modelSM_PermanentMagnet
Permanent magnet synchronous machine
Extends from Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).
Information
Model of a three-phase permanent magnet synchronous 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
| Type | Name | Default | Description |
|---|---|---|---|
| Integer | m (from PartialBasicInductionMachine) | 3 | Number of phases |
| Integer | p (from PartialBasicInductionMachine) | Number of pole pairs (Integer) | |
| SI.Frequency | fsNominal (from PartialBasicInductionMachine) | Nominal frequency | |
| Boolean | useZeroSystem (from PartialBasicInductionMachine) | true | = true, if zero current is explicitely computed |
| SI.Inertia | Jr (from PartialBasicMachine) | Rotor's moment of inertia | |
| Boolean | useSupport (from PartialBasicMachine) | false | Enable / disable (=fixed stator) support |
| SI.Inertia | Js (from PartialBasicMachine) | Jr | Stator's moment of inertia |
| Boolean | useThermalPort (from PartialBasicMachine) | false | Enable / disable (=fixed temperatures) thermal port |
| SI.Voltage | VsOpenCircuit | Open circuit RMS voltage per phase @ fsNominal | |
| Operational temperatures | |||
| SI.Temperature | TsOperational (from PartialBasicInductionMachine) | Operational temperature of stator resistance | |
| SI.Temperature | TpmOperational | 293.15 | Operational temperature of permanent magnet |
| SI.Temperature | TrOperational | Operational temperature of (optional) damper cage | |
| Nominal resistances and inductances | |||
| SI.Resistance | Rs (from PartialBasicInductionMachine) | Stator resistance per phase at TRef | |
| SI.Temperature | TsRef (from PartialBasicInductionMachine) | Reference temperature of stator resistance | |
| Machines.Thermal.LinearTemperatureCoefficient20 | alpha20s (from PartialBasicInductionMachine) | Temperature coefficient of stator resistance at 20 degC | |
| SI.Inductance | Lszero (from PartialBasicInductionMachine) | Lssigma | Stator zero sequence inductance |
| SI.Inductance | Lssigma (from PartialBasicInductionMachine) | Stator stray inductance per phase | |
| SI.Inductance | Lmd | Stator main field inductance per phase in d-axis | |
| SI.Inductance | Lmq | Stator main field inductance per phase in q-axis | |
| Losses | |||
| Machines.Losses.FrictionParameters | frictionParameters (from PartialBasicMachine) | Friction loss parameter record | |
| Machines.Losses.CoreParameters | statorCoreParameters (from PartialBasicInductionMachine) | Stator core loss parameter record; all parameters refer to stator side | |
| Machines.Losses.StrayLoadParameters | strayLoadParameters (from PartialBasicInductionMachine) | Stray load loss parameter record | |
| Machines.Losses.PermanentMagnetLossParameters | permanentMagnetLossParameters | Permanent magnet loss parameter record | |
| Nominal resistances and inductances › Damper cage | |||
| Boolean | useDamperCage | Enable / disable damper cage | |
| SI.Inductance | Lrsigmad | Damper stray inductance in d-axis | |
| SI.Inductance | Lrsigmaq | Lrsigmad | Damper stray inductance in q-axis |
| SI.Resistance | Rrd | Damper resistance in d-axis at TRef | |
| SI.Resistance | Rrq | Rrd | Damper resistance in q-axis at TRef |
| SI.Temperature | TrRef | Reference temperature of damper resistances in d- and q-axis | |
| Machines.Thermal.LinearTemperatureCoefficient20 | alpha20r | Temperature coefficient of damper resistances in d- and q-axis | |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Mechanics.Rotational.Interfaces.Flange_a | flange (from PartialBasicMachine) | Shaft | |
| Modelica.Mechanics.Rotational.Interfaces.Flange_a | support (from PartialBasicMachine) | Support at which the reaction torque is acting | |
| Modelica.Electrical.Polyphase.Interfaces.PositivePlug | plug_sp (from PartialBasicInductionMachine) | Positive stator plug | |
| Modelica.Electrical.Polyphase.Interfaces.NegativePlug | plug_sn (from PartialBasicInductionMachine) | Negative stator plug | |
| Machines.Interfaces.InductionMachines.PartialThermalPortInductionMachines | thermalPort (from PartialBasicInductionMachine) | ||
| Modelica.Blocks.Interfaces.RealOutput[2] | ir | Damper cage currents | |
| Modelica.Blocks.Interfaces.RealOutput[2] | idq_dr | Damper space phasor current / rotor fixed frame |