During the optimization of rotor configurations in the flux-switching permanent magnet (FSPM) machine, the contradiction between the pulsating torque suppression and the average torque improvement is a challenging aspect to be addressed. Accompanied by it is the absence of theoretical guidance on rotor design according to torque performance requirements. To address them, by virtue of general airgap field modulation theory (GAFMT), this paper focuses on investigating rotor topology evolution mechanisms that is not only applicable to FSPM machine, but also to flux-reversal PM (FRPM) machine and doubly-salient PM (DSPM) machine. The study proceeds with an analysis of impacts of PM placements on the rotor configurations in 12-stator-slot/10-rotor-pole stator-PM machines. Subsequently, a two-dimensional fast Fourier transformation (2D FFT) is employed to elucidate the trade-off between the increase of average torque and the decrease of pulsating torque. Thirdly, the concept of amplitude modulation is introduced, and under its guidance, two rotor configurations are designed according to their respective objective functions. Multi-objective optimization (MOP) is then applied to enhance the torque performance and evaluate the effectiveness of rotor topologies. Finally, the rotor topology evolution mechanism of stator-PM machines is verified through finite element analysis (FEA) and experimental results, specifically in the case of FSPM machines.

In order to conduct an explicit analysis of the induction machine (IM), the sole magnetic field parameter’s description of short-circuited coils (SCC) modulator is crucial, despite its absence in the literature. This article presents a novel concept of introducing magductance into the SCC, thus referring to the SCC modulator as the magductance modulator. The modulation operator is completely studied from magnetic field parameters, thereby adding in understanding the working principle of IM. Expressions for the modulated magnetomotive force (MMF) is elucidated specifically for the squirrel cage induction machine (SCIM). Unique vector modulation to the magductance modulator is unveiled. Then, the effects of modulator parameters on machine performance are investigated. The calculation process based on the proposed method is illustrated in detail, with the key performance parameter expressed. The proposed method is validated through comparisons with finite element analysis (FEA) and experimental results.

In this article, the surface-mounted permanent magnet machine is regarded as a salient pole reluctance machine to take into account the effect of stator teeth. The field modulation behavior of the magnetizing field is firstly introduced, and the field model is then derived using the general airgap field modulation theory (GAFMT). The properties of the modulated field harmonics are explored based on the proposed field model. Subsequently, a general cogging torque model based on the virtual work method and the GAFMT is proposed to describe the relationship between the field harmonics and the cogging torque. On this basis, the mechanism of the cogging torque is studied, its frequency, effective field harmonics, and the contribution of each harmonic are revealed. The proposed model is then validated by comparing its results with those obtained from the Maxwell Stress Tensor method and the finite-element analysis, and a good agreement is observed, demonstrating the effectiveness of the proposed model. Furthermore, the experimental results also confirm the effectiveness of the proposed model.

The efficiency of flux switching permeant magnet (FSPM) machine is a research focus in recent years. However, researches on different modulation strategies on iron loss are limited. In this paper, the influence of different rotor speeds on iron loss, eddy current loss, hysteresis loss is investigated. Each order harmonic in the rotor is also analyzed to learn about the constitute of iron loss. Then, magnetic flux density in the air gap when the machine is no load and supplied by pulse width modulation (PWM) inverter is calculated. Finally, iron loss and copper loss under different PWM strategies and working conditions are investigated by finite element analysis (FEA).

The magnetic circuit theory stands as a pivotal theory for electromagnetic devices like electrical machines and transformers,furnishing indispensable tools for addressing intricate electromagnetic challenges and optimizing the performance of electromagnetic apparatus.In this paper,the historical development of magnetic circuit theory is first traced,providing insights into the valuable contributions made by earlier researchers towards refining magnetic circuit theories,including magnetic circuit parameters and their respective theoretical development.Additionally,their limitations and the challenges they encounter in practical applications are analyzed.On this basis,this paper pioneers the definition of magductance and hysteretance from the fundamental physical properties of magnetic circuit,establishes the vector magnetic circuit theory encompassing three core components(reluctance,magductance,and hysteretance),systematically and completely characterizes the three basic properties of magnetization,eddy current and hysteresis in the magnetic circuit,reveals the intrinsic connection between the virtual magnetic power and the electric power,and puts forward the magnetoelectric power law.An exhaustive comparative analysis with other magnetic circuit theories or modeling methods is conducted to illustrate their interconnections and differences.In order to show the applicative value of the vector magnetic circuit theory in science and engineering,four practical application scenarios are presented.Finally,the unique features of the proposed vector magnetic circuit theory are highlighted and the future research directions are prospected.

Radial electromagnetic force analysis is an important step for further vibration and acoustic investigation in electric machines. This paper investigates and compares the radial electromagnetic force harmonics in rotor permanent magnet (PM) machines and stator-PM machines in no-load mode based on the general airgap field modulation theory (GAFMT), taking a surface-mounted permanent magnet (SPM) machine and flux-reversal permanent magnet (FRPM) machine respectively as examples. By GAFMT, the difference in force harmonics is explained by revealing the mechanism of force modulation in these two types of machines. The teeth modulation effect is investigated as well.

With the aid of general airgap field modulation theory, the torque production mechanism of flux-reversal permanent magnet (FRPM) machines is revealed, and it finds that multimodulation orders of the rotor salient pole reluctance, i.e., dc modulation, first order modulation and second order modulation, have effects on FRPM machine performances, regardless of pole pair combinations. Therefore, analysis and optimization of rotor salient pole reluctance can be further improved by considering these three modulation orders, and the 12/10, 12/14, and 12/16 pole FRPM machines are taken as optimization examples together with proving their identical optimum rotor configuration. Sensitivity analysis is applied to increase the machine optimization efficiency. By comparing symmetric and asymmetric rotor configurations’ differences in contributions to machine performance considering effects of multimodulation orders, a combined optimum rotor configuration is proposed. Both finite-element analysis and experiments verify the effectiveness of theoretical analysis.

Abstract The brushless doubly‐fed machine (BDFM) utilizes an asymmetric composite rotor featuring salient pole reluctance and magductance to effectively compensate for the phase shift in space, as well as enhance magnetic field modulation effects, and is therefore used as a modulator. This paper evaluates the modulation capability of the modulator from the perspective of the magnetic field conversion mechanism. The theoretical evolutions of the average magnetic field conversion factors and torque contributions of various airgap field harmonics are accomplished. Additionally, multi‐objective optimization is conducted for better performance, using stratified sensitivity analysis on typical 4/2 pole pair BDFMs featuring symmetrical and asymmetric composite rotors. As a result, further improved modulation of the air gap magnetic field is expected, the cross‐coupling efficiency of the rotor is improved, and a lower output torque ripple is also achieved compared to the conventional symmetrical counterpart. Theoretical investigation of the optimized BDFM, including its effectiveness in enhancing performance metrics such as coupling factor, airgap flux density, and phase shift mechanism, is verified through 2D finite element analysis. Furthermore, a proof‐of‐concept prototype for experimentation was manufactured, which achieved good agreement with the theoretical predictions.

Optimizing the rotor is a key issue in improving the torque performance of flux-switching permanent magnet (FSPM) machine. This paper investigates the contribution of rotor to cogging torque in a 12/10 FSPM machine using the general airgap field modulation theory (GAFMT). Then, two rotor configurations are proposed to reduce useless modulation orders theoretically. The multi-objective programming (MOP) is implemented for further optimizations and their effectiveness is verified through finite element analysis (FEA) results.

A hybrid model for the flux-switching permanent-magnet (FSPM) machine is proposed in this paper. In this hybrid model, the air-gap magnetic field in FSPM machine is investigated from the perspective of the stator modulation effect and rotor modulation effect. The stator modulation is discussed from the perspective of equivalent air-gap in the stator slots and permanent-magnets (PMs). The rotor modulation effect is divided to two aspects, namely the effect on the magnetomotive force (MMF) and the effect on stator modulation effect. Different from the conventional model where the stator modulation effect and the rotor modulation are independent of each other, stator modulation effect in the proposed model is coupled with the rotor modulation effect by the minimal reluctance principle. Therefore, MMF and the stator modulation effect in FSPM machine become susceptible to rotor positions with the influence of the rotor modulation effect. Air-gap flux density in FSPM machine is calculated by this hybrid model and compared with those by conventional model and finite element analysis (FEA). Finally, the effectiveness of the proposed hybrid model is validated by comparison of the electromotive force with FEA and experimental results.

It is well known that the magnetic circuit theory can directly reflect the real change of magnetic circuit parameters. In this paper, a new magnetic component - magductance, together with reluctance, is proposed to accurately describe the effect of operating frequency on the parameters of the magnetic circuit. According to the distribution of magnetic flux in the laminated core, the expressions of reluctance and magductance are derived by combining the electromagnetic theory and the vector magnetic circuit theory. The validity of these expressions is demonstrated by an experimental platform with Epstein frame.

Optimization method for rotor salient pole reluctance considering effects of its own slotting depth and other machine parameters are proposed in the paper, taking 12/10, 12/14 and 12/16 pole magnetically−geared machine as examples. With the aid of general airgap field modulation theory, the torque production mechanism of magnetically−geared machine considering differences in summation and differential modulation is revealed so as to prove identical optimization direction regardless of pole pair combinations. Further, by establishing the relationship between torque performance and rotor parameters, a combined optimum configuration of the rotor pole is proposed. The finite element analysis is carried out to verify the effectiveness of the proposed optimization method.