Modelica.Electrical.Machines.BasicMachines.AsynchronousInductionMachines

Information

• AIM_SquirrelCage: asynchronous induction machine with squirrel cage
• AIM_SlipRing: asynchronous induction machine with wound rotor

Package Content

Name	Description
AIM_SquirrelCage	Asynchronous induction machine with squirrel cage rotor
AIM_SlipRing	Asynchronous induction machine with slipring rotor

Modelica.Electrical.Machines.BasicMachines.AsynchronousInductionMachines.AIM_SquirrelCage

Information

Model of a three phase asynchronous induction machine with squirrel cage.
Resistance and stray inductance of stator is modeled directly in stator phases, then using space phasor transformation. Resistance and stray inductance of rotor's squirrel cage is modeled in two axis of the rotor-fixed coordinate system. Both together connected via a stator-fixed AirGap model. The machine models take the following loss effects into account:

• heat losses in the temperature dependent stator winding resistances
• heat losses in the temperature dependent cage resistances
• friction losses
• core losses (only eddy current losses, no hysteresis losses)
• stray load losses

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 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
total stray coefficient sigma	0.0667
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*fNominal)

Parameters

Name	Description
p	Number of pole pairs (Integer)
fsNominal	Nominal frequency [Hz]
Jr	Rotor's moment of inertia [kg.m2]
useSupport	Enable / disable (=fixed stator) support
Js	Stator's moment of inertia [kg.m2]
useThermalPort	Enable / disable (=fixed temperatures) thermal port
idq_ss[2]	Stator space phasor current / stator fixed frame [A]
idq_sr[2]	Stator space phasor current / rotor fixed frame [A]
idq_rs[2]	Rotor space phasor current / stator fixed frame [A]
idq_rr[2]	Rotor space phasor current / rotor fixed frame [A]
Operational temperatures
TsOperational	Operational temperature of stator resistance [K]
TrOperational	Operational temperature of rotor resistance [K]
Initialization
phiMechanical	Mechanical angle of rotor against stator [rad]
wMechanical	Mechanical angular velocity of rotor against stator [rad/s]
Nominal resistances and inductances
Rs	Stator resistance per phase at TRef [Ohm]
TsRef	Reference temperature of stator resistance [K]
alpha20s	Temperature coefficient of stator resistance at 20 degC [1/K]
Lszero	Stator zero sequence inductance [H]
Lssigma	Stator stray inductance [H]
Lm	Stator main field inductance [H]
Lrsigma	Rotor stray inductance (equivalent three phase winding) [H]
Rr	Rotor resistance (equivalent three phase winding) at TRef [Ohm]
TrRef	Reference temperature of rotor resistance [K]
alpha20r	Temperature coefficient of rotor resistance at 20 degC [1/K]
Losses
frictionParameters	Friction losses
statorCoreParameters	Stator core losses; all parameters refer to stator side
strayLoadParameters	Stray load losses

Connectors

Name	Description
flange	Shaft
support	Support at which the reaction torque is acting
plug_sp	Positive stator plug
plug_sn	Negative stator plug

Modelica.Electrical.Machines.BasicMachines.AsynchronousInductionMachines.AIM_SlipRing

Information

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:

• heat losses in the temperature dependent stator winding resistances
• heat losses in the temperature dependent rotor winding resistances
• friction losses
• core losses (only eddy current losses, no hysteresis losses)
• stray load losses

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 * V_R = V_s - (R_s + j X_s,sigma) I₀

Parameters

Name	Description
p	Number of pole pairs (Integer)
fsNominal	Nominal frequency [Hz]
Jr	Rotor's moment of inertia [kg.m2]
useSupport	Enable / disable (=fixed stator) support
Js	Stator's moment of inertia [kg.m2]
useThermalPort	Enable / disable (=fixed temperatures) thermal port
idq_ss[2]	Stator space phasor current / stator fixed frame [A]
idq_sr[2]	Stator space phasor current / rotor fixed frame [A]
idq_rs[2]	Rotor space phasor current / stator fixed frame [A]
idq_rr[2]	Rotor space phasor current / rotor fixed frame [A]
useTurnsRatio	Use turnsRatio or calculate from locked-rotor voltage?
turnsRatio	Effective number of stator turns / effective number of rotor turns
VsNominal	Nominal stator voltage per phase [V]
VrLockedRotor	Locked-rotor voltage per phase [V]
Operational temperatures
TsOperational	Operational temperature of stator resistance [K]
TrOperational	Operational temperature of rotor resistance [K]
Initialization
phiMechanical	Mechanical angle of rotor against stator [rad]
wMechanical	Mechanical angular velocity of rotor against stator [rad/s]
Nominal resistances and inductances
Rs	Stator resistance per phase at TRef [Ohm]
TsRef	Reference temperature of stator resistance [K]
alpha20s	Temperature coefficient of stator resistance at 20 degC [1/K]
Lszero	Stator zero sequence inductance [H]
Lssigma	Stator stray inductance [H]
Lm	Stator main field inductance [H]
Lrsigma	Rotor stray inductance w.r.t. rotor side [H]
Lrzero	Rotor zero sequence inductance w.r.t. rotor side [H]
Rr	Rotor resistance per phase at TRef w.r.t. rotor side [Ohm]
TrRef	Reference temperature of rotor resistance [K]
alpha20r	Temperature coefficient of rotor resistance at 20 degC [1/K]
Losses
frictionParameters	Friction losses
statorCoreParameters	Stator core losses; all parameters refer to stator side
strayLoadParameters	Stray load losses
rotorCoreParameters	Rotor core losses; all parameters refer to rotor side

Connectors

Name	Description
flange	Shaft
support	Support at which the reaction torque is acting
plug_sp	Positive stator plug
plug_sn	Negative stator plug
plug_rp	Positive rotor plug
plug_rn	Negative rotor plug