High Performance Control of AC Drives with Matlab / Simulink Models

2.3 Squirrel Cage Induction Motor

2.3.1 Space Vector Representation

A three-phase AC machine may be described using the space vector method [1–9], as was shown by Kovacs and Racz [6]. For this reason, the AC motor variables for a symmetrical machine fulfill the condition:

(2.28)

The summation of these variables gives the space vector:

(2.29)

where and

Figure 2.8 shows the stator current complex space vector.

Figure 2.8 Space vector representation for three-phase variables

The space vector K may represent the motor variables (e.g. current, voltage, and flux). The vector control principle on AC machines takes advantages of transforming the variables from the physical three-phase ABC system to a stationary frame αβ, or rotating frame dq [3, 6].

Let us analyze, as an example, the stator sinusoidal currents transformation. The first transformation can be done to a stationary frame αβ (Clark ...