857-3867.

    Line-starting permanent magnet synchronous motors (LSPMSM) are different from other permanent magnet motors due to their double-sided slotted characteristics of the stator and rotor, making it difficult to analyze the cogging torque. The overall optimization of motor cogging torque and torque ripple rate is also challenging. This paper optimizes the rotor design of the LSPMSM based on multi-objective particle swarm optimization algorithm, considering the saturation performance of the motor.

    Firstly, this paper establishes the relationship between harmonic magnetomotive force and cogging torque to predict the cogging torque of the LSPMSM. The cogging torque is analyzed as a dynamic function relationship of various motor parameters, providing corresponding optimization parameters for the subsequent optimization of the prototype. At the same time, under the premise that the maximum magnetic energy product of the permanent magnet remains unchanged, the relationship between the saturation degree of the motor and the parameters of the permanent magnet is determined, and the selection range of the motor's permanent magnet parameters is determined based on this relationship. Define three working states of the motor: unsaturated, peak saturation, and after saturation, to make the analysis and optimization results of the motor more accurate.

    Secondly, combined with response surface methodology (RSM) and multi-objective particle swarm optimization algorithm (MOPSO), this paper proposes a comprehensive optimization strategy to optimize key objectives such as motor cogging torque, torque ripple rate, and efficiency. The optimal design solutions in different regions can be obtained by using the response surface algorithm to classify numerical groups and shorten the computation time of the particle swarm optimization algorithm. The optimal solutions under six different conditions are determined after considering whether the stator is skewed and the three working states of the motor.

    Finally, simulation analysis verifies the relationship between cogging torque and harmonics under different saturation states, the trend of no-load back electromotive force, and the main harmonic order changing with the number of slots per pole of the rotor. An experimental platform is built to verify the accuracy of theoretical and simulation analysis. This paper provides optimization solutions for the design of motors of the same type.

  • Qingeng Shi, Junjie Zhu, Yi Han, Xiong Zeng
    Transactions of China Electrotechnical Society. 2025, 40(12): 3868-3882.

    Accurate load torque identification helps to improve the load disturbance resistance of complex nonlinear loaded permanent magnet drive systems. The sliding mode observer (SMO) has become a commonly used algorithm for load torque identification due to its advantages of high robustness to noise, fast response speed, and simple structure. However, the shortcomings of this algorithm, such as high-frequency chattering and slow response speed, limit its application in electric drive systems. This paper proposes a new adaptive sliding-mode load torque observer to solve the problem of the inherent contradiction between the convergence speed and high-frequency chattering of conventional sliding-mode observers.

    Firstly, from the perspective of quasi-sliding mode, the conventional sign function is replaced by the saturation function to suppress the high-frequency chattering of the load torque estimate. The sign function can effectively suppress the chattering phenomenon of SMO, but it still fails to balance the convergence speed and observation accuracy. Second, an adaptive convergence rate is designed to introduce an exponential convergence term based on the conventional isochronous convergence rate. The adaptive gain of the isochronous convergence term is designed to make the sliding-mode observer adaptively adjust the convergence speed along with the change of the system state. Thus, the observer has a short convergence time and strong robustness, and the high-frequency chattering phenomenon of the sliding-mode observer in the steady state is suppressed. Finally, this paper introduces the average estimated value of the load torque in the conventional slip mode identification algorithm and adds it to the feedback loop of the speed observer. The improved load torque observation algorithm can suppress the chattering of the estimated torque by adjusting the feedback gain g. Since the load torque indication signal U can characterize the load torque change without additional delay, it can be directly involved in the speed estimation. Therefore, the proposed algorithm has a fast response speed during transient processes while considering the chattering suppression of the system. Based on the principle of sliding mode variable structure control, the adaptive rate of feedback gain coefficient g is designed.

    Simulation and experimental results show that under varying speed and load disturbances, the proposed adaptive SMO has less chattering than traditional SMO and super-twisting SMO. Additionally, the adaptive SMO converges faster than traditional SMO and performs comparably to super-twisting SMO. In load disturbance experiments at a reference speed of 600 r/min, the speed fluctuations for no torque feedforward, traditional SMO with torque feedforward, and adaptive SMO with torque feedforward are 72.5 r/min, 56 r/min, and 35.5 r/min, respectively, with system recovery times of 0.7 s, 0.65 s, and 0.5 s. To further verify the impact of inertia parameter mismatch on the adaptive SMO, inertia was set to 2, 5, 0.5, and 0.2 times the rated value, with the maximum deviation in load torque observation being 6.7 N·m. The results indicate that the impact of parameter mismatch is not significant.

    The following conclusions can be drawn. (1) The designed adaptive SMO has a simple structure and high stability, is easy to implement, observes the load torque quickly and accurately, and requires fewer parameters. (2) Compared with the conventional SMO, the proposed adaptive SMO has less chattering and faster response speed during the transient change of the load torque. (3) The proposed adaptive SMO is more suitable for the scenario of variable load torque than the conventional SMO. The experimental results show that when the load torque recognized by the adaptive SMO is used as the feedforward term of the reference torque, the response speed and load disturbance resistance of the heavy-duty chain drive system can be effectively improved.

  • Hu Xiao, Gongping Wu, Zhuo Long, Jian Zheng, Zewen Li
    Transactions of China Electrotechnical Society. 2025, 40(12): 3883-3894.

    Permanent magnet synchronous motor (PMSM) has become a core component of complex electromechanical systems such as electric vehicles, new energy urban rail vehicles, and wind power generation due to its advantages of high efficiency, high power density, and high torque density. The model predictive control strategy based on the mathematical model of the controlled object has been widely applied in PMSMs. However, there is inevitably a mismatch between the actual parameters of the motor system and the application parameters of the model predictive controller, which seriously affects the performance of the predictive control system. This paper proposes a novel model-free stator flux sliding mode control (MF-FSMC) method to achieve high-performance control under parameter mismatch.

    The model-free flux sliding mode controller is adopted to replace the model predictive control algorithm that relies on the controlled object. First, a mathematical model of PMSM is established under parameter mismatch, and an ultralocal stator flux linkage model considering parameter mismatch is constructed under a rotating coordinate system. The novel MF-FSMC method is proposed, a model-free flux sliding mode controller based on a novel reaching law is designed, and a one-beat speed predictive controller is constructed. Finally, the composite integral sliding mode disturbance observer online estimation strategy is proposed, which can effectively observe the unknown disturbance part in the ultralocal model of PMSM under parameter mismatch.

    Simulation and experimental results show that the proposed method can effectively improve the steady-state performance, significantly reduce the stator flux and torque ripple, and enhance the robustness and anti- interference performance of the PMSM system under parameter mismatch. The designed composite integral sliding mode disturbance observer can accurately observe the stator flux values and unknown disturbances on the dq axis. Compared with conventional model predictive control methods, the proposed MF-FSMC method can reduce torque ripple from 75 N·m to 45 N·m in the case of flux linkage parameter mismatch. In addition, with the proposed MF-FSMC method, the distortion of stator current has also been significantly improved, and the static error of stator flux linkage has been reduced from 0.35 Wb to ±0.01 Wb. In the case of inductance parameter mismatch, the proposed MF-FSMC method can reduce torque ripple from 110 N·m to 80 N·m and the fluctuation value of stator flux linkage error from ±0.235 Wb to ±0.02 Wb.

    The MF-FSMC method proposed can obtain the following conclusions: (1) The composite integral sliding mode disturbance observer can accurately observe unknown disturbances and stator flux linkage, effectively enhancing the robustness of predictive control systems under parameter mismatch. (2) The proposed model-free stator flux sliding mode control method designs a model-free flux sliding mode controller in the inner loop of the controller and constructs a one-beat speed predictive controller in the outer loop of the controller. The proposed MF-FSMC method can effectively improve the control accuracy of stator flux, significantly reduce the stator flux/torque ripple of the motor, and ensure the strong robustness of the predictive control system under parameter mismatch.

  • Fu Li, Shuangchen Chen, Zhiyong Lan, Yunze Jiang, Yini Zhao
    Transactions of China Electrotechnical Society. 2025, 40(12): 3895-3904.

    Traditional I-f control for sensorless control of the permanent magnet synchronous motor (PMSM) suffers from poor damping and disturbance rejection, which lead to large speed oscillations at motor startup and long transition time when switching to close-loop control. It is unfavorable for multi-rotor unmanned aerial vehicles and electric vertical take-off vehicles. According to the differentiation of d-axis voltage and transition strategy, this paper proposes an improved I-f control strategy with frequency compensation to increase damping and improve disturbance rejection of the I-f control based on decoupling current dynamics and angle dynamics. Speed oscillations at motor startup are suppressed significantly, and a fast transition from I-f control to closed-loop control is achieved smoothly with less mechanical dynamics.

    Firstly, a small-signal perturbation model of the I-f control is deduced with detailed analyses of its damping characteristics. To increase damping and suppress speed oscillations, differentiation of the open-loop d-axis voltage is used to compensate for the open-loop frequency. Secondly, to improve the load disturbance rejection when switching to closed-loop control, the angle of the reference current vector is rotated via Park transformation. In contrast, the open loop angle is increased to gradually approach the real rotor angle obtained by the angle observer. Since the reference current vector is stationary relative to the real rotor angle during this transition process, no mechanical dynamics are generated. This transition can even be done at zero angle error between the real rotor coordinate and the open-loop coordinate, which indicates no current and angle dynamics at the switching instant. The amplitude of the reference current vector is kept unchanged throughout the whole I-f control. Therefore, the load disturbance is effectively rejected, even during the transition process. Finally, after switching to closed-loop control successfully, the d-axis current is decreased to 0 according to a certain trajectory, and normal closed-loop control takes over.

    Two experiments demonstrate the improvement of system damping and load disturbance rejection. In the first experiment, the proposed strategy is compared with the traditional I-f control and the perturbation of active power in literature. The experimental results show that under traditional I-f control, significant speed oscillations occur during the starting phase, and the peak-to-peak value of speed oscillations is about 80 r/min. With perturbation of active power, speed oscillations rapidly decay in 0.1 seconds, and the peak-to-peak value of speed drops to about 10 r/min in the steady state. The motor attenuates speed oscillations fast, and the peak-to-peak value of speed drops to about 5 r/min in the steady state.

    The second experiment compares the proposed transition strategy and the strategy by reducing the q-axis current in the literature. The experimental results show that reducing the q-axis current generates large mechanical dynamics at the transition stage under sudden load disturbances. The speed decreases by about 260 r/min at the load disturbance of 0.064 N·m, and the motor is out of control at the load disturbance of 0.16 N·m. Mechanical dynamics are much smaller using the proposed method. The speed decreases by about 40 r/min at the load disturbance of 0.064 N·m, and the motor can still maintain normal operation at the load disturbance of 0.512 N·m.

    The proposed improved I-f control strategy has better damping effect on speed oscillations and can transition to closed-loop control with strong rejection of load disturbances.