12
experimentally. [11] also reports experimental results with two different load inertias, but no
torque data is provided.
Although [12] does not include any shaft torque data, the interruption duration is shown to
greatly affect the magnitude of the motor current. Also shown are results demonstrating that
the magnitudes of the current transients generated during a momentary service interruption
are greater than the magnitude of the transients generated during a supply fault disturbance.
2.4 ANALYTICAL STUDIES
Induction machine current and electromagnetic torque transients have been analyzed since
the 1940's [13]. Early efforts focused on starting transients. Later, efforts focused on
induction motor transients due to momentary service interruptions and supply fault
disturbances. A frequently used analytical model for studying the induction motor transients
is the dq0 reference frame model, described in Appendix A.
2.4.1 Solutions Using the dq0 Frame
The first published analysis of induction motor transients due to a supply fault disturbance
and a momentary service interruption was in 1944 [14]. F.J. Maginnis and N.R. Schultz,
analyze the effect of "electrical torques due to sudden change in the applied voltage" and
"reclosing of stator circuit with trapped flux in the rotor". Using a Differential Analyzer, the
analysis is carried out for a three-phase induction motor.
Fig 7 and Fig 8 show the electrical torque and speed characteristics, respectively, due to
suddenly changing the supply voltage [14]. In both figures, before time t=0, the motor is
running at steady state conditions with a constant torque load. In Run 26, the stator supply
voltage is suddenly dropped to zero at time t=0, simulating a short at the motor terminals.
For Run 32, the supply voltage is reduced to half of the steady state value. In both cases, the
supply voltage is restored to the nominal value after nine cycles. Figure 7 shows that
suddenly dropping the supply voltage to zero volts causes a negative torque peak of five
times the rated steady state torque, or -5 pu. A sudden drop to half of the supply voltage only
causes a negative torque peak of -2 pu. Clearly, the magnitude of the torque transients are
worse for the case of shorting the motor terminals. Several more runs are made where the