An improved conformal mapping method for magnetic field analysis in surface mounted permanent magnet motors

Abstract

Purpose The purpose of this paper is to present an improved conformal mapping (ICM) method that simultaneously considers the influence of relative recoil permeability of PMs, the armature reaction, the stator slotting, and the magnetic saturation on determination of the PM operating point in its different parts. Design/methodology/approach The ICM method is a time-effective method that considers the magnetic saturation by suitable increments in air-gap length under each tooth and also the width of slot openings. In this paper, the analytical and numerical conformal mappings such as the Schwarz-Christoffel (SC) mapping are used for magnetic field analysis due to the permanent magnets and the armature reaction in one slotted air gap. The field solution in the slotted air gap is obtained through the modulation of field solution in one slotless air-gap using the complex air-gap permeance. Findings The ICM method can consider the magnetic saturation in different electric loadings, and also the variation of PM operating points in its different parts. Practical implications The ICM method is applied to one surface mounted permanent magnet (SMPM) motor and is verified by comparing with the corresponding results obtained through finite element method (FEM), and frozen permeability finite element method (FP-FEM). Originality/value This paper presents an ICM method with a new technique for saturation effect modeling, which can be used to separate and calculate the on-load components of air-gap field and torque.

Analytical modelling of one cage rotor induction motor for electric submersible pumps

“…For modelling the CRIM by the CM method, each half-coil of stator and each rotor bar should be replaced with an equivalent line current so that the current magnitude of equivalent line current is equal to the total MMF of respective half-coil or rotor bar [18,19]. Figure 3 shows the slotless air-gap of analysed CRIM including equivalent line currents in s-plane, which considers the winding distribution.…”

“…As shown in Figure 3, the equivalent line currents are also mapped into the Ψ-plane. The CMs used for mapping are introduced as shown in ( 1)-(3) [15,18].…”

Hybrid winding function method for inductance analysis of a line start synchronous reluctance machine

“…However, the classical winding function theory analysis gives only accurate results for machines with small smoothed air gap topologies. The rotor permeance equivalent function using the Fourier series often does not provide an accurate model for slotted structures [20], [21].…”

Induction machine model with space harmonics for fault diagnosis based on the convolution theorem

“…One approach for building such 2D analytical models relies on finding the analytical solution of the magnetic field in the air-gap of the eccentric machine [71]. In [37] this solution is obtained considering only the fundamental component of the stator airgap flux density, and in in [72][73][74][75][76] a conformal transformation is applied to the expressions of the magnetic field of a healthy machine. Nevertheless, the conformal transformations presented in these works result in infinite series expansions for the air-gap magnetic field, which converge slowly.…”