The role of coenergy & the development of a comprehensive analytical model for a PM motor

This paper develops a comprehensive generalized model of Internal Permanent Magnet (IPM) motors to be used for simulation and control models. The equations include an arbitrary number of harmonics due to machine geometry, and the effects of material saturation. We employ dq-transformed equations, which require a knowledge of the d- and q-axis flux linkages, as well as the magnetic torque. These quantities are obtained through derivatives of the coenergy functional, which is the most economical package of the physical information for the machine. We show how to create a generalized parameterized model of the coenergy as a function of d- and q-axis MMF, as well as rotor angle. We obtain a sampled version of the coenergy function through static FEA simulations, and then extract parameter values in the analytical representation of this data through a non-linear fitting exercise. We compare the harmonic contest of the comprehensive model to that of a standard IPM motor model.