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.

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.

Implementing sensorless control is necessary to reduce the system volume of linear oscillatory machines (LOM) used in linear compressors and achieve efficient and reliable operation. The existing piston stroke observers have low observation accuracy and are susceptible to DC components, resulting in a decrease in system compression performance or cylinder collision risk. Therefore, this paper designs an improved high-precision piston stroke observer for linear oscillation machines based on a high-order generalized integrator (HOGI).

Firstly, a theoretical analysis is conducted on traditional back electromotive force integration, low-pass filter (LPF), and second-order generalized integrator (SOGI), elucidating the existence of integral saturation problems in back electromotive force integration, amplitude attenuation, and phase shift problems in LPF. SOGI performs slightly better than the previous two but still cannot eliminate the DC component. When operating at low resonant frequencies or in systems with large DC components, SOGI is no longer applicable. Secondly, in response to the shortcomings of traditional integrators, this paper adopts HOGI as a piston stroke observer. This method can eliminate the DC component, and no DC bias exists in the observed stroke signal. The paper also uses the forward Euler method to derive the digital implementation method of HOGI. Finally, experiments are conducted to compare SOGI and HOGI. The experimental results show that the piston stroke observed by HOGI is more accurate than SOGI without additional DC bias. Furthermore, when an additional 0.2 A DC bias is added, the piston stroke average offset observed by SOGI at the given value of 5 mm, 6 mm, and 8 mm is 1.367 5 mm, 1.365 mm, and 1.351 5 mm, respectively. The piston stroke observed by HOGI is unaffected by DC bias. Therefore, the piston stroke observer with HOGI is suitable for occasions with serious DC disturbance.

The contributions of this paper are as follows. (1) Based on traditional SOGI, an improved HOGI piston stroke observation structure is designed. Multiple filtering feedback characteristics are used to eliminate the influence of DC components on stroke observation results, improving the accuracy of the piston stroke observation. (2) The complex frequency domain method is used to analyze the pure integrator, LPF, SOGI, and HOGI. The superiority of HOGI is theoretically proven. (3) Based on the forward Euler method for discretization and digital implementation of HOGI, this method has the advantages of simple calculation and easy implementation.

Regarding the sensorless control system of permanent magnet synchronous motors (PMSM), this paper combines extended Kalman filtering (EKF) and improved inertial active disturbance rejection control (IADRC). By establishing a mathematical model under the new coordinate system and applying the EKF algorithm, the state of the motor is accurately estimated, thus ensuring the accuracy and stability of the control system. Aiming at the current harmonic disturbance caused by the sudden load change, this paper introduces the second-order oscillation function to optimize the traditional linear active disturbance rejection control and proposes an improved IADRC strategy, which significantly attenuates the harmonic disturbances and strengthens the system's immunity to disturbances.

According to the traditional mathematical model of the PMSM motor under the $\gamma \delta $-axis, the mathematical model of the PMSM motor under the estimated rotational coordinate system $\gamma \delta $ is constructed, and the angle ${{e}_{\theta \gamma }}$ between the dq-axis and the $\gamma \delta $-axis is directly estimated, eliminating the influence of the other observers. After that, through the mutual validation of simulation and the mathematical model, the second-order oscillating function is connected in parallel to suppress current harmonics. The 3rd, 5th, and 7th periodic harmonics with high harmonic contents are suppressed. Its effectiveness and stability are proved by Bode's plot and the Nyquist curve plot, respectively.

The EKF's direct estimation method of error angle ${{e}_{\theta \gamma }}$ in $\gamma \delta $ coordinate system is verified Through simulation and experiment, speed step, sudden load addition, and starting with rated load. Meanwhile, compared with the traditional PI control and LADRC control, IADRC plays a role in suppressing the low harmonics when the motor is running stably at 1 000 r/min with rated load. The 5th and 7th harmonic contents are reduced by 50.5% and 77.4% compared to PI. The IADRC algorithm based on the LADRC algorithm can suppress specific harmonics, with a 41.3% reduction in 5th harmonic content compared to the LADRC and a 49.4% reduction in 7th harmonic content compared to the PI. Comparative analysis of the three-phase currents after a sudden change in the rated load shows that compared to PI, the 5th harmonic content of the LADRC is reduced by 70.5%, the 7th harmonic content is reduced by 79.1%, and the 3rd harmonic content is reduced by 54.8%. Meanwhile, compared to LADRC, the 5th harmonic decreases by 44%, the 7th harmonic decreases by 13%, and the 3rd harmonic decreases by 88%.

In the inverter-driven permanent magnet synchronous machine (PMSM) control system, high-frequency current harmonics near the switching frequency and its multiples are generated using space vector pulse width modulation (SVPWM), which brings high-frequency electromagnetic vibration. Therefore, a double random SVPWM control method combining random switching frequency and random zero vector is applied to the high-frequency current harmonic spectrum expansion. Meanwhile, the random number is generated by the improved Mersenne twister (MT) algorithm, which enhances the random performance of the random sequences and ensures the spreading effect of the double random SVPWM control method.

Firstly, random zero vector control can be achieved by changing the action time of the zero vector and reassigning the randomized zero vectors into the space vectors. Secondly, the switching frequency of the traditional SVPWM control method is fixed, and the random switching frequency control can be achieved by changing the fixed switching frequency of the inverter and dispersing the harmonics at the switching frequency and its multiples into the specified frequency domain. Thirdly, the random number is generated by the improved MT algorithm, which is applied to the double random SVPWM control of the permanent magnet synchronous machine to enhance the degree of freedom and spatial traversal of the random sequence. The new control method proposed is named LKMT-DRC.

Experimental verifications are conducted on a 4.4 kW fractional-slot permanent magnet synchronous machine. The PMSM phase current harmonics and vibration acceleration under the conventional SVPWM control and LKMT-DRC control are compared, and the vibration suppression effect of the LKMT-DRC control is analyzed using different spreading ranges. Under the inverter power supply mode, the harmonic frequencies introduced by the SVPWM control mode are mainly f_k±2f₀ and f_k±4f₀, and the frequency of the introduced high-frequency radial electromagnetic force wave is mainly f_k±f₀. Compared with the traditional SVPWM control mode, the high-frequency harmonics concentrated on the switching frequency. Its integer multiples can be effectively dispersed using LKMT-DRC control mode, and the vibration suppression effect caused by the high-frequency electromagnetic force wave can be significantly reduced. Meanwhile, the random numbers generated by the proposed LKMT algorithm can improve the randomness and spatial traversability of the random sequences, which ensures the effectiveness of the double-random SVPWM control method.

The contributions of the proposed double random SVPWM control method based on the improved MT algorithm are as follows. (1) A mathematical model of the high-frequency radial electromagnetic force introduced by PMSM under inverter power supply conditions is derived, and the effect of the high-frequency electromagnetic force under inverter power supply mode on motor vibration is analyzed. (2) The LKMT-DRC control method is proposed, which effectively reduces high-frequency harmonic content and suppresses high-frequency electromagnetic vibration. (3) The effects of different spreading ranges on the final damping under the LKMT-DRC control mode are analyzed, and the appropriate ranges are indicated.

The coupling between spatial-harmonic and time-harmonic currents in asymmetric multiphase motors (AMM) increases torque ripple and decreases efficiency, limiting their widespread application. Currently, active harmonic suppression strategies rely on complex filters or observers to extract harmonics and require the construction of numerous proportional resonance (PR) controllers at different frequencies, making the complexity and impracticality of harmonic suppression. Therefore, this paper proposes a single-frequency PR harmonic suppression strategy without filters based on the harmonic mapping law.

Firstly, based on the magnetic electromotive force equivalence principle, the universal space vector decoupling matrixes for AMM are established. Then, a mapping formula for harmonics of different frequency components on the subspaces is established. The general formula is decomposed into two independent components: amplitude and phase. The amplitude and phase mapping law of harmonics on the subspaces is derived according to the characteristics of the two components. Secondly, three criteria are proposed to search for the AMM with the minimum number of phases to ensure the unique mapping of harmonics. Based on the graphical representation of the mapping laws, the mapping trajectories of all harmonics are obtained to optimize the AMM topology and establish the subspaces for harmonic mapping. Then, based on the current phase-shifting method, a virtual AMM is constructed, and harmonics are extracted through the vector decoupling transformation subspaces. Finally, after unifying the frequency through linear space rotation transformation, PR controllers with the same resonant frequency are used to regulate harmonics.

Harmonic extraction and suppression experiments under steady-state and transient conditions are conducted using a dual three-phase motor. The extracted harmonic amplitudes can reach over 92% of the actual harmonics, demonstrating that the proposed algorithm can effectively separate harmonics. In the harmonic suppression experiment, the strategies of no harmonic suppression, current harmonic suppression under multiple synchronous rotating frames, and the proposed harmonic suppression strategy are compared. The proposed strategy decreases the proportions of the 5th, 7th, 11th, and 13th harmonic currents from 13.92%, 5.31%, 4.05%, and 2.96% before suppression to 3.02%, 0.43%, 0.39%, and 1.19%, respectively. The total harmonic distortion (THD) is decreased from 15.36% to 2.86%. Moreover, the harmonic suppression exhibited robustness under various operating conditions across the entire speed range.

The following conclusions can be drawn. (1) There are two harmonic mapping methods: full mapping with equal amplitudes and partial mapping with reduced amplitudes. The phase of mapping components can be divided into the α component leads or lags the β component by π/2. (2) Based on the harmonic mapping law, an optimal AMM topology selection criterion is established, and a virtual AMM is constructed, effectively avoiding the complex and inaccurate problem of harmonic extraction caused by constructing filters or harmonic observers. (3) The features of harmonic pair mapping on the selected subspace are that the difference in frequency order is equal, and the phase sequence is opposite. Thus, linear spatial rotation coordinate transformations are applied to unify frequencies, which enables single-frequency PR controllers with half the number of harmonics to regulate all harmonics.

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.

Electrical isolation in advanced power supply systems typically relies on power frequency transformers or high-frequency isolation DC-DC converters. However, the transformers result in multiple converter stages and increase the system’s complexity and cost. To reduce the cost of advanced traction power supply system, this paper proposes a two-phase to single-phase non-isolated power electronic transformer (NI-PET) topology based on the existing traction transformer and has the advantages of fewer transformation stages and higher system efficiency.

Some switch states can result in short-circuit paths of the DC-link capacitance in NI-PET topology. The traditional modulation strategy fails to avoid the short-circuit paths. A three-dimensional space-vector pulse width modulation (3D-SVPWM) strategy is proposed based on the 3D space vector distribution diagram, taking the vectors of three ports as the coordinate axis. According to the number of available vectors, the 3D space is divided into different ranges. In addition, the proposed strategy determines the range of reference voltage vectors and selects available space vectors to complex the demanded reference vector. Finally, based on the V-v traction transformer, the simulation model and experimental platform are built.

Simulation and experimental results show that compared to the traditional space pulse width modulation (SPWM) strategy, the proposed modulation strategy can realize the stable operation of the system. When the load and grid-side voltage fluctuate repeatedly in a short period, the two-phase to single-phase NI-PET system restores a steady state within 0.2 s, the grid-side power factor remains above 0.99, and the THD of input and output current is less than 3%. With the same load, the three-phase current unbalance degree of the proposed topology is about 45% less than the traditional power supply system. It is verified that the proposed topology and modulation can adapt to harsh conditions such as continuous load and grid-side voltage fluctuations. Compared to PET, NI-PET avoids the loss caused by the isolation stage, thus significantly improving the efficiency. In the low-power experimental platform, the efficiency of NI-PET is about 10% higher than PET.

The following conclusions can be drawn. (1) The proposed two-phase to single-phase NI-PET topology can adapt to the harsh conditions of advanced traction power supply systems. It has the advantages of low cost and good power quality. (2) Compared to the traditional modulation strategy, the proposed one can avoid the short-circuit paths of DC-link capacitance. There is no short-circuit current that is much larger than the load current on the cascade line. (3) The proposed topology can achieve about 10% efficiency improvement in a low-power experimental platform and is expected to increase the efficiency by about 2% in industrial PET.

The single-stage Totem pole dual active bridge (DAB) AC-DC converter has the advantages of low component count, high power density, and low cost, which has a broad application prospect in the field of on-board chargers (OBC). However, in the available research, the traditional single phase shift (SPS) and extended phase shift (EPS) modulation strategies are unable to optimize the quality of grid-connected current and efficiency of the Totem pole DAB AC-DC converter at the same time due to the problem of insufficient modulation degrees of freedom, limiting the further application in on-board chargers.

This paper introduces the asymmetric modulation based on the extended phase shift modulation strategy when the duty cycle of the secondary side switching tubes is no longer 50%. An asymmetric extended phase shift (AEPS) modulation strategy with three degrees of freedom is proposed. Accordingly, a multi-objective optimal modulation strategy is solved by considering the simultaneous optimization of the grid-connected current quality and efficiency of the Totem pole DAB AC-DC converter.

Firstly, the steady-state analytical model of AEPS modulation is established by using the time domain analysis method. The initial value decoupling constraint of the inductor current is considered to optimize the quality of grid-connected current, and the peak-to-peak inductor current is taken as the optimization objective. According to the Lagrange algorithm and Karush Kuhn Tucker conditions, the above multi-objective optimization problem is transformed into mathematical equations to solve the optimization solution of modulation variables. Matlab simulations show that the inductor current’s initial value decoupling and peak-to-peak value optimization are realized under the AEPS optimization modulation strategy. Compared with the SPS and EPS modulation, the proposed AEPS optimization modulation strategy reduces the peak-to-peak and RMS levels of the inductor current in the full power band, which reduces the conduction loss of the converter. Moreover, the optimized solutions in different operating modes under APES modulation are continuous, making seamless switching between different operating modes available.

An experimental prototype of a totem pole DAB AC-DC converter with a rated power of 800 W is constructed. Experimental results show that the converter achieves a peak efficiency of 93.5% under the proposed AEPS optimized modulation strategy, 5% and 14.7% higher than the SPS strategy at full load and light load, respectively; 1.5% and 14.7% higher than the EPS modulation strategy at full load and light load, respectively. The converter's grid-connected current THD is significantly reduced in the full power range, improving its grid-connected current quality. Simulation and experimental results verify the effectiveness of the proposed AEPS-optimized modulation strategy.

As a typical multilevel inverter, a neutral point clamped (NPC) three-level inverter is suitable for large-capacity and high-voltage converters, which can effectively reduce current harmonic content. However, the NPC three-level inverter has the problem of neutral point voltage imbalance due to the structural characteristics of capacitive voltage division. The traditional virtual space-vector pulse width modulation (VSVPWM) has limited ability to suppress neutral point voltage fluctuation. Correcting its offset is challenging, especially in the medium and high modulation depths. Therefore, this paper proposes a sector reconfiguration VSVPWM. By introducing equivalent medium vectors and reconstructing sectors in medium and high modulation depths, small and medium vectors can fully participate in neutral point balance adjustment while retaining fixed sector division. This method can effectively suppress the neutral point voltage fluctuation and accelerate the recovery of the neutral point offset. There is only one balance coefficient for each fixed sector, which is easy to implement.

Firstly, the equivalent relationship between a large vector and a medium vector is analyzed. An equivalent medium vector with constant amplitude is then constructed. The equivalent medium vector can participate in the neutral point balance by adjusting the proportion of medium and large vectors. After that, a virtual vector group, including equivalent medium vectors, is constructed. Furthermore, an equivalent medium vector VSVPWM (EMV-VSVPWM) is proposed, which improves the neutral point adjustment ability in the sector with a medium vector. Secondly, the level of modulation depth is divided based on the operational sector position, and the neutral point margin of the EMV-VSVPWM strategy depths is analyzed in one modulation period. It is found that the regions with weaker capacity of neutral point balance exist in high modulation depth. Therefore, a sector reconstruction VSVPWM (SR-VSVPWM) is then designed. The sector boundary and vector selection boundary in the medium and high modulation depths are separated to increase the proportion of small and medium vectors in such regions, which can enhance the neutral point adjustment margin. Furthermore, the neutral point balance coefficient of small and medium vectors is unified to reduce the computational complexity. Meanwhile, the vector sequence is optimized according to the principle of constant switching state, and the switching loss is reduced.

The initial neutral point voltage offset and modulation depth experiments are carried out on a hardware experimental platform in the loop. The results indicate that the SR-VSVPWM strategy can achieve the fast balance of the middle point in pure resistor load and resistor-inductance load conditions. Compared with the traditional VSVPWM single small vector adjustment, the neutral point voltage offset is eliminated, and the balance time in the high modulation depth is reduced by about 46%. In addition, the current harmonics are also reduced. When the experiment on variable modulation depth is considered, SR-VSVPWM still exhibits strong suppression of neutral point fluctuations and good current quality in high modulation depth. After the switching frequency is reduced to 5 kHz, the neutral point fluctuation level of SR-VSVPWM is 79.1% of the traditional VSVPWM.