tailieunhanh - Chapter 6: Dynamic model of the induction motor

In chapter 6, we define and illustrate space vectors of induction motor variables in the stator reference frame, dq. Dynamic equations of the induction motor are expressed in this frame. The idea of a revolving reference frame, DQ, is introduced to transform the ac components of the vectors in the stator frame into dc signals, and formulas for the straight and inverse abc_dq and dq_D Q transformations are provided. We finish by explaining adaptation of dynamic equations of the motor to a revolving reference frame. | 6 DYNAMIC MODEL OF THE INDUCTION MOTOR In Chapter 6 we define and illustrate space vectors of induction motor variables in the stator reference frame dq. Dynamic equations of the induction motor are expressed in this frame. The idea of a revolving reference frame DQ is introduced to ttansform the ac components of the vectors in the stator frame into de signals and formulas for the sttaight and inverse abc dq and dq DQ transformations are provided. We finish by explaining adaptation of dynamic equations of the motor to a revolving reference frame. SPACE VECTORS OF MOTOR VARIABLES Space vectors of three-phase variables such as the voltage current or flux are very convenient for the analysis and control of induction motors. Voltage space vectors of the voltage source inverter have already been formally introduced in Section . Here the physical background of the concept of space vectors is illustrated. 107 108 CONTROL OF INDUCTION MOTORS Space vectors of stator MMFs in a two-pole motor have been shown in Chapter 2 in Figures through . The vector of total stator MMF is a vectorial sum of phase MMFs J s J s and J s that is _ _ 2 __ 4 ___ ás - as where .i s and denote magnitudes of J s J s and respectively. In the stationary set of stator coordinates dq the vector of stator MMF can be expressed as a complex variable . s J e- 0S as depicted in Figure . Because 2_ 1 V3 ____ and 4_ e then Eq. can be rewritten as FIGURE Space vector of stator MMF. CHAPTER 6 DYNAMIC MODEL OF THE INDUCTION MOTOR 109 which explains the abc dq transformation described by Eq. . For the stator MMFs and Transformation equations and apply to all three-phase variables of the induction motor generally of any three-phase system which add up to zero. Stator MMFs are true physical vectors because their direction and polarity in the real space of the motor can easily be ascertained. Because an MMF is a product of the current in a coil and the number of