A Nonlinear $q$-Axis Inductance Modeling of a 12-Slot 10-Pole IPM Using Approximate Analytical Methods

This article introduces a novel nonlinear model for the q-axis inductance of a Fractional Slot Concentrated Winding Interior Permanent Magnet (FSCW-IPM) machine in order to decrease the time needed to obtain a solution. The complicated geometry and nonlinear magnetic behavior of the core make analytical modeling difficult. So numerical methods are usually used to model machines in which magnetic saturation plays an important role. The winding function of a 12-slot 10-pole FSCW-IPM machine is analyzed and a magnetic equivalent circuit is obtained using the Lumped Parameter Method (LPM) according to the MMF distribution analysis. A mathematical function which represents the magnetic behavior of the core material is appropritely selected to reduce the equations, which show the relationship between the flux and MMF of every lumped parameter into the one equivalent equation. After that, perturbation theory and Pade approximants are used to solve the nonlinear equivalent equation. Finally, a new nonlinear analytical model and solution method is introduced for 12-slots 10-pole FSCW-IPM and the simulation time is decreased to under 0.5 s while it takes about 10 mins with FEA because the proposed method does not need any iteration. The proposed method is compared with FEA and experimental results and the comparison shows the proposed method has sufficient accuracy.