IM_SquirrelCage
IM_SlipRing
Models of induction machines
Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).
| Name | Description |
|---|---|
| IM_SquirrelCage
|
Induction machine with squirrel cage rotor |
| IM_SlipRing
|
Induction machine with slipring rotor |
Modelica.Electrical.Machines.BasicMachines.InductionMachines.IM_SquirrelCageInduction machine with squirrel cage rotor
Model of a three-phase 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:
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) |
Extends from Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).
| 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 |
| 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] |
| Custom Parameters | |
| 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] |
| 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 per phase [H] |
| Lm | Stator main field inductance per phase [H] |
| Lrsigma | Rotor stray inductance per phase (equivalent three-phase winding) [H] |
| Rr | Rotor resistance per phase (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 loss parameter record |
| statorCoreParameters | Stator core loss parameter record; all parameters refer to stator side |
| strayLoadParameters | Stray load loss parameter record |
| 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.InductionMachines.IM_SlipRingInduction machine with slipring rotor
Model of a three-phase 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
Extends from Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).
| 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 |
| 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] |
| Custom Parameters | |
| 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] |
| 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 per phase [H] |
| Lm | Stator main field inductance per phase [H] |
| Lrsigma | Rotor stray inductance per phase 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 loss parameter record |
| statorCoreParameters | Stator core loss parameter record; all parameters refer to stator side |
| strayLoadParameters | Stray load loss parameter record |
| rotorCoreParameters | Rotor core loss parameter record; all parameters refer to rotor side |
| 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 |