Model of a three phase permanent magnet synchronous
induction machine.
Resistance and stray inductance of stator is modeled directly in
stator phases, then using space phasor transformation and a
rotor-fixed AirGap model. Resistance and stray inductance
of rotor's squirrel cage is modeled in two axis of the rotor-fixed
coordinate system. Permanent magnet excitation is modelled by a
constant equivalent excitation current feeding the d-axis. The
machine models take the following loss effects into account:
Whether a damper cage is present or not, can be selected with
Boolean parameter useDamperCage (default = true).
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 |
no-load voltage per phase | 112.3 | V RMS @ nominal speed |
nominal current per phase | 100 | A RMS |
nominal torque | 181.4 | Nm |
nominal speed | 1500 | rpm |
nominal mechanical output | 28.5 | kW |
nominal rotor angle | 20.75 | degree |
efficiency | 95.0 | % |
power factor | 0.98 | |
stator resistance | 0.03 | Ohm per phase at reference temperature |
reference temperature TsRef | 20 | °C |
temperature coefficient alpha20s | 0 | 1/K |
stator reactance Xd | 0.4 | Ohm per phase in d-axis |
stator reactance Xq | 0.4 | Ohm per phase in q-axis |
stator stray reactance Xss | 0.1 | Ohm per phase |
damper resistance in d-axis | 0.04 | Ohm at reference temperature |
damper resistance in q-axis | same as d-axis | |
reference temperature TrRef | 20 | °C |
temperature coefficient alpha20r | 0 | 1/K |
damper stray reactance in d-axis XDds | 0.05 | Ohm |
damper stray reactance in q-axis XDqs | same as d-axis | |
stator operational temperature TsOperational | 20 | °C |
damper operational temperature TrOperational | 20 | °C |
These values give the following inductances: | ||
main field inductance in d-axis | (Xd - Xss)/(2*pi*fNominal) | |
main field inductance in q-axis | (Xq - Xss)/(2*pi*fNominal) | |
stator stray inductance per phase | Xss/(2*pi*fNominal) | |
damper stray inductance in d-axis | XDds/(2*pi*fNominal) | |
damper stray inductance in q-axis | XDqs/(2*pi*fNominal) |