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.

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.

In this article, a new space vector pulsewidth modulation (SVPWM) strategy is proposed for dual three-phase (DTP) machine drives. The proposed strategy is based on vector space decomposition (VSD) and mainly targets the scenario where power of the two subthree-phase winding sets of the machine is unequal. In the basic VSD-based SVPWM strategies, the constraints of non-negative dwell time of the basic vectors result in zero linear modulation range when the DTP machine is under unbalanced power sharing conditions. Different from them, this article investigates the maximum linear modulation capability of VSD-based SVPWM under power sharing by removing the dwell time constraints of the basic vectors. In this regard, only the physical limitations of the dwell time of each phase need to be guaranteed. According to this principle, a two-step-based design procedure of the proposed modulation strategy is presented in detail, followed by a numerical analysis regarding its linear modulation boundary. Moreover, the performance comparisons with many other typical VSD-based SVPWM strategies are also conducted. It has been theoretically and experimentally proven that the proposed SVPWM solution can obtain maximum linear modulation range when the DTP machine is under unbalanced power sharing.

This paper develops a modified particle swarm optimization algorithm with an embedded extreme learning machine (ELM-MPSO), improving accuracy and efficiency for global optimization of a micro-jointed motor with multiple modes. Different from conventional optimization, ELM acts as an indirect surrogate model (indirect-SM) to drive the MPSO algorithm online. To enhance the generalization ability of ELM, a fitness grading strategy is formulated. By just training optimized samples, indirect-SM can be built into the algorithm to form an online interaction mechanism. With this mechanism, optimized particles are pre-filtered and pre-supplemented online according to grade, thereby enhancing their quality. Sobol sampling and double updating techniques are introduced to ensure particle global and local characteristics. In addition, fitness is evaluated according to its complexity during optimization, which reduces function calls. Optimization evaluation results show that the ELM-MPSO algorithm improves convergence and diversity for global optimization. An optimal candidate design is obtained by applying the proposed algorithm to representative points (RPs) optimization of a micro-joint motor. Finally, the prototype experiments demonstrate that the entire optimization strategy is effective.