SM_PermanentMagnet
Permanent magnet synchronous induction machine
Library
Modelica/Electrical/Machines/BasicMachines/SynchronousInductionMachines
Description
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 | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_m | m | Number of phases | Scalar | |
mo_p | p | Number of pole pairs (Integer) | Scalar | |
mo_fsNominal | fsNominal | Nominal frequency | Scalar | |
mo_TsOperational | TsOperational | Operational temperature of stator resistance | Scalar | |
mo_Jr | Jr | Rotor's moment of inertia | Scalar | |
mo_useSupport | useSupport | Enable / disable (=fixed stator) support | Number | 0 |
mo_Js | Js | Stator's moment of inertia | Scalar | |
mo_useThermalPort | useThermalPort | Enable / disable (=fixed temperatures) thermal port | Number | 0 |
mo_pi | pi | Scalar | ||
mo_TpmOperational | TpmOperational | Operational temperature of permanent magnet | Scalar | |
mo_TrOperational | TrOperational | Operational temperature of (optional) damper cage | Scalar | |
mo_VsOpenCircuit | VsOpenCircuit | Open circuit RMS voltage per phase @ fsNominal | Scalar | |
mo_Ie | Ie | Equivalent excitation current | Scalar |
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_Rs | Rs | Stator resistance per phase at TRef | Scalar | |
mo_TsRef | TsRef | Reference temperature of stator resistance | Scalar | |
mo_alpha20s | alpha20s | Temperature coefficient of stator resistance at 20 degC | Scalar | |
mo_Lszero | Lszero | Stator zero sequence inductance | Scalar | |
mo_Lssigma | Lssigma | Stator stray inductance per phase | Scalar | |
mo_Lmd | Lmd | Stator main field inductance per phase in d-axis | Scalar | |
mo_Lmq | Lmq | Stator main field inductance per phase in q-axis | Scalar | |
mo_useDamperCage | useDamperCage | Enable / disable damper cage | Scalar | true |
mo_Lrsigmad | Lrsigmad | Damper stray inductance in d-axis | Scalar | |
mo_Lrsigmaq | Lrsigmaq | Damper stray inductance in q-axis | Scalar | |
mo_Rrd | Rrd | Damper resistance in d-axis at TRef | Scalar | |
mo_Rrq | Rrq | Damper resistance in q-axis at TRef | Scalar | |
mo_TrRef | TrRef | Reference temperature of damper resistances in d- and q-axis | Scalar | |
mo_alpha20r | alpha20r | Temperature coefficient of damper resistances in d- and q-axis | Scalar |
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_frictionParameters | frictionParameters | Friction loss parameter record | FromModelica('Modelica.Electrical.Machines.Losses.FrictionParameters') | |
mo_statorCoreParameters | statorCoreParameters | Stator core loss parameter record; all parameters refer to stator side | FromModelica('Modelica.Electrical.Machines.Losses.CoreParameters') | |
mo_strayLoadParameters | strayLoadParameters | Stray load loss parameter record | FromModelica('Modelica.Electrical.Machines.Losses.StrayLoadParameters') | |
mo_permanentMagnetLossParameters | permanentMagnetLossParameters | Permanent magnet loss parameter record | FromModelica('Modelica.Electrical.Machines.Losses.PermanentMagnetLossParameters') |
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_phiMechanical | phiMechanical | phiMechanical | Structure | |
mo_phiMechanical/fixed | fixed | Cell of scalars | true | |
mo_phiMechanical/start | start | Cell of scalars | ||
mo_wMechanical | wMechanical | wMechanical | Structure | |
mo_wMechanical/fixed | fixed | Cell of scalars | true | |
mo_wMechanical/start | start | Cell of scalars | ||
mo_tauElectrical | tauElectrical | tauElectrical | Structure | |
mo_tauElectrical/fixed | fixed | Cell of scalars | true | |
mo_tauElectrical/start | start | Cell of scalars | ||
mo_tauShaft | tauShaft | tauShaft | Structure | |
mo_tauShaft/fixed | fixed | Cell of scalars | true | |
mo_tauShaft/start | start | Cell of scalars | ||
mo_vs | vs | vs | Structure | |
mo_vs/fixed | fixed | Cell of vectors | true | |
mo_vs/start | start | Cell of vectors | ||
mo_is | is | is | Structure | |
mo_is/fixed | fixed | Cell of vectors | true | |
mo_is/start | start | Cell of vectors | ||
mo_i_0_s | i_0_s | i_0_s | Structure | |
mo_i_0_s/fixed | fixed | Cell of scalars | true | |
mo_i_0_s/start | start | Cell of scalars | ||
mo_idq_ss | idq_ss | idq_ss | Structure | |
mo_idq_ss/fixed | fixed | Cell of vectors of size 2 | true | |
mo_idq_ss/start | start | Cell of vectors of size 2 | ||
mo_idq_sr | idq_sr | idq_sr | Structure | |
mo_idq_sr/fixed | fixed | Cell of vectors of size 2 | true | |
mo_idq_sr/start | start | Cell of vectors of size 2 | ||
mo_idq_rs | idq_rs | idq_rs | Structure | |
mo_idq_rs/fixed | fixed | Cell of vectors of size 2 | true | |
mo_idq_rs/start | start | Cell of vectors of size 2 | ||
mo_idq_rr | idq_rr | idq_rr | Structure | |
mo_idq_rr/fixed | fixed | Cell of vectors of size 2 | true | |
mo_idq_rr/start | start | Cell of vectors of size 2 | ||
mo_ir | ir | ir | Structure | |
mo_ir/fixed | fixed | Cell of vectors of size 2 | true | |
mo_ir/start | start | Cell of vectors of size 2 | ||
mo_idq_dr | idq_dr | idq_dr | Structure | |
mo_idq_dr/fixed | fixed | Cell of vectors of size 2 | true | |
mo_idq_dr/start | start | Cell of vectors of size 2 |
Ports
| Name | Type | Description | IO Type | Number |
|---|---|---|---|---|
flange | implicit | Shaft | input | 1 |
plug_sp | implicit | Positive stator plug | input | 2 |
plug_sn | implicit | Negative stator plug | output | 1 |
Port 4 | implicit | Support at which the reaction torque is acting | input | mo_useSupport |
Port 5 | implicit | input | mo_useThermalPort |