Due to the existence of important loads, the new distribution network needs to be supplied with power when the equipment of the original distribution network is overhauled. Two closing types exist when accessing the new distribution network: loop and ring-closing. The distribution network is cut off for loop closing, leading to power supply interruption, or the ring of the distribution network is directly closed, producing a large impulse current due to the large voltage difference between the two distribution networks. As a result, the relay protection malfunction occurs, which affects the reliability and stability of the power grid. Two ways are adopted to avoid the above issues. One is to provide the loop closing condition through theoretical calculation, and the voltage of the loop closing point is similar by controlling the whole distribution network. The loop is directly closed after meeting the ring closing conditions. However, the control process is more complex, and the loop closing current is still large. The second is to use the voltage regulating device to change the voltage of one side of the ring closing point and carry out the ring-closing. Although the control effect of the ring-closing device is better, the price and maintenance costs are high.

This paper proposes an improved phase shifter (IPST) with an amplitude modulation winding (ETm) based on the amplitude modulation winding (ETp) of the traditional phase shifter. It can flexibly change the voltage amplitude and phase by adjusting the gears of ETp and ETm, thereby changing the voltage at the closing point. The voltage between the two distribution networks is similar, and the loop closure is realized. In addition, the voltage quality on the load side is degraded because of the internal impedance of the IPST after the load transfer. An IPST equivalence model is established based on the multi-port network theory. The impedance characteristics of the IPST port are converted into the equivalent analytical formula. The functional expressions of the regulation voltage on the amplitude modulation gear T_m and phase modulation gear T_p are derived. Thus, the target gear of the IPST is predicted, and the voltage quality is improved. Thirdly, to address the problem of the inrush current generated when the IPST exits bypass closing, the functional relationship of the inrush current on the IPST gear is derived. The IPST target gear is predicted by combining the current regulation target and the voltage quality constraint. The voltage quality can be ensured, and the impulse current can drop and safely exit the IPST. Finally, the impedance expression’s correctness and the control strategy’s effectiveness are verified through PSCAD/ EMTDC.

Permanent magnet synchronous motors are widely used in industrial production and other fields due to their advantages of high power density, high reliability, and high efficiency. Real-time and accurate three-phase current feedback is the key to AC drive system control. Compared with the traditional multi-current sensor drive control, using a single current sensor to achieve three-phase current reconstruction can reduce costs and improve the reliability of the motor system under complex working conditions. Combined with the improved IRTPWM algorithm and the BSPWM algorithm, this paper forms a hybrid pulse width modulation algorithm to solve the low-key brake dead zone and the reconstructed dead zone at the sector boundary. Then, an improved two-point sampling strategy is adopted to eliminate the second type of time-sharing sampling error and simplify the current compensation step, which fixes the sampling time of the two samples and the sampling spacing as the minimum sampling time.

Based on the traditional RTPWM algorithm, the improved IRTPWM algorithm calculates the action time of the other two effective voltage vectors. The action time of the vector is fixed with the least influence on the synthetic reference voltage vector among the three vectors, and the three effective voltage vectors and zero vectors are recorded. It collects the phase current at the beginning and end of the optimal measurement vector.

The traditional RTPWM algorithm cannot achieve medium and high-speed operation alone. The measurement phase backward shift modulation method (BSPWM) is proposed to eliminate the dead zone of current reconstruction by combining the measurement phase backward shift modulation method and the IRTPWM algorithm outside the working area of the IRTPWM algorithm. The mixed pulse width modulation algorithm can complete the current acquisition twice at two fixed particular sampling points, and the first type of time-sharing sampling error only needs to be compensated. Therefore, the current compensation steps of the traditional mixed pulse width modulation algorithm are reduced from four steps to two steps, and the computing burden of the processing unit is reduced.

The simulation and experimental results show that the error between the reconstruction and the actual current is tiny, which proves that the proposed current reconstruction has high accuracy in both steady-state and transient states. Under the dynamic working conditions of fixed load torque of 2 N·m with the rotation speed of 300 r/min and 600 r/min back and forth and fixed speed of 400 r/min with load torque switching back and forth between 1 N·m and 3 N·m, the motor speed, q-axis current, and three-phase current do not cause great disturbance due to the switching of the algorithm.

The following conclusions can be drawn. (1) The combination of the IRTPWM algorithm and BSPWM algorithm effectively eliminates the influence of the dead zone of current reconstruction. (2) The IRTPWM algorithm has higher current reconstruction accuracy and lower current harmonic value than the traditional RTPWM, and the BSPWM algorithm has higher current reconstruction accuracy than the traditional phase-shifting method. (3) The improved two-point sampling strategy can reduce the number of current compensations and current reconstruction errors, simplifying the experimental algorithm and improving the control performance of PMSM.

The rotating rectifier is the key part of multiphase annular brushless excitation systems. Nevertheless, the rectifiers often experience faults caused by diode failures, which brings security risks in practice. Accurately diagnosing faults in the rotating rectifier is pivotal for ensuring the safe operation of multiphase annular brushless excitation systems. However, the types of rotating rectifier faults are diverse, and the characteristics of different faults are inherently weak. Traditional mechanism-driven diagnostic schemes offer interpretability but often struggle with precise fault diagnosis. New data-driven diagnostic schemes exhibit speed and accuracy but encounter challenges in training and debugging in practical applications. This paper proposes a hybrid mechanism-data-driven diagnostic scheme for rotating rectifier faults.

Based on the fault mechanism, the frequency domain characteristics of the excitation current after the fault are derived, and the fault characteristic patterns are summarized. Then, thresholds of the mechanism diagnosis model are calculated using finite element simulation data. Extracting the frequency domain characteristics of the excitation current allows the fault mechanism to be clearly described, thus providing a solid foundation for subsequent fault diagnosis. The current waveform under normal operation and different fault conditions can be simulated by adjusting the models, which allows for determining thresholds for various operating conditions.

Then, the fast dynamic time warping (Fast-DTW) algorithm is introduced to calculate the similarity of excitation current time-domain waveforms, subsequently forming a data-driven model combined with the k-nearest neighbors (kNN) classifier. The fast-DTW algorithm can align waveforms of different time lengths and start points to capture subtle differences between waveforms. By combining the fast-DTW algorithm with the kNN classifier, the data-driven model can realize the diagnosis of rotating rectifier faults.

Mechanism-driven and data-driven diagnostic schemes are integrated based on ensemble learning principles. Ensemble learning significantly enhances the overall performance of the model by combining the results of multiple learners. Five mechanism-driven and five data-driven models are established to obtain a final diagnostic result based on the absolute majority voting method. The hybrid diagnostic scheme exhibits the advantages of mechanism-driven and data-driven models, effectively overcoming the limitations of a single-driven model.

Finally, the verification of prototype experiments indicates that the hybrid scheme’s diagnostic accuracy reaches 100%, significantly surpassing single-driven models. Establishing diagnostic models requires offline simulation data, reducing training difficulty and improving practicality on-site. The hybrid scheme maintains a reasonable diagnostic speed while ensuring high accuracy.

In conclusion, the proposed hybrid mechanism-data-driven fault diagnosis scheme combines mechanism analysis and data-driven methods to enhance the accuracy and robustness of fault diagnosis, demonstrating excellent test performance in prototype experiments. The diagnostic approach based on the time-frequency characteristics of the excitation current demonstrates excellent interpretability, achieving accurate fault diagnosis solely through training with simulation data.

Fractional-order elements (FOEs) serve as fundamental components in fractional-order circuits, forming the cornerstone of research into fractional-order circuit systems. Unlike single-component counterparts, the multi-component method offers greater flexibility in selecting constituent elements, enabling the adjustment of order and impedance coefficients for enhanced practicality. This paper provides a comprehensive overview of prevailing construction methods to facilitate the selection of appropriate multi-component FOEs for specific application needs. These methods are classified into three categories based on the type of constituent devices: passive devices, operational amplifiers, and power electronic converters.

In the construction method based on passive devices, two approaches involving Foster RLC ladder circuits are discussed. Passive RLC networks are used to create circuits that match the impedance characteristics of the transfer function. Reducing phase error requires increasing the order and using numerous components, leading to complex structures and cumbersome calculations. When standard off-the-shelf components cannot be used, replacing analytical parameters with standard ones increases the phase angle deviation. Adjusting the FOE order or impedance coefficients requires replacing all circuit components. This method is most suitable for fixed FOE order and impedance coefficients, which are effective in medium to low-frequency scenarios.

Next, the paper introduces the construction method based on operational amplifiers. The method of constructing FOEs based on generalized impedance converter (GIC) circuits can realize FOEs with orders varying from -2 to 2. However, the limited open-loop gain and gain instability of operational amplifiers often result in significant deviations of the obtained FOE performance from its ideal characteristics. Therefore, exploring how to use other active devices, such as operational transconductance amplifiers (OTA) and current feedback operational amplifiers (CFOA), to construct FOEs is an exploration direction. GIC circuits offer great integration and functionality, making them suitable for applications where precise impedance and phase characteristics are crucial.

The construction method based on power electronic converters is also discussed in detail. Multi-component FOEs based on power electronic converters have wide applications because their power level depends on the inverter, and their order and impedance can be adjusted by changing the control parameters. However, different structures of filters affect the operating performance of fractional-order elements. Therefore, exploring the application of different filter structures on multi-component FOEs and optimizing the parameters of the filters become the direction of development for power electronic converter-based FOEs. Power electronic converters provide the advantage of handling higher power levels and dynamic adaptability. The ability to digitally control the fractional order and impedance in real-time makes these elements highly versatile.

Lastly, this paper proposes a three-phase fractional-order electrical spring (TPFES). TPFES controls the order of the equivalent fractional-order capacitance of each phase and the pseudo-capacitance. The effect of stabilizing the load voltage is realized, the power factor is improved, and the power is balanced. The application in grid power compensation demonstrates that multi-component FOEs can effectively enhance the performance of practical circuit systems. This work provides a reference for future applications of fractional order components in electrical engineering.

As an important parameter in power electronic converters, the leakage inductance of high-frequency transformers is of great significance in improving the operating mode and power transmission characteristics of isolated DC-DC converters. Compared with the solid round wire, the Litz wire can reduce eddy current losses in high-frequency magnetic components. However, the complicated structure of the Litz-wire windings poses a serious challenge to predicting leakage inductance in high-frequency transformers. On the one hand, it is difficult to precisely extract the magnetic field energy in various regions of the core window. On the other hand, it is hard to accurately characterize the multi-stranded and twisting structures of the Litz wires. Therefore, this paper presents a fast calculation method of leakage inductance in the high-frequency transformer with Litz-wire winding.

Firstly, a homogenized equivalent process for Litz wire is proposed to enhance the flexibility of modeling and the efficiency of computation. The magnetic field energy variation with frequency inside the Litz-wire conductors are analyzed. Then, the 2-D magnetic field energy inside the core window is extracted based on the method of images to eliminate the impact of the edge effect. The internal and external magnetic fields at different locations in the winding are accurately characterized by introducing the meshing into the method of images, and a coordinate transformation method is proposed to consider the twisting structure of the Litz wires. Finally, two high-frequency transformer prototypes with different structures are designed and fabricated. Compared with the measurement results and two existing methods, the accuracy and efficiency of the proposed approach are verified.

The following conclusions can be drawn. (1) A homogenized equivalent model of the Litz-wire twisting structure is developed by introducing the relative complex permeability, which simplifies the model building and reduces the computational cost. The variation of the magnetic field energy in the Litz wires with frequency is analyzed, and the magnetic field energy stored in the Litz wires gradually decreases with the frequency increase. (2) The meshing process is introduced into the method of images, and the coordinate transformation method is proposed to characterize the twisting structure of the Litz wire. It can counteract a part of the external magnetic field and reduce the magnetic field energy in the conductors. (3) Considering the twisting characteristics of the Litz wire and the high-frequency effect, a leakage inductance prediction model is developed based on the magnetic field energy variation with frequency. (4) The accuracy and efficiency of the proposed method are verified compared with the measurement and the current two analytical methods. The maximum error does not exceed 4% throughout the measurement frequency range, and the calculation time is about 20 seconds. Moreover, the proposed method can be effectively applied to fast iterative calculations in the optimal design of high-frequency transformers.

Permanent magnet linear synchronous motors with section power supply are affected by disturbances like load force, detent force, and friction force. In the field of electromagnetic drive, the stator track is long. Linear motors usually adopt a segmented structure to save inverter capacity. However, it is difficult to ensure that the air gap of each segmented stator is equal during installation. Therefore, the mover is affected by the normal force. In addition, the load is usually accelerated to the target speed in a short time, so electromagnetic drive devices are usually operated under high current and high acceleration conditions, where the motor parameters are prone to change. Due to the lack of intermediate transmission devices in PMLSMs, these disturbances will directly affect the motor drive system and are included in the output of the controller. An SMSC with a novel convergence law is designed to ensure the fast convergence of speed and suppress the chattering. The designed TSMDO observes the disturbance output to ensure the disturbance suppression performance. Then, the acceleration fluctuations are reduced, and the thrust fluctuations are suppressed in the motor output.

Firstly, a mechanical motion model of PMLSM is established based on Newton's second law. It takes the disturbances as the lumped disturbance d(t) caused by load force, detent force, friction force, normal force, and parameter variation. Secondly, the shortcomings of conventional sliding mode control are analyzed, and a new adaptive sliding mode approaching law is proposed. The designed sliding mode approaching law ensures that variables can approach the sliding mode surface at a fast speed. As the state variables of the system gradually approach the sliding mode surface, the designed sliding mode approaching law can reduce the speed to weaken chattering. Then, due to the presence of d(t) in the output of the sliding mode speed controller, the TSMDO is designed to compensate for it. This observer is equivalent to a first-order low-pass filter. Finally, the proposed SMSC strategy is compared with PI control and conventional SMSC.

The experiments show that the PI controller can improve the dynamic tracking performance of speed by increasing h. However, this increases the acceleration fluctuation. At the same time, there is a noticeable overshoot when the rotor enters the constant speed range. The conventional SMSC has better dynamic tracking performance than PI control, resulting in small acceleration fluctuations. However, due to the fixed sliding mode gain, the increasing sliding mode gain increases the overshoot. The proposed SMSC has a faster tracking speed and better dynamic response than the conventional approaching law because of the new sliding mode approaching law. The proposed SMSC can adaptively change its gain when the speed state changes, ensuring good speed-tracking performance and reducing overshoot. The designed TSMDO effectively reduces the impact of thrust disturbances, acceleration fluctuations, and thrust fluctuations.

The main conclusions are as follows. (1) The proposed new sliding mode approaching law has a fast convergence speed due to the adaptive gain function f(x₁, s) for adaptively adjusting the sliding mode gain. It can weaken chattering, ensuring speed dynamic tracking performance and convergence speed. (2) The designed TSMDO has a small chattering phenomenon. The introduction of TSMDO effectively suppresses the total disturbance d(t) in the SMSC output, reduces acceleration fluctuations, and ensures stable thrust output of the motor.

The equivalent circuit is valuable for designing an induction machine and its driving system, and its parameters are essential for analyzing the electromagnetic performance and establishing the driving model, especially the magnetizing inductance that characterizes the main flux distribution in the machine. The finite element analysis can precisely determine the magnetizing inductance. However, it is unsuitable for the initial design stage when the design parameters need frequent adjustment. Traditional analytical calculations like the flux linkage method neglect the influence factors, such as core saturation, tooth-slot effect, and rotor movement in the actual operation, causing accuracy issues. The improved analytical calculation method can significantly enhance the accuracy. However, the magnetic circuit in each core segment still needs to be more accurate, and the local saturation points are easily ignored. Besides, the solving process contains nonlinear iterations of multi-segment of the magnetic circuit, which has repeating calculations under different slips.

This paper proposes an elementary layer method based on the main and leakage magnetic circuits to calculate the magnetizing inductance. Firstly, the magnetic voltage drop of each pole of the main magnetic circuit under different air-gap flux densities is calculated, and the magnetic voltage drop and the air-gap flux density are converted into the electromotive force and the magnetizing current to obtain the objective function. Secondly, the distribution of the leakage flux in the stator slot and the current induced in the rotor bar is analyzed to calculate the slot leakage inductance of the stator and rotor, together with the rotor AC resistance. The stator terminal voltage expression is constructed as the constraint condition. Finally, each set of the electromotive force and the magnetizing current on the objective function are substituted into the constraint condition to make the results equal to the rated phase voltage of the stator. The ratio of the set is the value of the magnetizing reactance, and therefore, the magnetizing inductance is obtained. In the main and leakage flux circuits, the irregular and nonlinear magnetic and electric circuits are regularized and linearized using the thin layer elements to substitute theoretical integral. Hence, the tooth-slot structure and the nonlinear material properties can be considered more accurately when calculating the magnetic voltage drop and leakage inductance.

A wet submersible induction machine is an example of the analytical calculation of the magnetizing inductance using the proposed elementary layer method and the traditional flux leakage method. Besides, the steady-state outputs of the equivalent circuit are obtained. The prototype test and the finite element simulation under the magnetic saturation of the stator teeth are conducted. The results show that the elementary layer method considers the distribution of the magnetic voltage drop in the core segment, which is more effective than the flux linkage method when the tooth magnetic circuit is saturated. Therefore, the calculation of the magnetizing inductance is more accurate, and in the steady-state outputs of the equivalent circuit, the stator current, input power, and power factor curves are consistent with the finite element analysis. The error is less than 0.5% when the finite element results are used as the reference. The proposed method links the design parameters and the magnetizing inductance, providing convenience for the initial design and optimization of the submersible induction machine and other types of machines.