In this article, a nonlinear semianalytical model (SAM) is presented to predict the magnetic field distribution (MFD) and electromagnetic performances (EPs) in the cubic spoke-type permanent magnet (PM) machine. To model the rectangular PMs, the rectangular PM is simplified as a combination of fan-shaped regions with different arc angles. Then, the MFD and EPs of the cubic spoke-type machines can be obtained by the harmonic modeling technique. Particularly, the saturation of the magnetic bridges is considered by the nonlinear iterative algorithm. The proposed nonlinear SAM is studied on a 12-slot/8-pole cubic PM prototype, and the nonlinear finite element model and experiment verify its correctness. The main contribution of this article is to present a general analytical modeling method for cubic spoke-type PM machines and consider the magnetic saturation of magnetic bridges.

This article proposes a nonlinear semianalytical model (SAM) of the multiphase Halbach array axial flux permanent-magnet motor (AFPMM) to speed up the computation of its magnetic field. Compared to the existing analytical models, the proposed nonlinear SAM can directly consider magnetic saturation to obtain more accurate results. To this end, the multiphase Halbach array AFPMM is equivalent to several 2-D models by the quasi-3-D method under the Cartesian coordinate system. Then, the nonlinear SAM is developed by using the convolution theorem and the fast Fourier factorization. The proposed nonlinear SAM is studied on a five-phase Halbach array AFPMM with different rotors, and the nonlinear finite element (FE) model and experiment verify its effectiveness. The proposed SAM is computationally efficient and accurate, and it is also applicable to other types of multiphase Halbach array permanent magnet (PM) electrical motors in Cartesian coordinates.

In this article, a new analytical model for predicting the magnetic field of the U-shaped interior permanent magnet motor (IPMM) is proposed. In the polar coordinates, rectangular permanent magnets are equivalent to the combination of consistent fan-shaped subdomains, and after that, the Laplace or Poisson equation of each solution domain can be obtained. Furthermore, based on the harmonic modeling (HM) technique, the saturation characteristics of the magnetic bridge are accurately considered, and then its magnetic field distribution (MFD) and electromagnetic performances (EPs) can be obtained. The approach proposed in this article includes but is not limited to U-shaped IPMMs, and it can also be applied to spoke-type or V-shaped IPMMs with a minor modification.

This article proposes a hybrid analytical model (HAM) for predicting ac copper losses in hairpin windings. The HAM combines the nonlinear semi-analytical model (SAM) and the 1-D ac copper loss computation model to solve the inaccurate boundary solutions of the 1-D ac copper loss computation model when magnetic saturation occurs in the stator teeth. The HAM is used to study the ac losses of the hairpin windings with four different conductor arrangements under different current excitation conditions, and the versatility of the HAM is verified. The HAM has high calculation accuracy, and the calculation speed is 66% faster than the finite element (FE) model. The primary contribution of this research is to present a quick and simple approach for accurately predicting ac copper losses in hairpin windings with arbitrary conductor arrangements.

In this article, an efficient multi-objective optimization strategy for the Halbach array permanent magnet synchronous machine (PMSM) is developed by taking into consideration the nonlinear B-H behavior of soft magnetic materials. Based on the harmonic modeling (HM) technology, the electromagnetic performances (EPs) of the Halbach array PMSM can be computed. To specifically model the local magnetic saturation, the stator teeth are separated into several annular layers, and each tooth is further divided into several regions along the tangential direction. Then, the parameters of the Halbach array PMSM are optimized utilizing combined nonlinear semi-analytical model (SAM) and non-dominated sorting genetic algorithm II (NSGA-II). To validate the effectiveness and accuracy of the developed optimization scheme, a Halbach array prototype is then manufactured in accordance with the optimization results. The multi-objective rapid optimization strategy developed in this article, which includes but is not limited to Halbach array permanent magnet (PM) machines, serves as a reference for the design and optimization of various PM machines.

To facilitate the active magnetic bearing (AMB) design and analysis, an accurate and fast model that considers both rotor eccentricity and the saturation effect is necessary. In this article, a novel hybrid analytical model (HAM) for effective calculation of the magnetic field of the AMB is proposed. Eccentricity and local saturation are considered in the proposed HAM. In the proposed HAM, the stator and rotor are modeled by elementary subdomains (ESDs) and the air-gap is modeled by magnetic equivalent circuit (MEC). Direct coupling between the solutions in the ESD regions with MEC completes the whole model matrices. Compared to the existing literature, the proposed model considers both the rotor eccentricity and material nonlinearity. The effectiveness and accuracy of the proposed HAM are validated by both the finite element model and experimental results. The results show that the proposed HAM can accurately predict the magnetic quantities of the AMB.

Position sensing is one of the crucial parts of the active magnetic bearing (AMB) system. The printed circuit board (PCB) eddy current position sensor is a new type of position sensor for the AMB system, which makes a compact structure, high sensing quality, and is low cost. In this article, an improved driver circuit is proposed for this new sensor. The driver circuit includes an excitation circuit and signal conditioning circuits. A crystal oscillator circuit with a power stage is used to provide the excitation coil with a stable excitation source of high stability and good precision of frequency. The analog demodulation circuit is designed for signal conditioning circuits to extract the rotor displacement information from the sensing coil outputs. Compared with the state-of-art driver schemes, the proposed method reduces the circuit complexity and cost. Accordingly, the experimental results show that the designed sensor has good linearity and sensitivity, and it can ensure AMB stable operation at the rated speed.

This article proposes a discrete-time dynamic-decoupled current controller for an LCL-equipped high-speed permanent magnet synchronous machine with only the motor currents measured. The controller is designed in the synchronous coordinate based on a complex z-domain transfer function. The main contribution of the proposed current controller is the robust dynamic decoupling performance to achieve better transient behavior. Moreover, an effective coefficient selection method is developed to acquire sufficient phase margin and gain margin, even with the system parameters varying ± 50%. Additionally, the stable region of the LCL resonance with the proposed method is discussed. Finally, the effectiveness of the proposed method is verified by driving the tested motor to 100 kr/min.

In this article, we propose a novel nonlinear semianalytical model (AM) for the magnetic field calculation of electric machines. The nonlinear properties and local saturation effect of the iron part are taken into consideration in Cartesian coordinates, which is the main contribution of the proposed model. Thus, high accuracy of electromagnetic field results can be obtained with the low computational time cost. The model is developed based on the harmonic modeling technique by solving Maxwell's equations. The detailed theoretical derivations, which use the complex Fourier series and the Cauchy product, are presented. To verify the proposed model, an axial flux permanent-magnet (PM) machine is selected to be investigated. Both finite-element model and experimental results agree well with that of the proposed model. Moreover, the nonlinear AM has potential application for other types of PM electrical motor in Cartesian coordinates, such as flat PM linear machines.

This article proposes a compensation method of position estimation error for high-speed surface-mounted permanent magnet synchronous motors based on robust inductance estimation. The proposed method relies on the variation of the estimated δ-axis back back-electromotive force when a small current is injected into the γ axis. The inductance estimation error is limited within pm !5% when the nominal resistance and inductance vary bf pm 30% of their real values. With the estimated inductance, the position estimation error can be well compensated. Compared with the conventional current-injection method, the proposed method has enhanced robustness against the system noises. Benefiting from this, it is effective to estimate the inductance with a small injected current ( bf 0.5% of the rated current), where the conventional methods fail. Finally, the effectiveness of the proposed method is validated by simulation and experiment results on a 100 kr/min (1.67 kHz) high-speed permanent magnet synchronous machines accurately with 10-kHz sampling frequency.

In this article, a novel dynamic-decoupled active damping current controller is proposed for an LCL-equipped high-speed permanent magnet synchronous machine. Compared with the conventional stationary current-control method for the LCL-type system, the proposed method is established in the synchronous rotating frame for improving the current transient performance. When taking the controller into the synchronous coordinate, there are two following challenges: first, the synchronous resonance frequency varying in a wide range because of the synchronous coordinate transformation, and second, eliminating the coupling between the dq coordinate. To address these issues, an improved synchronous capacitor-current-feedback active damping method is designed based on arbitrary pole assignment and is significantly effective for the LCL resonance within the Nyquist frequency. Moreover, a novel dynamic-decoupled motor-current controller is proposed to eliminate the coupling between the dq-axis motor current. The gain selection method is discussed to acquire sufficient phase margin and gain margin. Finally, the effectiveness of the proposed method is verified by driving the tested motor to 72 kr/min.

This article proposes a sliding-mode position estimation method for high-speed surface-mounted permanent magnet synchronous machines with LCL filter. The implementation of the LCL filter aims at smoothing the motor current and reducing the iron loss caused by the harmonic currents. First, the discrete-time model of the LCL-filtered motor drive system is developed. Based on the developed model, the sliding-mode observer is proposed with more robustness against the parameter variation to estimate the back EMF, which contains the information of the rotor speed and position. Because of the elimination of the capacitor voltage sensors, the augmented sliding surface is designed to achieve arbitrary pole placement with only output feedback. Besides, considering the analog-to-digital scaling error and pulsewidth modulation harmonics, a reaching law with enhanced chattering suppression ability is proposed. Compared with the conventional methods, the chattering problem is well alleviated and thus the speed estimation ripple is much reduced. Finally, the effectiveness of the proposed method, even with the mismatched parameters adopted is validated at 100 kr/min with the sampling frequency 20 kHz.

The zero-sequence inductance is a vital parameter for the performance analysis of permanent magnet machines, especially under faulty conditions or in open-winding machines. This paper focuses on the zero-sequence inductance calculation of fractional slot concentrated winding permanent magnet synchronous machines (FSCW-PMSMs), and reveals the variation regularity of this kind of inductance and its various components against pole/slot combinations, using the winding function and finite element methods. Moreover, based on the analysis of 36-slot FSCW-PMSMs with different pole numbers, the dependency of each inductance component on the pole/slot combination is discussed in detail. To validate the regularities, experimental measurements of zero-sequence inductance are implemented in the prototype of the 36-slot stator. It is found that the regularities are independent of specific slot or pole numbers, which provide guidelines for optimum pole/slot combination selection, to mitigate the problems caused by zero-sequence current.

This article proposes a rotor position and speed estimation method for the interior permanent magnet synchronous machine (IPMSM) in the full-speed range. The proposed method is implemented in the synchronous rotating frame. Based on the voltage equation of the IPMSM in the synchronous rotating frame, a single-variable optimization problem is formulated to solve the rotor position at each current sampling step. After that, the solved position is fed into a phase-locked loop observer to obtain the estimated rotor speed and smooth out the estimation. The proposed position and speed estimation methods are effective from standstill to high speed, and no estimation algorithm switching is needed during speed variation. Details about the convexity of the optimization problem, the effects of parameter mismatch and sampling noise, and the solving method of the problem are discussed. Finally, experiments are conducted in both steady and dynamic situations to validate the effectiveness and robustness of the proposed algorithm.

This paper proposes an analytical model for the prediction of air gap magnetic field distribution for axial flux permanent magnet (AFPM) machine with various types of misalignments. The AFPM machine geometry is first transformed to a polar representation. Consequently, the subdomain model based on current sheet technique is developed. Then the stator coordinate system is chosen as reference coordinate to consider both static/dynamic angular and axis misalignments. The back electromagnetic forces and cogging torque are obtained accordingly based on Maxwell's equations. The results show that the proposed approach agrees with the finite-element method. The model is further validated by experiments under healthy, dynamic angular and axis misalignment conditions, which can validate the proposed approach. It turns out that the proposed approach can predict the performance of AFPM machines with types of misalignment quickly and effectively, which is greatly significant for further fault detection.

This article presents a new rotor design to reduce rotor eddy current loss of a high-speed permanent magnet synchronous machine for flywheel energy storage system. Instead of using common nonmagnetic sleeves, the new rotor incorporates permeable retaining sleeves (PRSs) to fix permanent magnets on the rotor hub. The PRSs are made of permalloy that features high permeability and high electrical conductivity. Thus, skin depths for asynchronous harmonics are extremely small. On the other hand, the PRSs are electrically insulated along the circumferential direction. Owing to these two reasons, rotor eddy current loss at open circuit decreases by 64.2% without sacrificing torque output, compared with an original rotor with nonmagnetic retaining sleeve. In addition, thermal and structural finite element analyses are performed to calculate rotor temperature distribution and evaluate the structural integrity of the new rotor. Rotor eddy current loss reduction benefits lowering rotor temperature rise. Prototype machine with the new rotor is fabricated, and preliminary tests are carried out to confirm the analysis results.

This paper applies two different analytical methods, i.e., the perturbation method and superposition method, to calculate the magnetic flux density distribution and the magnetic force of the active magnetic bearing (AMB) with the rotor eccentricity. These two methods are thoroughly analyzed, compared and validated by the finite element model (FEM). The perturbation method is theoretically complex while the superposition method is intuitive. The valid range of the superposition method is larger than the perturbation method. However, the superposition method requires longer computation time. The main contribution of this paper is assessing the effectiveness of two analytical methods for predicting the AMB performance with the rotor eccentricity and giving a comprehensive guideline for engineers to choose the proper analytical method to design AMB.

In this article, an improved deadbeat predictive current control (DPCC) method with parameters identification for surface-mounted permanent magnet synchronous machines (SPMSMs) is proposed. With the proposed DPCC method, zero steady-state current error and deadbeat dynamic current response could be achieved, even with inaccurate initial motor parameters. On basis of the conventional DPCC method, a novel parameters identification for the stator resistance and inductance is developed, which is the main contribution of this article. The proposed parameters identification method works based on a reconstructed characteristic vector from the disturbance observer with current injection. Compared with traditional recursive-least-square methods, the proposed method can be implemented with greatly reduced computation burden. Additionally, since the design is established based on the fully discretized model, the effectiveness will be guaranteed on both low-frequency and high-frequency motors, which is a significant advantage of the proposed method.

In this article, a position sensorless drive and online parameter estimation method for surface-mounted permanent magnet synchronous machines-based on adaptive full-state feedback current control is proposed. The position sensorless drive is established by the detection of the back-electromotive force in the gamma delta synchronous reference frame, which is effective at the medium-speed and high-speed range. Besides, accurate estimation of the winding resistance, the stator inductance, and the flux linkage of the PM is achieved independently. Compared with the traditional recursive-least-square methods, the proposed parameter identification method can be easily implemented because of the significantly reduced execution time. With the help of the parameter identification, the precise position estimation can be achieved by the proposed sensorless control method regardless of the parameter variation during the operation. The stability of the proposed method is proved by the Lyapunov-function method. Finally, the effectiveness of the proposed method is validated by the simulation and experimental results.