We have developed novel mathematical models of d-axis and q-axis magnetic fluxes
ϕd and
ϕq for permanent magnet synchronous motors (PMSMs). The models can be used to approximate magnetic characteristics using simple fractional equations with
id and
iq as variables. They include eight constants, and some of them represent the degree of magnetic saturation and cross-coupling. However, the magnetic characteristics are varied with the temperature rise in PMSMs, which are dependent on the load torque and motor speed. In this paper, the characteristics of the eight constants that vary with the motor temperature and the residual flux density
Br are shown. Further, we propose to extend the mathematical models by considering the temperature and
Br variation.
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