9.2 Machine Equations

A PMSM with three-phase stator windings and a sinusoidal flux distribution is considered in this chapter. The machine is fed by a three-phase inverter as shown in Figure 9.1.

Figure 9.1 PMSM fed by a three-phase inverter

9.1

By defining the following space vector definitions for the stator voltage, stator current, and stator flux, respectively,

9.2 9.2

9.3 9.3

9.4 9.4

the stator dynamics can be described as

9.5 9.5

where Rs is the stator resistance.

The stator flux linkage ψs is generated by the rotor magnets and the self-linked flux produced by the stator currents. This relation is described by

9.6 9.6

where Ls is the stator self-inductance, ψm is the flux magnitude due to the rotor magnets, and θr is the rotor position.

Inserting (9.6) into (9.5) we obtain

9.7 9.7

where ωr = dθr/dt is the ...

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