High Performance Control of AC Drives with Matlab / Simulink Models

2.4 Mathematical Model of Permanent Magnet Synchronous Motor

The mathematical model of PMSM per unit in an arbitrary reference frame rotating with ω_k is [16–20, 22, 23]

(2.97)

(2.98)

(2.99)

(2.100)

where ω_r is the rotor angular speed; θ is the position of the rotor angle; and ψ_f is the permanent magnet flux.

2.4.1 Motor Model in dq Rotating Frame

It is convenient to design the control scheme and represent the motor model in a dq frame rotating with rotor speed. The variables transformation from/to the stationary frame (αβ) to/from the rotating one (dq) is realized according to space vector theory, using the equations presented earlier in this chapter.

The schematic of the PMSM for the dq-axis is represented in Figure 2.14.

Figure 2.14 Schematics of the PMSM in dq frame

In the PMSM, the main magnetic field is produced by permanent magnets. Those magnets are placed on the rotor. The result flux is constant in time, assuming that stator current has no effect (no armature reaction). In ...