1. Motors in Power System Dynamics Studies John Undrill NATF - Dallas - June 2015

2. Rapid changes of amplitude or phase of supply voltage produce significant transient variations of electrical torque Phenomenon is common to all electrical machines: 3 phase synchronous 3 phase induction 1 phase / capacitor induction Transient torques are characterized by: unidirectional components components that oscillate at frequency of supply voltage Amplitude of torque transients is strongly dependent on subtransient impedance of the machine and can exceed five times rated torque Physics of motor behavior

3. Sudden phase retard Transient torque has braking direction Sudden phase advance Transient torque has motor direction Motor speed Electrical torque Transients induced by sudden change of phase of supply voltage with no change in amplitude Point-On-Wave simulation of single phase air conditioner motor

4. Voltage dips instantaneously to 0.4 pu At phase = 0 deg Peak braking torque = 140 n-m Voltage dips instantaneously to 0.4 pu At phase = 90 deg Peak braking torque = 90 n-m Voltage ramps to 0.0 pu in 3 cycles At phase = 0 deg Peak braking torque = 30 n-m Transients induced by sudden change of amplitude of supply voltage with no change in phase Point-On-Wave simulation of single phase air conditioner motor speed torque

5. Present understanding of motor behavior in power system transients: Three phase motors: - stalling is an issue - is well understood on an individual motor basis - reaccelerating after voltage depressions is a long standing concern of the industrial power sector - most three phase motors are protected by relays and are tripped by overcurrent or undervoltage elements if they fail to reaccelerate Air conditioner motors: - single phase - permanently connected capacitor - inertia constant is 50 milliseconds or less - deceleration when voltage dips is very rapid - can stall within normal fault clearing time - starting/restarting torque is seldom enough to overcome the breakout torque of the compressor load - motors are not protected by relays - when stalled will draw ~5 time rated current at very low power factor until tripped by thermal overcurrent switches

6. Factors that affect stalling of single phase motors: depth of voltage dip stalling threshold is in region of 60% when dip is initiated at unfavorable point on the voltage wave phase of voltage when dip is initiated stalling is most likely when dip is initiated near voltage zero crossing is least likely when dip is initiated near voltage maximum rate of change of voltage likelihood of stalling is reduced if voltage change occurs over 50 msec or longer

7. Will air conditioners stall or reaccelerate In the foregoing examples: Load is about 5.5 KW Load torque is a triangular wave between 9 n-m and 29 n-m - average = 14.5n-m Peaks of electrical torque transients are as high as 150 n-m - in either direction If in braking direction, a large electrical torque transient can stop the motor very quickly Thus - stalling is an electromagnetic matter The time scale of air conditioner stalling is that of the point-on-wave timing of electrical events

8. Air conditioner motor modeling in fundamental frequency power system simulations Fundamental frequency power system simulations (PSLF-PSS/E-PW) cannot represent the point-on-wave behavior of motors Modeling of motor behavior is necessarily empirical Stalling is not decided by modeling motor dynamics; it is declared on basis of a threshold voltage P,Q are related to voltage by running curves until stall is declared P,Q follow locked-rotor admittance characteristic after stall and until the motor is tripped This modeling is imbedded in the cmpldw composite load model Test data real power versus voltage Simulation real/reactive power versus voltage