Induction Machine Squirrel Cage

Asynchronous machine with a closed-loop rotor with parameterization in the system of relative units or according to the SI system.

blockType: AcausalElectricPowerSystems.Electromechanical.Asynchronous.InductionMachineSquirrelCage

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Description

Block Induction Machine Squirrel Cage simulates an asynchronous machine with a closed-loop rotor, the main parameters of which are expressed in relative units (OE) or in the International System of Units (SI). A closed-loop asynchronous machine is a type of asynchronous machine. All stator and rotor connections are available on the unit. Therefore, it is possible to simulate soft-start modes using switching between Y configurations (connection type «star») and Δ (connection by type «triangle») or increasing the resistance of the rotor.

Initialization of an asynchronous machine using target energy flow values

If the unit is located in a network compatible with the time-frequency simulation mode, then an analysis of the energy flow in the network can be performed. The energy flow analysis introduces steady-state values that can be used to initialize the machine.

Asynchronous machine equations

To implement the parameters in SI units, the unit converts the entered SI values to OE. The converted values are based on connecting the windings of the machine with a triangle.

To implement the measurement in relative units, it is necessary to set the resistance and inductance in the parameter group *Impedances * based on the fact that the windings of the machine are connected by a triangle.

The equations of an asynchronous machine are expressed with respect to a synchronous frame of reference, defined as follows

where — the rated frequency of the electric current.

The Park—Gorev transformation translates the stator equations into a reference frame fixed relative to the nominal frequency of the electric current. It is written as follows:

where — electric angle.

The rotor equations are compared with another frame of reference, determined by the difference between the electric angle and the product of the rotation angle of the rotor. and the number of pairs of poles :

The Park—Gorev transform is used to define asynchronous machine equations in relative units. The equations for the stator voltage are defined as follows:

where

and — zero-sequence stator voltages along the axes and , defined by the formula:
and — stator voltages at ports ~1 and ~2;
— base speed in relative units;
and — zero-sequence flow coupling of the stator along the axes and _ ;
— stator resistance;
and — stator currents along the axis , and zero-sequence stator currents, defined as:

where and — Stator currents flowing from port ~1 to port ~2.

The rotor voltage equations are defined as:

where

and — rotor voltage along the axis and and the rotor voltage of the zero sequence, defined by the expression:
and — rotor voltages at ports ~1r' and ~2r';
— flow coupling of the rotor along the axes , and the zero sequence;
— synchronous speed in relative units. For a synchronous reference frame, the value is 1;
— mechanical rotation speed in relative units;
— resistance of the rotor in relation to the stator;
— rotor currents along the axis , and the zero sequence, defined by the expression:
— rotor currents flowing from port ~1r' to port ~2r'.

The stator flow coupling equations are defined as follows:

where — self-induction of the stator, and — magnetization inductance.

The rotor flow coupling equations are defined as follows:

where — self-induction of the rotor relative to the stator.

The rotor torque is defined as

Stator self-induction , stator scattering inductance and the magnetization inductance they are related as follows

Rotor self-induction , rotor scattering inductance and the magnetization inductance they are related as follows

In the presence of a saturation curve, the equations for determining the saturated magnetization inductance as a function of the magnetizing flux have the form:

For the absence of saturation, the equation reduces to

Variables

Use the parameter group Initial Targets to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

Ports

Conserving

# R — the rotor of the machine
rotational mechanics

Details

A mechanical port connected to the rotor of the machine.

Program usage name

rod_flange

# C — machine body
rotational mechanics

Details

A mechanical port connected to the machine body.

Program usage name

case_flange

# ~1 — the beginning of the stator winding output
electricity

Details

Expandable three-phase port connected to the start of the stator winding output.

Program usage name

port1

# ~2 — the end of the stator winding output
electricity

Details

Expandable three-phase port connected to the terminal end of the stator winding.

Program usage name

port2

Output

# o — The output port for displaying measurement results in relative units
vector

Details

The vector of the output port associated with measurements in relative units. The elements of the vector are:

Data types	`Float64`
Complex numbers support	No

Parameters

Main

# Rated apparent power — Rated full power
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

Rated total electrical power.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`15e3 V*A`
Program usage name	`S_rated`
Evaluatable	Yes

# Rated voltage — current voltage
V | uV | mV | kV | MV

Details

RMS linear voltage.

Units	`V` \| `uV` \| `mV` \| `kV` \| `MV`
Default value	`220 V`
Program usage name	`V_rated`
Evaluatable	Yes

# Rated electrical frequency — rated frequency of electric current
Hz | kHz | MHz | GHz

Details

The rated electrical frequency corresponding to the rated full power.

Units	`Hz` \| `kHz` \| `MHz` \| `GHz`
Default value	`50 Hz`
Program usage name	`f_rated`
Evaluatable	Yes

# Number of pole pairs — pairs of poles of the machine

Details

The number of pairs of poles of the machine.

Default value	`1`
Program usage name	`N_pole_pairs`
Evaluatable	Yes

# Parameterization unit — a system of units for parameterizing blocks
Per unit | SI

Details

A system of measurement units for parameterizing blocks. Choose one of the options: SI — the international system of units and Per unit — the system of relative units:

SI discloses measurement parameters in the SI system in parameter groups Impedances and Saturation.
Per unit exposes parameters in relative units in parameter groups Impedances and Saturation.

Values	`Per unit` \| `SI`
Default value	`SI`
Program usage name	`parameter_units`
Evaluatable	No

# Squirrel cage — a short-circuit rotor configuration option
Single squirrel cage | Double squirrel cage

Details

Sets the type of squirrel cage: single or double.

Setting this parameter to Double squirrel cage opens the parameters Impedances for the second cell.

Values	`Single squirrel cage` \| `Double squirrel cage`
Default value	`Single squirrel cage`
Program usage name	`squirrel_cage`
Evaluatable	No

# Zero sequence — the zero sequence

Details

The zero-sequence model:

If this option is selected, the accuracy priority of the model is used.

If this option is not selected, simulation speed priority is used for desktop simulation or real-time deployment.

Default value	`true (switched on)`
Program usage name	`zero_sequence`
Evaluatable	No

# Initialization option — initialization method
Set targets for flux variables

Details

Initialization method. Either flow data or load flow analysis data can be used to initialize the machine during steady-state simulation.

If the parameter is selected Set targets for flux variables, then in order to fully specify the initial state, it is necessary to enable the initialization restriction in the form of a high-priority target value. For example, if an asynchronous machine is connected to the block Inertia, then the initial state of the asynchronous machine will be fully determined if in the section Initial Targets the block Inertia The Priority for Rotational velocity parameter will be set to Tall.

Dependencies

The type of variables displayed in the section Initial Targets, depends on the initialization method selected in the section Main for the parameter Initialization option.

Values	`Set targets for flux variables`
Default value	`Set targets for flux variables`
Program usage name	`initialization_option`
Evaluatable	No

Impedances

# Stator resistance Rs — stator resistance
Ohm | mOhm | kOhm | MOhm | GOhm

Details

Stator resistance.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set SI.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.25 Ohm`
Program usage name	`R_s`
Evaluatable	Yes

# Stator leakage reactance Xls — stator scattering reactance
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The reactive resistance of the stator scattering.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set SI.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.4 Ohm`
Program usage name	`X_ls`
Evaluatable	Yes

# Referred rotor resistance Rr' — reduced rotor resistance
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The resistance of the rotor, brought to the stator.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set SI, and for the parameter Squirrel cage the value is set Single squirrel cage.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.14 Ohm`
Program usage name	`R_r`
Evaluatable	Yes

# Referred rotor leakage reactance Xlr' — reduced reactance of the rotor scattering
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The reduced reactance of the rotor scattering.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set SI, and for the parameter Squirrel cage the value is set Single squirrel cage.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.41 Ohm`
Program usage name	`X_lr`
Evaluatable	Yes

# Referred rotor resistance in cage 1 Rr1' — reduced resistance of the first squirrel cage
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The reduced resistance of the first squirrel cage.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set SI, and for the parameter Squirrel cage the value is set Double squirrel cage.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.28 Ohm`
Program usage name	`R_r1`
Evaluatable	Yes

# Referred rotor leakage reactance in cage 1 Xlr1' — reduced reactance of the first squirrel cage
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The reduced reactance of the first squirrel cage.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set SI, and for the parameter Squirrel cage the value is set Double squirrel cage.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.82 Ohm`
Program usage name	`X_lr1`
Evaluatable	Yes

# Referred rotor resistance in cage 2 Rr2' — reduced resistance of the second squirrel cage
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The reduced resistance of the second squirrel cage.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set SI, and for the parameter Squirrel cage the value is set Double squirrel cage.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.28 Ohm`
Program usage name	`R_r2`
Evaluatable	Yes

# Referred rotor leakage reactance in cage 2 Xlr2' — reduced reactance of the second squirrel cage
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The reduced reactance of the second squirrel cage.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set SI, and for the parameter Squirrel cage the value is set Double squirrel cage.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.82 Ohm`
Program usage name	`X_lr2`
Evaluatable	Yes

# Magnetizing reactance Xm — magnetization reactivity
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The reactance of magnetization.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set SI.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`17 Ohm`
Program usage name	`X_m`
Evaluatable	Yes

# Stator zero-sequence reactance X0 — reactance of the zero sequence of the stator
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The reactance of the zero sequence of the stator.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set SI, and the flag is set Zero sequence.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.4 Ohm`
Program usage name	`X_0`
Evaluatable	Yes

# Stator resistance Rs, pu — stator resistance in relative units

Details

Stator resistance in relative units.

Dependencies

This parameter is used if for the parameter Parameterization unit in the settings Main the value is set Per unit.

Default value	`0.0258`
Program usage name	`R_s_pu`
Evaluatable	Yes

# Stator leakage inductance Lls, pu — stator scattering inductance in relative units

Details

Stator scattering inductance in relative units.

Dependencies

This parameter is used if for the parameter Parameterization unit in the settings Main the value is set Per unit.

Default value	`0.0413`
Program usage name	`L_ls_pu`
Evaluatable	Yes

# Referred rotor resistance Rr', pu — reduced rotor resistance in relative units

Details

The reduced resistance of the rotor in relative units.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set Relative units, and for the parameter Zero sequence the value is set Single squirrel cage.

Default value	`0.0145`
Program usage name	`R_r_pu`
Evaluatable	Yes

# Referred rotor leakage inductance Llr', pu — reduced rotor scattering inductance in relative units

Details

The reduced inductance of the rotor scattering in relative units.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set Relative units, and for the parameter Zero sequence the value is set Single squirrel cage.

Default value	`0.0424`
Program usage name	`L_lr_pu`
Evaluatable	Yes

# Referred rotor resistance in cage 1 Rr1', pu — the reduced resistance of the first squirrel cage, O.E.

Details

The reduced resistance of the first squirrel cage in relative units.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set Double squirrel cage.

Default value	`0.029`
Program usage name	`R_r1_pu`
Evaluatable	Yes

# Referred rotor leakage reactance in cage 1 Llr1', pu — reduced scattering inductance of the first squirrel cage, O.E.

Details

Reduced scattering inductance of the first squirrel cage, O.E.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set Double squirrel cage.

Default value	`0.0848`
Program usage name	`L_lr1_pu`
Evaluatable	Yes

# Referred rotor resistance in cage 2 Rr2', pu — reduced resistance of the second squirrel cage, O.E.

Details

The reduced resistance of the first squirrel cage in relative units.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set Double squirrel cage.

Default value	`0.029`
Program usage name	`R_r2_pu`
Evaluatable	Yes

# Referred rotor leakage reactance in cage 2 Llr2', pu — reduced scattering inductance of the second squirrel cage, O.E.

Details

Reduced scattering inductance of the second squirrel cage, O.E.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set Relative units, and for the parameter Zero sequence the value is set Double squirrel cage.

Default value	`0.0848`
Program usage name	`L_lr2_pu`
Evaluatable	Yes

# Magnetizing inductance Lm, pu — magnetization inductance in relative units

Details

The magnetization inductance in relative units, i.e. the peak value of the mutual inductance of the stator and rotor.

Dependencies

This parameter is used if for the parameter Parameterization unit the value is set Relative units, and for the parameter Zero sequence the value is set Double squirrel cage.

Default value	`1.7562`
Program usage name	`L_m_pu`
Evaluatable	Yes

# Stator zero-sequence inductance L0, pu — relative inductance of the zero sequence of the stator in relative units

Details

The inductance of the zero sequence of the stator in relative units.

Dependencies

This option is used if the check box is selected. Parameterization unit.

Default value	`0.0413`
Program usage name	`L_0_pu`
Evaluatable	Yes

Induction Machine Squirrel Cage

Description

Initialization of an asynchronous machine using target energy flow values

Asynchronous machine equations

Variables

Ports

Conserving

Output

Parameters

Main

Impedances

Examples