A double-layer permanent magnet spherical motor (PMSM) with same spatial distribution of stator poles and rotor poles is designed based on spherical harmonic theory in this paper. The stator coils are equivalent to permanent magnets to simplify the calculation, and the torque model based on virtual work method is derived. Firstly, the torque model of single pair of poles is derived on the premise of considering the fundamental component of the magnetic field. Then, the relative positions of stator poles and rotor poles, the direction angles of torque components are discussed. Finally, the torque model is obtained by space vector theory and superposition theorem. Moreover, the simulation and experiment are implemented to verify the feasibility and correctness of the proposed torque model. The obtained torque model in this paper has similar expression with that of traditional motor, which lays a theoretical foundation for the structure optimization and control strategy of PMSM.

The state of charge (SOC) of lithium-ion batteries is the core parameter of the battery management system. Accurate SOC can guide the effective management of the battery system and prevent the battery overcharge and over-discharge, which can extend the battery life. This paper uses an electrochemistry battery model for the SOC estimation of lithium-ion batteries, and then, the forgetting factor least squares method is used for model identification. Then, the Gauss-Hermite particle filter (GHPF) technique is proposed to estimate the SOC. The experiment results show that the GHPF not only improves the estimation accuracy but also reduces the number of sampling particles, which reduces the complexity of the algorithm. The method shows the superiority on accuracy and real-time performance over the standard PF, EPF, and UPF methods.

This article develops an improved equivalent magnetic network (EMN) model for analysis of a modular interior permanent magnet (IPM) machine. First, focusing on the local magnetic saturation, the stator tooth crown is divided into three parts based on its structure and flux density distribution. To model the specific flux path, the tooth tips on both sides are approximated to right-angled trapezoids and the middle part is divided into isosceles trapezoid. Second, an improved air-gap model is proposed, which divides the air-gap magnetic network into three layers. The middle network uses cross-shaped mesh (CS-M) elements to represent the path of tangential and radial fluxes. The top and bottom layers are composed of parametrized nonlinear permeances between stator, rotor edge nodes, and middle network nodes, whose values are the function of angle respect to CS-M elements. In this way, as the machine rotates, the structure of the EMN model can be kept invariant, and only permeances of bottom layers should be modified. Then, the EMN model is extended to the analysis of the machine with skewed stator. The accuracy and effectiveness of the proposed EMN model are verified through comparisons with finite element analysis and experimental tests.

Considering the basic role of the stator magnetic field (MF), this paper presents a synthesis strategy for stator MF of a permanent magnet spherical motor (PMSM). Given the structure of the PMSM, the MF of a stator coil group with unit current is obtained, and the spherical harmonic components are decomposed, so the relationship between the whole stator MF and coils currents can be deduced by the rotary transformation and superposition. Referring to the rotor MF, the expected stator MF is determined; then, the stator coil currents are calculated by solving a constrained optimization. Finally, the current excitation strategy of stator coils is verified by finite-element analysis and experiments.

Five-phase permanent-magnet synchronous motor (PMSM) has the ability of fault-tolerant operation, which is beneficial for high reliability occasions. A fault-tolerant current vector control strategy based on five-phase six-leg inverter is proposed for open-circuit fault in this article. It deals with single-, double-, and triple-phase fault conditions. First, the overall control scheme is established based on the mathematical model of five-phase surface-mounted PMSM. To release more control degrees of freedom, the constraint for the sum of fault-tolerant phase currents is removed, and the control variates method is used to calculate the optimal fault-tolerant currents. Furthermore, to achieve the current tracking, the corresponding reduced-order current transformation matrices are derived, and the corresponding main power topology, the five-phase six-leg voltage source inverter (VSI), is established. The unbalanced operation of the topology is investigated, the equivalence to the full-bridge VSI is proved, and the voltage utilization and voltage unbalance of five phase half-bridge, full-bridge, and six-leg inverter are compared. Then, the corresponding carrier-based PWM control strategy based on zero-sequence injection has been proposed, which is equivalent with the three-dimensional space vector PWM algorithm and is computationally efficient. The experimental results confirm the effectiveness of the proposed fault-tolerant control strategy.

The fundamental harmonic amplitude and waveform distortion rate of the air-gap flux density directly affect the performance of a permanent magnet spherical motor (PMSM). Therefore, in the paper, the axial air-gap magnetic field including the end leakage of the Halbach array PMSM is analyzed and optimized. In order to reduce the calculation time of the objective function, the air gap magnetic field model adopts a non-linear regression model based on support vector machine (SVM). At the same time, the improved grid search (GS) algorithm is used to optimize the parameters of SVM model, which improves the efficiency and accuracy of parameter optimization. Considering the influence of moment of inertia on the dynamic response of the motor, the moment of inertia of the PMSM is calculated. This paper takes the air gap magnetic density fundamental wave amplitude, waveform distortion rate and rotor moment of inertia as the optimization objectives. The particle swarm optimization (PSO) algorithm is used to optimize the motor structure with multiple objectives. The optimal structure design of the PMSM is selected from all of non-dominated solutions by the technique for order preference by similarity to an ideal solution (TOPSIS). The performance of the motor before and after the optimization is analyzed by the method of finite element (FEM) and experimental verification. The results verify the effectiveness and efficiency of the optimization method for the optimal structure designing of the complex PMSM.