8.2 Dynamic Model of an Induction Machine
A three-phase current system can be represented by a three-axis coordinate system, as shown in Figure 8.1a. Unfortunately, the three axes are linearly dependent, a fact that makes the mathematical description of a three-phase machine difficult. However, the linear dependence means that only two variables are necessary to describe three physical quantities. Hence, a complex, linearly independent coordinate system can be selected. Figure 8.1b shows the equivalent representation.
Figure 8.1 Coordinate transformation. (a) Currents expressed in a three-phase reference frame (a, b, c). (b) Currents expressed in a complex reference frame αβ
A three-phase stator currents system, with angular frequency ω0, can be defined in a fixed three-phase coordinate frame:
8.1 
8.2 
8.3 
For the stator currents, the transformation from a three- to a two-phase system is described by
8.4 
8.5
8.6
The same coordinate transformation shown above is used for the electromagnetic ...
Get Predictive Control of Power Converters and Electrical Drives now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
