Induction Machines Handbook Transients, Control Principles, Design and Testing Third Edition by Ion Boldea

Induction machines (IMs) undergo transients when voltage, current, and/or speed undergo changes. Turning on or off the power grid leads to transients in induction motors. Reconnecting an IM after a short-lived power fault (zero current) is yet another transient. Bus switching for high-power IMs feeding urgent loads also qualifies as large deviation transients. 

Sudden short circuits, at the terminals of large induction motors, lead to very large peak transient currents and torques. On the other hand, more and more induction motors are used in variable speed drives with fast electromagnetic and mechanical transients. So, modelling transients is required for power-grid-fed (constant voltage and frequency) and pulse width modulation (PWM) converter-fed IM drives control.

Modelling the transients of IMs may be carried out through circuit models or through coupled field/circuit models (through finite element modelling or FEM). We will deal first with phasecoordinate abc model with inductance matrix exhibiting terms dependent on rotor position. Subsequently, the space-phasor (d–q) model is derived. Both single- and double-rotor circuit models are dealt with. Saturation is included also in the space-phasor (d–q) model. The abc–d-q model is then derived and applied, as it is adequate for nonsymmetrical voltage supplies and for PWM converter-fed IMs.

Reduced-order d–q models are used to simplify the study of transients for low- and high-power motors, respectively. Modelling transients with the computation of cage bar and end-ring currents is required when cage and/or end-ring faults occur. Finally, the FEM-coupled field circuit approach is dealt with.

Autonomous generator transients are left out as they are treated in Chapter 10 dedicated to induction generators (IGs) (in Volume 2).

The IM may be viewed as a system of electric and magnetic circuits which are coupled magnetically

and/or electrically. An assembly of resistances, self-inductances and mutual inductances is thus obtained. Let us first deal with the inductance matrix. A symmetrical (healthy) cage may be replaced by a wound three-phase rotor [2]. Consequently, the IM is represented by six circuits (phases) (Figure 1.1). Each of them is characterized by a self-inductance and five mutual inductances.