Model of a three phase asynchronous induction machine
with slipring rotor.
Resistance and stray inductance of stator and rotor are modeled
directly in stator respectively rotor phases, then using space
phasor transformation and a stator-fixed AirGap model. The
machine models take the following loss effects into account:
Default values for machine's parameters (a realistic
example) are:
number of pole pairs p | 2 | |
stator's moment of inertia | 0.29 | kg.m2 |
rotor's moment of inertia | 0.29 | kg.m2 |
nominal frequency fNominal | 50 | Hz |
nominal voltage per phase | 100 | V RMS |
nominal current per phase | 100 | A RMS |
nominal torque | 161.4 | Nm |
nominal speed | 1440.45 | rpm |
nominal mechanical output | 24.346 | kW |
efficiency | 92.7 | % |
power factor | 0.875 | |
stator resistance | 0.03 | Ohm per phase at reference temperature |
reference temperature TsRef | 20 | °C |
temperature coefficient alpha20s | 0 | 1/K |
rotor resistance | 0.04 | Ohm per phase at reference temperature |
reference temperature TrRef | 20 | °C |
temperature coefficient alpha20r | 0 | 1/K |
stator reactance Xs | 3 | Ohm per phase |
rotor reactance Xr | 3 | Ohm per phase |
total stray coefficient sigma | 0.0667 | |
turnsRatio | 1 | effective ratio of stator and rotor current |
stator operational temperature TsOperational | 20 | °C |
rotor operational temperature TrOperational | 20 | °C |
These values give the following inductances: | ||
stator stray inductance per phase | Xs * (1 - sqrt(1-sigma))/(2*pi*fNominal) | |
rotor stray inductance | Xr * (1 - sqrt(1-sigma))/(2*pi*fNominal) | |
main field inductance per phase | sqrt(Xs*Xr * (1-sigma))/(2*pi*f) |
Parameter turnsRatio could be obtained from the following
relationship at standstill with open rotor circuit at nominal
voltage and nominal frequency,
using the locked-rotor voltage VR, no-load stator current I0 and
powerfactor PF0:
turnsRatio * VR = Vs -
(Rs + j Xs,sigma) I0