Proposal of Mathematical Models Taking into Consideration Magnetic Saturation and Cross-Coupling Effects in Permanent Magnet Synchronous Motors

In this paper, we propose novel mathematical models of magnetic fluxes φd and φq for permanent magnet synchronous motors. The models can be used to approximate magnetic characteristics using simple fractional equations by taking magnetic saturation and cross-coupling effects into account. They include only eight constants and some of the constants represent the degree of magnetic saturation and cross-coupling. Because the functions used in our models are low-order functions, they can be transformed into inverse functions. Therefore, a motor model in which saturation characteristics are taken into consideration can be constructed using our models, and it can be used to approximate motor torque accurately. In addition, the introduction of a normalization method facilitates a comparison of motor characteristics that is independent of motor power and size. The normalized constants in our models can function as indices that help to evaluate the saturation characteristics.