Electromagnetic Equivalent Circle Modelling of Interior Permanent Magnet Synchronous Machine Using Modelica

This paper proposes an electromagnetic equivalent circle (EMEC) model to evaluate and analyze the performance of interior permanent magnet synchronous machine (IPMSM). This model is implemented with Modelica language and it provides magnetic field simulation which is not included in PMSM model from Modelica standard library (MSL). Moreover, this model simulates the variable working states of permanent magnet (PM) instead of a constant flux source. The electric part of EMEC model is similar to that in MSL, except that the calculation of induced electromotive force (EMF) is divided into motional EMF and back EMF. As for magnetic part, this physical model considers the magnetic fields distribute evenly in several lines and takes magnetomotive force (MMF) as potential variable and the magnetic flux as flow variable. This paper doesn’t adopt lumped inductance parameters, and the permeances of icon core, air gap and magnets are based solely on geometrical data and material parameters. The model takes into account local saturation of individual stator teeth by considering the permeance of iron core is nonlinear. A dq framework is utilized to determine the directions of electric and magnetic space vectors. The magnetic flux produced by magnets is oriented in d-axis and its density is constant over one pole pitch. And the working points of magnets follow its demagnetization curve. The MMF produced by a balanced three-phase sinusoidal winding current system is supposed to be circumferential traveling wave with sinusoidal waveform, and only the daxis component of its resulting magnetic flux crosses magnets. Finally, EMEC model is validated through comparisons with a finite element model confronting the selected analytical waveforms, as well as the electromagnetic torques, and it is used in a system model to help developing motor control algorithms.