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

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5Mathematical Description of Vector Control in Induction Machines

In vector control described qualitatively in Chapter 4, the d-axis is aligned with the rotor flux linkage space vector such that the rotor flux linkage in the q-axis is zero. With this as the motivation, we will first develop a model of the induction machine where this condition is always met. Such a model of the machine would be valid regardless if the machine is vector controlled, or if the voltages and currents are applied as under a general-purpose operation (line-fed or in adjustable speed drives described in the previous course).

After developing the motor model, we will study vector control of induction-motor drives, assuming that the exact motor parameters are known—effects of errors in parameter estimates are discussed in the next chapter. We will first use an idealized current-regulated PWM (CR-PWM) inverter to supply motor currents calculated by the controller. As the last step in this chapter, we will use an idealized space vector pulse width-modulated inverter (discussed in detail in Chapter 7) to supply motor voltages that result in the desired currents calculated by the controller.

5-1    Motor Model with the d-Axis Aligned Along the Rotor Flux Linkage c5-math-5001-Axis

As noted in the qualitative description of vector control, we will align the d-axis (common to both the stator and the rotor) to be along the rotor ...

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