D- and Q-Axis Inductance Calculation of IPMSM Using Approximate Analytical Model

This paper presents a new lumped parameter method (LPM) to capture nonlinear magnetic behavior of interior permanent magnet synchronous machines (IPMSM). Firstly, the nonlinear B-H curve is modeled as a mathematical expression using Matlab curve fitting toolbox. Using the geometry of the machine, the flux density B versus magnetic field intensity relation is transformed to flux versus MMF relation. By using an approximation for the flux-MMF relation, d- and q-axis equivalent circuits are obtained. Then the nonlinear equations are solved using perturbation theory without any iteration. Finally, perturbation series are converted to rational series using Pade approximant to ensure convergence. As a result, d- and q-axis inductance are obtained as a function of the current.