Analytical Modeling of Open-Circuit Air-Gap Flux Density in Interior Permanent Magnet Machine

In this article, a general analytical model suitable for the magnetic analysis of the interior permanent magnet (IPM) machine is proposed by coupling the equivalent model and Maxwell’s equation-based 3-D analytical model. In the proposed analytical model, to reduce boundary conditions, the IPM topology is transformed into the surface-mounted permanent magnet (SPM) topology through the equivalent model with universality. Meanwhile, Maxwell’s equation-based 3-D analytical model is established to conduct magnetic analysis and then gives a unified expression of air-gap flux density of the IPM machine. Then, the saliency effect is considered using the saliency coefficient, which is deduced by the magnetomotive force (MMF) and flux-path permeance model. In addition, the slotting effect is considered by conformal mapping. The saliency and slotting effect act on additional functions in the analytical model. Finally, the accuracy of the analytical method is validated by the finite-element method (FEM) in the IPM machine condition.