Advanced Electric Drives: Analysis, Control, and Modeling Using MATLAB/Simulink

3    Dynamic Analysis of Induction Machines in Terms of dq Windings

3-1    Introduction

In this chapter, we will develop equations to analyze induction machine operation under dynamic conditions. We will make use of space vectors as intermediary in transforming a-b-c phase winding quantities into equivalent dq-winding quantities that we will use for dynamic (nonsteady state) analysis. We will see in later chapters the benefits of d- and q-axis analysis in controlling ac machines.

3-2    dq Winding Representation

We studied in the previous chapter that the stator and the rotor flux linkages and depend on the rotor angle θ_m because the mutual inductances between the stator and the rotor windings are position dependent. The main reason for the d- and q-axis analysis in machines like the induction machines is to control them properly, for example, using vector control principles. In most textbooks, this analysis is discussed as a mathematical transformation called the Park's transformation. In this chapter, we will take a physical approach to this transformation, which is much easier to visualize and arrive at identical results.

3-2-1    Stator dq Winding Representation

In Fig. 3-1a at time t, phase currents i_a (t), i_b (t), and i_c (t) are represented by a stator current space vector