Modelica.Electrical.Machines.Examples.InductionMachines

Test examples of induction machines

Information

This package contains test examples of induction machines.

Extends from Modelica.Icons.ExamplesPackage (Icon for packages containing runnable examples).

Package Content

Name	Description
IMC_DOL	Test example: InductionMachineSquirrelCage direct-on-line
IMC_YD	Test example: InductionMachineSquirrelCage Y-D
IMC_YDarc	Test example: InductionMachineSquirrelCage Y-D
IMC_Transformer	Test example: InductionMachineSquirrelCage transformer starting
IMS_Start	Test example: InductionMachineSlipRing
IMC_Inverter	Test example: InductionMachineSquirrelCage with inverter
IMC_Conveyor	Test example: InductionMachineSquirrelCage with inverter driving a conveyor
IMC_InverterDrive	Test example: InductionMachineSquirrelCage inverter drive
IMC_Steinmetz	InductionMachineSquirrelCage Steinmetz-connection
IMC_withLosses	Test example: InductionMachineSquirrelCage with losses
IMC_Initialize	Test example: Steady-State Initialization of InductionMachineSquirrelCage
IMC_DCBraking	Induction machine with DC current braking

Modelica.Electrical.Machines.Examples.InductionMachines.IMC_DOL

Test example: InductionMachineSquirrelCage direct-on-line

Information

At start time tStart three-phase voltage is supplied to the induction machine with squirrel cage; the machine starts from standstill, accelerating inertias against load torque quadratic dependent on speed, finally reaching nominal speed.

Simulate for 1.5 seconds and plot (versus time):

currentQuasiRMSSensor.I: stator current RMS
aimc.wMechanical: motor's speed
aimc.tauElectrical: motor's torque

Default machine parameters are used.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
VNominal	Nominal RMS voltage per phase [V]
fNominal	Nominal frequency [Hz]
tStart1	Start time [s]
TLoad	Nominal load torque [N.m]
wLoad	Nominal load speed [rad/s]
JLoad	Load's moment of inertia [kg.m2]
aimcData	Induction machine data

Modelica.Electrical.Machines.Examples.InductionMachines.IMC_YD

Test example: InductionMachineSquirrelCage Y-D

Information

At start time tStart three-phase voltage is supplied to the induction machine with squirrel cage, first star-connected, then delta-connected; the machine starts from standstill, accelerating inertias against load torque quadratic dependent on speed, finally reaching nominal speed.

Simulate for 2.5 seconds and plot (versus time):

currentQuasiRMSSensor.I: stator current RMS
aimc.wMechanical: motor's speed
aimc.tauElectrical: motor's torque

Default machine parameters are used.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
VNominal	Nominal RMS voltage per phase [V]
fNominal	Nominal frequency [Hz]
tStart1	Start time [s]
tStart2	Start time from Y to D [s]
TLoad	Nominal load torque [N.m]
wLoad	Nominal load speed [rad/s]
JLoad	Load's moment of inertia [kg.m2]
aimcData	Induction machine data

Modelica.Electrical.Machines.Examples.InductionMachines.IMC_YDarc

Test example: InductionMachineSquirrelCage Y-D

Information

Same example as IMC_YD, but with a time delay between Y off and D on.

Note that a switchYDwithArc is used to avoid unphysical voltage peaks when opening Y connection.

Default machine parameters are used.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
VNominal	Nominal RMS voltage per phase [V]
fNominal	Nominal frequency [Hz]
RLine	Line resistance [Ohm]
LLine	Line inductance [H]
tStart1	Start time [s]
tStart2	Start time from Y to D [s]
TLoad	Nominal load torque [N.m]
wLoad	Nominal load speed [rad/s]
JLoad	Load's moment of inertia [kg.m2]
aimcData	Induction machine data

Modelica.Electrical.Machines.Examples.InductionMachines.IMC_Transformer

Test example: InductionMachineSquirrelCage transformer starting

Information

At start time tStart1 three-phase voltage is supplied to the induction machine with squirrel cage via the transformer; the machine starts from standstill, accelerating inertias against load torque quadratic dependent on speed; at start time tStart2 the machine is fed directly from the voltage source, finally reaching nominal speed.

Simulate for 2.5 seconds and plot (versus time):

currentQuasiRMSSensor.I: stator current RMS
aimc.wMechanical: motor's speed
aimc.tauElectrical: motor's torque

Default machine parameters are used.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
VNominal	Nominal RMS voltage per phase [V]
fNominal	Nominal frequency [Hz]
tStart1	Start time [s]
tStart2	Start time of bypass transformer [s]
TLoad	Nominal load torque [N.m]
wLoad	Nominal load speed [rad/s]
JLoad	Load's moment of inertia [kg.m2]
transformerData	Transformer data
aimcData	Induction machine data

Modelica.Electrical.Machines.Examples.InductionMachines.IMS_Start

Test example: InductionMachineSlipRing

Information

At start time tStart1 three-phase voltage is supplied to the induction machine with sliprings; the machine starts from standstill, accelerating inertias against load torque quadratic dependent on speed, using a starting resistance. At time tStart2 external rotor resistance is shortened, finally reaching nominal speed.

Simulate for 1.5 seconds and plot (versus time):

currentQuasiRMSSensor.I: stator current RMS
aims.wMechanical: motor's speed
aims.tauElectrical: motor's torque

Default machine parameters are used.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
VNominal	Nominal RMS voltage per phase [V]
fNominal	Nominal frequency [Hz]
tStart1	Start time [s]
Rstart	Starting resistance [Ohm]
tStart2	Start time of shorting starting resistance [s]
TLoad	Nominal load torque [N.m]
wLoad	Nominal load speed [rad/s]
JLoad	Load's moment of inertia [kg.m2]
aimsData	Induction machine data

Modelica.Electrical.Machines.Examples.InductionMachines.IMC_Inverter

Test example: InductionMachineSquirrelCage with inverter

Information

An ideal frequency inverter is modeled by using a VfController and a three-phase SignalVoltage. Frequency is raised by a ramp, causing the induction machine with squirrel cage to start, and accelerating inertias.
At time tStep a load step is applied.

Simulate for 1.5 seconds and plot (versus time):

currentQuasiRMSSensor.I: stator current RMS
aimc.wMechanical: motor's speed
aimc.tauElectrical: motor's torque

Default machine parameters are used.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
VNominal	Nominal RMS voltage per phase [V]
fNominal	Nominal frequency [Hz]
f	Actual frequency [Hz]
tRamp	Frequency ramp [s]
TLoad	Nominal load torque [N.m]
tStep	Time of load torque step [s]
JLoad	Load's moment of inertia [kg.m2]
aimcData	Induction machine data

Modelica.Electrical.Machines.Examples.InductionMachines.IMC_Conveyor

Test example: InductionMachineSquirrelCage with inverter driving a conveyor

Information

An ideal frequency inverter is modeled by using a VfController and a three-phase SignalVoltage. Frequency is driven by a load cycle of acceleration, constant speed, deceleration and standstill. The mechanical load is a constant torque like a conveyor (with regularization around zero speed).

Simulate for 20 seconds and plot (versus time):

currentQuasiRMSSensor.I: stator current RMS
aimc.wMechanical: motor's speed
aimc.tauElectrical: motor's torque

Default machine parameters are used.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
VNominal	Nominal RMS voltage per phase [V]
fNominal	Nominal frequency [Hz]
wNominal	Nominal speed [rad/s]
TLoad	Nominal load torque [N.m]
JLoad	Load's moment of inertia [kg.m2]
r	Transmission radius [m]
aimcData	Induction machine data

Modelica.Electrical.Machines.Examples.InductionMachines.IMC_InverterDrive

Test example: InductionMachineSquirrelCage inverter drive

Information

This is a model of a complete inverter drive comprising:

a grid model and a line choke
a diode rectifier
a buffer capacitor
a switching inverter
a pulse width modulation
a voltage/frequency characteristic
the reference frequency ramped up
an induction machine with squirrel cage
a load inertia and quadratic speed dependent load torque (like a fan or pump)

Please note: Be patient, two switching devices cause many event iterations which cost performance.

Note that due to the voltage drop the voltage at the machine can't reach the full voltage which means torque reduction.

Default machine parameters are adapted to nominal phase voltage 400 V and nominal phase current 25 A.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
VNominal	Nominal RMS voltage per phase [V]
fNominal	Nominal frequency [Hz]
RGrid	Grid choke resistance [Ohm]
LGrid	Grid choke inductance [H]
VDC	Theoretical DC voltage [V]
CDC	DC capacitor [F]
TLoad	Nominal load torque [N.m]
wLoad	Nominal load speed [rad/s]
JLoad	Load's moment of inertia [kg.m2]
aimcData	Induction machine data

Modelica.Electrical.Machines.Examples.InductionMachines.IMC_Steinmetz

InductionMachineSquirrelCage Steinmetz-connection

Information

At start time tStart single-phase voltage is supplied to the induction machine with squirrel cage; the machine starts from standstill, accelerating inertias against load torque quadratic dependent on speed, finally reaching nominal speed.

Default machine parameters are used.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
VNominal	Nominal RMS voltage per phase [V]
fNominal	Nominal frequency [Hz]
tStart1	Start time [s]
Cr	Motor's running capacitor [F]
Cs	Motor's (additional) starting capacitor [F]
wSwitch	Speed for switching off the starting capacitor [rad/s]
TLoad	Nominal load torque [N.m]
wLoad	Nominal load speed [rad/s]
JLoad	Load's moment of inertia [kg.m2]
aimcData

Modelica.Electrical.Machines.Examples.InductionMachines.IMC_withLosses

Test example: InductionMachineSquirrelCage with losses

Information

Simulate for 5 seconds: The machine is started at nominal speed, flux is build up in the machine.
Continue the simulation for additional 5 seconds: Subsequently a load ramp is applied.
Compare by plotting versus Pmech:

Current	I_sim	I_meas
Speed	w_sim	w_meas
Power factor	pf_sim	pf_meas
Efficiency	eff_sim	eff_meas

Machine parameters are taken from a standard 18.5 kW 400 V 50 Hz motor, simulation results are compared with measurements.

Nominal stator current	32.85	A
Power factor	0.898
Speed	1462.5	rpm
Electrical input	20,443.95	W
Stator copper losses	770.13	W
Stator core losses	410.00	W
Rotor copper losses	481.60	W
Stray load losses	102.22	W
Friction losses	180.00	W
Mechanical output	18,500.00	W
Efficiency	90.49	%
Nominal torque	120.79	Nm

Stator resistance per phase	0.56	Ω
Temperature coefficient	copper
Reference temperature	20	°C
Operation temperature	90	°C
Stator leakage reactance at 50 Hz	1.52	Ω
Main field reactance at 50 Hz	66.40	Ω
Rotor leakage reactance at 50 Hz	2.31	Ω
Rotor resistance per phase	0.42	Ω
Temperature coefficient	aluminium
Reference temperature	20	°C
Operation temperature	90	°C

See:
Anton Haumer, Christian Kral, Hansjörg Kapeller, Thomas Bäuml, Johannes V. Gragger
The AdvancedMachines Library: Loss Models for Electric Machines
Modelica 2009, 7^th International Modelica Conference

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
aimcData	Induction machine data

Modelica.Electrical.Machines.Examples.InductionMachines.IMC_Initialize

Test example: Steady-State Initialization of InductionMachineSquirrelCage

Information

The induction machine with squirrel cage is initialized in steady-state at no-load; at time tStart a load torque step is applied.

Simulate for 1.5 seconds and plot (versus time):

currentQuasiRMSSensor.I: stator current RMS
aimc.wMechanical: motor's speed
aimc.tauElectrical: motor's torque

Default machine parameters are used.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
VNominal	Nominal RMS voltage per phase [V]
fNominal	Nominal frequency [Hz]
wSync	Synchronous speed [rad/s]
tStart	Start time [s]
TLoad	Nominal load torque [N.m]
wLoad	Nominal load speed [rad/s]
JLoad	Load's moment of inertia [kg.m2]
aimcData	Induction machine data

Modelica.Electrical.Machines.Examples.InductionMachines.IMC_DCBraking

Induction machine with DC current braking

Information

The stator windings of an induction machine are fed by a DC current, causing a stationary current space phasor. Since the rotor is turning, voltage is induced in the rotor cage which in turn drives rotor currents. This creates a braking torque.

Choose a layout and plot tauElectrical and tauShaft versus wMechanical.

Default machine parameters are used.

References

[Fischer2017]

R. Fischer, Elektrische Maschinen, 17^th ed., chapter 5.3.3., Hanser, ISBN 978-3-446-45218-3, 2017.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Name	Description
w0	Initial mechanical speed [rad/s]
JLoad	Load's moment of inertia [kg.m2]
settings
imcData

Automatically generated Thu Oct 1 16:07:40 2020.