This paper deals with the nonlinear analytical harmonic modeling (HM) of three phases, and 6/4 conventional switched reluctance machine (SRM). The proposed model consists in computing magnetic field distribution and electromagnetic performances of an SRM with conventional winding. Because an SRM has inherently nonlinear characteristics, the analytical subdomain model that does not take into account the saturation has a limited accuracy. This is due to the assumption of infinite tooth permeability. The new analytical model (AM) based on the HM technique, which overcomes this limitation, is presented with the consideration of the local magnetic saturation on the stator and rotor teeth. The results obtained with the nonlinear AM have been compared with the linear AM based on the subdomain method (i.e., without the saturation effect) and nonlinear finite-element method solutions.

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.

In this article, we propose a novel nonlinear semianalytical model (AM) for the magnetic field calculation of electric machines. The nonlinear properties and local saturation effect of the iron part are taken into consideration in Cartesian coordinates, which is the main contribution of the proposed model. Thus, high accuracy of electromagnetic field results can be obtained with the low computational time cost. The model is developed based on the harmonic modeling technique by solving Maxwell's equations. The detailed theoretical derivations, which use the complex Fourier series and the Cauchy product, are presented. To verify the proposed model, an axial flux permanent-magnet (PM) machine is selected to be investigated. Both finite-element model and experimental results agree well with that of the proposed model. Moreover, the nonlinear AM has potential application for other types of PM electrical motor in Cartesian coordinates, such as flat PM linear machines.

In this paper, an analytical approach allowing the prediction of iron-core losses in flux-modulated permanent-magnet synchronous machines. According to the Maxwell-Fourier method (viz., the multi-layer model) and Cauchy's product theorem, the magnetic field distribution is determined in different parts of machine by considering the iron permeability on the basis of the solving both Poisson's and Laplace's equations. Next to the dc bias flux density and the minor hysteresis loops, which are taken into account, the Bertotti's model and the flux variation locus are employed to calculate the iron-core losses under load and no-load conditions in post-processing from the magnetic field analytical calculation. Finally, in order to validate the proposed analytical method, the results are verified by the comparison with the finite-element method. The comparisons show good results of the proposed model.

In this article, a nonlinear semianalytical model (SAM) is presented to predict the magnetic field distribution (MFD) and electromagnetic performances (EPs) in the cubic spoke-type permanent magnet (PM) machine. To model the rectangular PMs, the rectangular PM is simplified as a combination of fan-shaped regions with different arc angles. Then, the MFD and EPs of the cubic spoke-type machines can be obtained by the harmonic modeling technique. Particularly, the saturation of the magnetic bridges is considered by the nonlinear iterative algorithm. The proposed nonlinear SAM is studied on a 12-slot/8-pole cubic PM prototype, and the nonlinear finite element model and experiment verify its correctness. The main contribution of this article is to present a general analytical modeling method for cubic spoke-type PM machines and consider the magnetic saturation of magnetic bridges.

In this article, a thermal semi-analytical model (T-SAM) considering water-cooled structure is proposed for the first time, which is based on harmonic modeling (HM) technology and takes into account material inhomogeneities, that is, different thermal conductivities of the motor parts. Then, the calculation process of steady-state heat distribution of the water-cooled permanent magnet (PM) motor is proposed by combining with the electromagnetic finite element method (FEM) and computational fluid dynamic (CFD). The results obtained from thermal FEM serve as a reference for comparison with the outcomes of T-SAM. Remarkably, T-SAM exhibits a high concordance with thermal FEM and a noteworthy reduction in computational time—only a quarter of that required by thermal FEM. Validation of T-SAM is further demonstrated through experimental results obtained from a prototype with a surface-attached cooling structure (SACS). Notably, the T-SAM has potential application for other types of PM electrical motors, such as slotted surface-mounted, slotted surface–inset or slotted spoke-type PM motors.