SM_ElectricalExcited
Electrical excited synchronous machine with damper cage
Library
Modelica/Electrical/Machines/BasicMachines/SynchronousMachines
Description
Model of a three-phase electrical excited synchronous 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 | 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_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_turnsRatio | turnsRatio | Stator current / excitation current | Scalar | |
mo_Lesigma | Lesigma | Scalar | ||
mo_TsOperational | TsOperational | Operational temperature of stator resistance | Scalar | |
mo_TrOperational | TrOperational | Operational temperature of (optional) damper cage | Scalar | |
mo_TeOperational | TeOperational | Operational excitation temperature | Scalar | |
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_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 |
| 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_brushParameters | brushParameters | Brush loss parameter record | FromModelica('Modelica.Electrical.Machines.Losses.BrushParameters') |
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_VsNominal | VsNominal | Nominal stator RMS voltage per phase | Scalar | |
mo_IeOpenCircuit | IeOpenCircuit | Open circuit excitation current @ nominal voltage and frequency | Scalar | |
mo_Re | Re | Excitation resistance at TRef | Scalar | |
mo_TeRef | TeRef | Reference temperature of excitation resistance | Scalar | |
mo_alpha20e | alpha20e | Temperature coefficient of excitation resistance | Scalar | |
mo_sigmae | sigmae | Stray fraction of total excitation inductance | Scalar |
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo__nmodifiers | Number of Modifiers | Specifies the number of modifiers | Number | |
mo__modifiers | Modifiers | Add new modifier | Structure | |
mo__modifiers/varname | Variable name | Cell of strings | 'tauElectrical' | |
mo__modifiers/attribute | Attribute | Cell of strings | 'start' | |
mo__modifiers/value | Value |
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 |
pin_ep | implicit | Positive excitation pin | input | 3 |
pin_en | implicit | Negative excitation pin | output | 2 |
Port 6 | implicit | Support at which the reaction torque is acting | input | mo_useSupport |
Port 7 | implicit | input | mo_useThermalPort |