Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines

Information

• SM_PermanentMagnet: synchronous induction machine with permanent magnet excitation, with damper cage
• SM_ElectricalExcited: synchronous induction machine with electrical excitation and damper cage
• SM_ReluctanceRotor: induction machine with reluctance rotor and damper cage
  i.e., a squirrel cage rotor with magnetic poles due to different airgap width

• We keep the same reference system as for motors, i.e.:
  Positive RotorDisplacementAngle means acting as motor,
  with positive electric power consumption and positive mechanical power output.
• ElectricalAngle = p * MechanicalAngle
• real axis = d-axis
  imaginary= q-axis
• Voltage induced by the magnet wheel (d-axis) is located in the q-axis.

Package Content

Name	Description
SM_PermanentMagnet	Permanent magnet synchronous induction machine
SM_ElectricalExcited	Electrical excited synchronous induction machine with damper cage
SM_ReluctanceRotor	Synchronous induction machine with reluctance rotor and damper cage

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_PermanentMagnet

Information

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:

• heat losses in the temperature dependent stator winding resistances
• optional, when enabled: heat losses in the temperature dependent damper cage resistances
• friction losses
• core losses (only eddy current losses, no hysteresis losses)
• stray load losses
• permanent magnet losses

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)

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]
VsOpenCircuit	Open circuit RMS voltage per phase @ fsNominal [V]
Operational temperatures
TsOperational	Operational temperature of stator resistance [K]
TrOperational	Operational temperature of (optional) damper cage [K]
Initialization
phiMechanical	Mechanical angle of rotor against stator [rad]
wMechanical	Mechanical angular velocity of rotor against stator [rad/s]
ir[2]	Damper cage currents [A]
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]
Lmd	Stator main field inductance in d-axis [H]
Lmq	Stator main field inductance in q-axis [H]
DamperCage
useDamperCage	Enable / disable damper cage
Lrsigmad	Damper stray inductance in d-axis [H]
Lrsigmaq	Damper stray inductance in q-axis [H]
Rrd	Damper resistance in d-axis at TRef [Ohm]
Rrq	Damper resistance in q-axis at TRef [Ohm]
TrRef	Reference temperature of damper resistances in d- and q-axis [K]
alpha20r	Temperature coefficient of damper resistances in d- and q-axis [1/K]
Losses
frictionParameters	Friction losses
statorCoreParameters	Stator core losses; all parameters refer to stator side
strayLoadParameters	Stray load losses
permanentMagnetLossParameters	Permanent magnet loss 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
idq_dr[2]	Damper space phasor current / rotor fixed frame [A]
Initialization
ir[2]	Damper cage currents [A]

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ElectricalExcited

Information

Model of a three phase electrical excited synchronous induction machine with damper cage.
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. Electrical excitation is modelled by converting excitation current and voltage to d-axis space phasors. 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 excitation winding resistance
• optional, when enabled: heat losses in the temperature dependent damper cage resistances
• brush losses in the excitation circuit
• friction losses
• core losses (only eddy current losses, no hysteresis losses)
• stray load losses

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 excitation current @ nominal voltage and frequency	10	A DC
warm excitation resistance	2.5	Ohm
nominal current per phase	100	A RMS
nominal apparent power	-30000	VA
power factor	-1.0	ind./cap.
nominal excitation current	19	A
efficiency w/o excitation	97.1	%
nominal torque	-196.7	Nm
nominal speed	1500	rpm
nominal rotor angle	-57.23	degree
stator resistance	0.03	Ohm per phase at reference temperature
reference temperature TsRef	20	°C
temperature coefficient alpha20s	0	1/K
stator reactance Xd	1.6	Ohm per phase in d-axis
giving Kc	0.625
stator reactance Xq	1.6	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
excitation resistance	2.5	Ohm at reference temperature
reference temperature TeRef	20	°C
temperature coefficient alpha20e	0	1/K
excitation stray inductance	2.5	% of total excitation inductance
stator operational temperature TsOperational	20	°C
damper operational temperature TrOperational	20	°C
excitation operational temperature TeOperational	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)

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 (optional) damper cage [K]
TeOperational	Operational excitation temperature [K]
Initialization
phiMechanical	Mechanical angle of rotor against stator [rad]
wMechanical	Mechanical angular velocity of rotor against stator [rad/s]
ir[2]	Damper cage currents [A]
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]
Lmd	Stator main field inductance in d-axis [H]
Lmq	Stator main field inductance in q-axis [H]
DamperCage
useDamperCage	Enable / disable damper cage
Lrsigmad	Damper stray inductance in d-axis [H]
Lrsigmaq	Damper stray inductance in q-axis [H]
Rrd	Damper resistance in d-axis at TRef [Ohm]
Rrq	Damper resistance in q-axis at TRef [Ohm]
TrRef	Reference temperature of damper resistances in d- and q-axis [K]
alpha20r	Temperature coefficient of damper resistances in d- and q-axis [1/K]
Losses
frictionParameters	Friction losses
statorCoreParameters	Stator core losses; all parameters refer to stator side
strayLoadParameters	Stray load losses
brushParameters	Brush losses
Excitation
VsNominal	Nominal stator RMS voltage per phase [V]
IeOpenCircuit	Open circuit excitation current @ nominal voltage and frequency [A]
Re	Excitation resistance at TRef [Ohm]
TeRef	Reference temperature of excitation resistance [K]
alpha20e	Temperature coefficient of excitation resistance [1/K]
sigmae	Stray fraction of total excitation inductance

Connectors

Name	Description
flange	Shaft
support	Support at which the reaction torque is acting
plug_sp	Positive stator plug
plug_sn	Negative stator plug
idq_dr[2]	Damper space phasor current / rotor fixed frame [A]
pin_ep	Positive excitation pin
pin_en	Negative excitation pin
Initialization
ir[2]	Damper cage currents [A]

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ReluctanceRotor

Information

Model of a three phase synchronous induction machine with reluctance rotor and damper 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 rotor-fixed AirGap model. The machine models take the following loss effects into account:

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

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
nominal current per phase	50	A RMS
nominal torque	46	Nm
nominal speed	1500	rpm
nominal mechanical output	7.23	kW
efficiency	96.98	%
power factor	0.497
stator resistance	0.03	Ohm per phase at reference temperature
reference temperature TsRef	20	°C
temperature coefficient alpha20s	0	1/K
rotor resistance in d-axis	0.04	Ohm at reference temperature
rotor resistance in q-axis	same as d-axis
reference temperature TrRef	20	°C
temperature coefficient alpha20r	0	1/K
stator reactance Xsd in d-axis	3	Ohm per phase
stator reactance Xsq in q-axis	1	Ohm
stator stray reactance Xss	0.1	Ohm per phase
rotor stray reactance in d-axis Xrds	0.05	Ohm per phase
rotor stray reactance in q-axis Xrqs	same as d-axis
stator operational temperature TsOperational	20	°C
damper operational temperature TrOperational	20	°C
These values give the following inductances:
stator stray inductance per phase	Xss/(2*pi*fNominal)
rotor stray inductance in d-axis	Xrds/(2*pi*fNominal)
rotor stray inductance in q-axis	Xrqs/(2*pi*fNominal)
main field inductance per phase in d-axis	(Xsd-Xss)/(2*pi*fNominal)
main field inductance per phase in q-axis	(Xsq-Xss)/(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 (optional) damper cage [K]
Initialization
phiMechanical	Mechanical angle of rotor against stator [rad]
wMechanical	Mechanical angular velocity of rotor against stator [rad/s]
ir[2]	Damper cage currents [A]
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]
Lmd	Stator main field inductance in d-axis [H]
Lmq	Stator main field inductance in q-axis [H]
DamperCage
useDamperCage	Enable / disable damper cage
Lrsigmad	Damper stray inductance in d-axis [H]
Lrsigmaq	Damper stray inductance in q-axis [H]
Rrd	Damper resistance in d-axis at TRef [Ohm]
Rrq	Damper resistance in q-axis at TRef [Ohm]
TrRef	Reference temperature of damper resistances in d- and q-axis [K]
alpha20r	Temperature coefficient of damper resistances in d- and q-axis [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
idq_dr[2]	Damper space phasor current / rotor fixed frame [A]
Initialization
ir[2]	Damper cage currents [A]