Mathematical model of four pole PMSM motor

The authors of [1] have presented a mathematical model of four pole permanent magnet synchronous motor (PMSM). They made some usual assumptions like neglecting the saturation effect, sinusoidal emf and negligible losses.The stator d-q reference equations written in a rotor reference frame is given as

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where vds and vqs are the staotr d and q axis voltages, id and iq are the stator d and q axis currents, Ld and Lq are the d and q axis inductances and R and ws are the stator resistance and inverter frequency respectively. Also lambda is a flux linkage due to the rotor magnets linking the stator. The inveter frequency related to the rotor speed wr and the electrical torque are expressed as follows

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Where P is the no. of pole pairs. And this is a non linear model as it contains product terms such as speed with id and iq. here wr, id and iq are state variables.


Reference

[1] Oh, I.H., Jung, Y.S. and Youn, M.J., 1999. A source voltage-clamped resonant link inverter for a PMSM using a predictive current control technique. Power Electronics, IEEE Transactions on, 14(6), pp.1122-1132.