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Accurate modeling of slotting and magnetic saturation effects has been two main challenges for analytical modeling of electric machines. In this article, first, different techniques such as sub‐domain (S‐D) model, winding function theory, magnetic equivalent circuit (MEC) model, and conformal mapping (CM) method are introduced to analytical model and analysis of electric machines. These techniques are also compared in terms of their accuracy, and computational complexity. Second, with respect to the comparison results, a new hybrid analytical model is presented for electromagnetic modeling of wound rotor induction motors, which consider the modeling accuracy of slotting and magnetic saturation effect, simultaneously. In this way, the air‐gap region is modeled by using S‐D model, and the iron parts are considered by using MEC model assisted by CMs. In final, the analytical results are verified by comparing with corresponding results obtained through finite element method and experiment set‐up. [ABSTRACT FROM AUTHOR]

This paper presents an analytical model for predicting the magnetic field performance of permanent magnet synchronous motor with permanent magnet cutting. In order to satisfy the boundary conditions, the defective permanent magnet is equivalent to a double-layer sector permanent magnet, and the size of the sector-shaped permanent magnet is determined, this process is obtained by an equivalent magnetic circuit model. Then, the motor is divided into four sub-domains: inner sector permanent magnet sub-domain, outer sector permanent magnet sub-domain, air gap sub-domain and stator slot sub-domain. Under the boundary conditions, the analytical solution and harmonic decomposition of the air gap magnetic flux density and cogging torque for several different permanent magnet cutting sizes under no-load condition are obtained by solving the Poisson equation and Laplace equation with the method of separating variables. The analytical model is verified by the finite element method. The results show that the error between the analytical method and the finite element method is less than 6%, and the solution time of the analytical method is only 0.59% of the finite element method, the chamfered structure proposed in the paper reduces the cogging torque amplitude 35%. Therefore, this method can provide powerful help for the initial design of permanent magnet motors.

The flux switching permanent magnet motor is a kind of double-salient machine with good speed regulation performances and application prospects. However, in traditional sub-domain models which are used to exactly calculate the magnetic field of the flux switching permanent magnet motor, the orders of major harmonics can not be intuitively obtained. The computational efficiency and practicality of the sub-domain models are limited. Meanwhile, some errors are caused in the equivalent process of iron slot shapes. Aiming at these problems, an improved sub-domain model is proposed in this paper. The major magnetic field harmonics are selected in advance for each sub-domain region by the magnetic permeance function model of the air gap. In addition, the influence of the slot shape equivalence is corrected by the magnetic permeability of slots, and the accuracy of the sub-domain calculation is improved. The proposed model is verified to have the advantages of high accuracy and fast computing speeds by 2-D finite element analysis. A convenient and reliable approach for flux switching permanent magnet motor designs is provided thereby.

Computational complexity, magnetic saturation, complex stator structure and time consumption due to repeated iteration compels researchers to adopt alternate analytical model for initial design of electric machines especially Switched Flux Machine (SFM). To overcomes the abovesaid demerits, In this article alternate analytical sub-domain model (SDM) for magnetic field computation in Segmented PM switched flux consequent pole machine (SPMSFCPM) with flux bridge and flux barriers accounting boundary and interface conditions, radial magnetized PMs (RM-PMs) and circumferential magnetized PMs (CM-PMs), interaction between stator slots and inner/outer rotor topologies is proposed. Overall field domain is divided into air gap, stator slots and Permanent Magnet (PM) accounting influence of CM/RM-PMs under no-load and on-load conditions. Analytical expression of field domain is obtained by solving magnetic vector potential utilizing Maxwell’s equations. Based on the magnetic field computation especially no-load and on-load condition, Magnetic Flux Density (MFD) components, open-circuit flux linkage, mechanical torque and cogging torque are computed utilizing Maxwell Stress Tensor (MST) method. Moreover, developed analytical SDM is validated with globally accepted Finite Element Analysis (FEA) utilizing JMAG Commercial FEA Package v. 18.1 which shows good agreement with accuracy of ~98%. Hence, authors are confident to propose analytical SDM for initial design of SPMSFCPM to suppress computation time and complexity and eliminate requirements of expensive hardware and software tools.

For an optimal design of a surface-mounted permanent magnet synchronous motor (SPMSM), many objective functions should be considered. The classical optimization methods, which have been habitually designed based on magnetic circuit law or finite element analysis (FEA), have inaccuracy or calculation time problems when solving the multi-objective problems. To address these problems, the multi-independent -population genetic algorithm (MGA) combined with subdomain (SD) model are proposed to improve the performance of SPMSM such as magnetic field distribution, cost and efficiency. In order to analyze the flux density harmonics accurately, the accurate SD model is first established. Then, the MGA with time-saving SD model are employed to search for solutions which belong to the Pareto optimal set. Finally, for the purpose of validation, the electromagnetic performance of the new design motor are investigated by FEA, comparing with the initial design and conventional GA optimal design to demonstrate the advantage of MGA optimization method.

Permanent magnet eddy current couplings are promising devices for torque and speed transmission without any mechanical contact. In this paper, flux-focusing permanent magnet eddy current couplings with double slotted conductor rotors are proposed and investigated. Given the drawback of the accurate 3-D finite element method, the purpose of this paper lies to establish an accurate and fast analytical model to evaluate the electromagnetic field and torque of such devices with non-homogeneous boundary conditions. Thus, based on the 2-D sub-domain method, the magnetic vector potential in each sub-domain is formulated and solved by the separation of variables method. Taking into account the eddy current effects and slotting effects, the closed-form expressions of magnetic field, induced current, electromagnetic force, and torque for such devices are obtained. Finally, the 3-D finite element method is employed to validate the analytical results.

Permanent-magnet vernier machine (PMVM) is a relatively new type of PM machines. An analytical subdomain model accounting for tooth-tips and flux modulation poles is developed to accurately predict on-load field distributions in PMVMs. Based on two-dimensional (2-D) polar coordinate and magnetic vector potential, this method solves the Maxwell’s equations in slot, air-gap, flux modulation pole slot (FMPS), and PM regions. Consequently, the electromagnetic performance such as cogging torque, back-electromotive force (EMF), electromagnetic torque, power factor, and magnet loss are calculated. In addition, the model can also be used for the evaluation of demagnetization withstand capability. The finite-element analysis (FEA) and experimental results validate the accuracy of the developed analytical model. [ABSTRACT FROM PUBLISHER]

This paper presents an analytical sub-domain model for predicting magnetic flux density and winding inductance flux switching permanent magnet (FS-PM) under armature reaction. It is obtained by solving Poisson and Laplace equations in polar coordinates for each domain, i.e. air gap, rotor and stator slots. The model accounts for the influence of interaction between the stator slots and air gap, as well as rotor slots and air gap and winding inductances are obtained from the analytical method and compared by finite element analysis (FEA).Magnetic field distribution are derived from the analytical method and verified by finite element analysis (FEA). [ABSTRACT FROM AUTHOR]

This article shows a two-dimensional analysis model for predicting eddy current loss in a winding flux-switching permanent magnet under an open-circuit. The finite-element method is used for electrical machine design; however, this numerical method is always time consuming. Depending on the geometry, the mesh quality of the finite-element method should be high, and thus the finite-element method is more time consuming for special electrical machines. To solve this problem, a sub-domain model using Fourier analysis is improved for a flux-switching permanent magnet machine. It is obtained by solving Poisson and Laplace equations in polar coordinates for each domain, i.e., the magnet, air gap, rotor and stator slots, as well as external region. The model accounts for the influence of interaction between the stator slots and air gap, as well as rotor slots and air gap. Magnetic field distribution, flux linkage, back-electromotive force, cogging torque, and eddy current loss waveforms are derived from the analytical method and verified by finite-element analysis. To the best knowledge of the authors, such an analysis has not been carried out previously. [ABSTRACT FROM PUBLISHER]