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.

Analytical On-Load Subdomain Field Model of Permanent-Magnet Vernier Machines

In this article, a new subdomain and magnetic circuit hybrid model (SMCHM) is proposed for on-load field prediction in the surface-mounted permanent-magnet machines. Equivalent current sheets are introduced to represent the nonlinearity effect, whose values are obtained by a magnetic circuit (MC) and correlated with boundary conditions in a subdomain model. The number of reluctances in the MC of the proposed model can be selected flexibly according to the nonlinearity effect. Instead of sectorial tooth in the conventional subdomain model, parallel tooth is considered in the proposed model to improve the accuracy. The SMCHM can accurately calculate the flux density distributions and electromagnetic performance considering the heavy nonlinearity effect under the load conditions with fast computation speed. The finite-element analysis is performed to validate the proposed model, which shows an excellent agreement between them. A prototype machine is manufactured to further prove these predictions.

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On-Load Field Prediction in SPM Machines by a Subdomain and Magnetic Circuit Hybrid Model

The most signiﬁcant assumptions in the subdomain technique (i.e., based on the formal resolution of Maxwell’s equations applied in subdomain) is deﬁned by: Theiron parts(i.e.,theteeth and the back-iron are considered to be inﬁnitely permeable, i.e., µiron → +∞, so that the saturation effect is neglected. In this paper, the authors present a new scientiﬁc contribution on improving of this method in two-dimensional (2-D) and in Cartesian coordinates by focusing on the consideration of iron. The subdomains connection is carried out in the two directions (i.e., x-andy-edges). Forexample,the improvement was performed by solving magnetostatic Maxwell’s equations for an air- or iron-cored coil supplied by a direct current. To evaluate the efﬁcacy of the proposed technique, the magnetic ﬂux density distributions have been compared with those obtained by the 2-D ﬁnite-element analysis (FEA). The semi-analytical results are in quite satisfying agreement with those obtained by the 2-D FEA, considering both amplitude and waveform.

New Scientific Contribution on the 2-D Subdomain Technique in Polar Coordinates: Taking into Account of Iron Parts

This paper deals with an adaptable semi-analytical model to calculate the open-circuit and armature reaction field distributions as well as the electromagnetic performances in many structures of permanent-magnet synchronous machines (PMSMs). It is based on the multi-layer models considering the iron permeability with the convolution theorem (i.e., Cauchy’s product theorem) using the harmonic modeling technique (or the Maxwell–Fourier method). The 2-D semi-analytical model can be used for surface-mounted–inset-mounted or spoke-type PMSMs with different permanent-magnet (PM) magnetization patterns, winding structures, internal/external rotors, and slotless or slotted stators without the need to adopt the model equations to a specific PM machine type. For example, this scientific contribution has been applied to three types of PMSM with different topologies, viz.: i) slotted surface-mounted external rotor PMSM; ii) slotted surface–inset internal rotor PMSM; and iii) slotless external rotor spoke-type tangential PMSM. Finally, the results of semi-analytical method are compared with those found by the finite-element method.

Semi-Analytical Magnetic Field Predicting in Many Structures of Permanent-Magnet Synchronous Machines Considering the Iron Permeability

This paper presents a 2-D hybrid analytical modeling method for the analysis of the magnetostatic field distribution with the capability of including nonlinear materials. The model combines Fourier modeling, which is accurate and fast, with meshed magnetic equivalent circuits that have unique permeability in mesh elements and, therefore, can model local saturation. To present the diverse applicability of the proposed method, it is applied to a linear machine with permanent magnet excitation and a rotary machine with current excitation. Magnetic field calculations are compared with finite-element analysis (FEA) with good agreement.

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Hybrid Analytical Modeling of Saturated Linear and Rotary Electrical Machines: Integration of Fourier Modeling and Magnetic Equivalent Circuits

In highly concurrential markets the time to market is reduced, which implies a need of design tools having relatively high accuracy to computation time ratio. It is to address this problematic that the presented modelling approach has been developed. A general framework for the analysis and design of electromagnetic devices is presented. This framework is based on a new hybrid analytical model (HAM) [1]-[4]. The HAM can be applied to different electric machines types (synchronous and asynchronous) and structures (rotating with radial field or axial field, linear flat or tubular structures, or multi-degree-of-freedom structures). It is based on a direct coupling of analytical solution of Maxwell's equations (AM) with reluctance networks (RN). This new technique allows to combine advantages of both methods and should help reduce computation time as compared to finite elements method [3]. This modeling approach is relatively simple and allows the accurate prediction of performances of electromagnetic devices.

A general framework based on a new hybrid analytical model for the analysis and design of permanent magnet machines

The aim of this contribution is to compare two hybrid analytical models for the study of a series hybrid excited synchronous structure performance. Hybrid excited synchronous machines, due to their advantageous characteristics and performance, are good candidates in a large variety of applications. The goal of this study is to address two problems related to the use of analytical models for design and analysis purposes. The first is to find methods helping to overcome numerical problems met when analytical models based on the formal resolution of Maxwell's equations are used for the analysis and design of series double excitation machines. The second goal is to find methods allowing speeding up of the pre-design and analysis of series double excitation machines.

Modeling of a series hybrid excited synchronous structure using two different hybrid analytical models

The aim of this contribution is to assess the capabilities of a quasi-3D hybrid analytical model for the estimation of iron loss in axial flux permanent magnets machines. The hybrid analytical modelling (HAM) approach is based on a direct coupling of analytical solution of Maxwell's equations with reluctance networks (RN). The quasi-3D hybrid analytical modelling approach consists of dividing the axial field machines in a certain number of concentric slices, each of which can be modelled using a 2D hybrid analytical model. The results obtained from the proposed approach are compared to corresponding results obtained from a quasi-3D finite element method (Quasi-3D FEM) and a 3D finite element method (3D FEM).

A. Aden Diriye

Papers

A general framework based on a new hybrid analytical model for the analysis and design of permanent magnet machines

Modeling of a series hybrid excited synchronous structure using two different hybrid analytical models

Iron loss estimation in axial field PM machines using a quasi-3D hybrid analytical model