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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Path in the library: |
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 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 by switching between configurations Y (star connection) and Δ (triangle connection) or by 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 SI parameters, the block 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 on the resistance tab, based on the fact that the machine windings 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:
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and — zero-sequence stator voltages along the axes and , defined by the formula:
.
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, and — stator voltages at ports ~1 and ~2.
-
— base speed in relative units.
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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 equation is determined by the formula:
,
,
,
where:
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and — rotor voltage along the axis and and the rotor voltage of the zero sequence, defined by the expression:
.
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and — rotor voltages at ports ~1r' and ~2r'.
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— flow coupling of the rotor along the axes , and the zero sequence.
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— synchronous speed in relative units. For a synchronous reference frame, the value is 1.
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— the mechanical speed of rotation in relative units.
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— the resistance of the rotor in relation to the stator.
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— rotor currents along the axis , and the zero sequence, defined by the expression:
.
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— 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 determined by
.
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
Ports
Output
o — output port for output of measurement results in relative units of
vector
The vector of the output port associated with measurements in relative units. The elements of the vector are:
Non-directional
R — rotor of the pass machine:q[<br>] rotational mechanics
A mechanical port connected to the rotor of the machine.
C — machine body
rotational mechanics
A mechanical port connected to the machine body.
~1 — start of stator winding output
electricity
Expandable three-phase port connected to the start of the stator winding output.
~2 — end of the stator winding output
electricity
Expandable three-phase port connected to the terminal end of the stator winding.
Parameters
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All default parameter values are based on connecting the stator windings with a triangle. |
Main
Rated apparent power — rated full power
15e3 In*A (default)
Rated total electrical power.
Rated voltage — current pass voltage:q[<br>] 220 V (default)
RMS linear voltage.
Rated electrical frequency — rated frequency of electric current
50 Hz (default)
The rated electrical frequency corresponding to the rated full power.
Number of pole pairs — pairs of poles of the machine
1 (default)
The number of pairs of poles of the machine.
Parameterization unit — a system of units for parameterization of pass blocks:q[<br>] SI (default) | Per unit
A system of measurement units for parameterizing blocks. Choose one of the options: SI — the international system of units and Per unit — a system of relative units.
Dependencies
Choose one:
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sireveals the measurement parameters in the SI system in the Impedances and Saturation settings. -
Relative unitsThe parameters reveal the relative units in the Impedances and Saturation settings.
Squirrel cage — setting option for the short-circuited rotor
Single squirrel cage (default) | Double squirrel cage
Sets the type of squirrel cage: single or double.
Setting this parameter to Double squirrel cage opens the Impedances parameters for the second cell.
Zero sequence — zero sequence
enabled (by default) | turned off
The zero-sequence model:
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Enabled— the priority of model accuracy.
-
Turned off— Prioritize simulation speed for desktop simulation or real-time deployment.
Dependencies
If this parameter is set to:
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Enabledand the Parameterization unit is set tosi— the parameter Stator zero-sequence reactance, X0 will be visible in the resistance settings. -
Enabledand the Parameterization unit is set toRelative units— the parameter Stator zero-sequence induction, pu_L0 (pu) will be visible in the resistance settings. -
Turned off— the inductance parameter of the zero sequence of the stator is not visible in the resistance settings.
Impedances
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For the parameter Parameterization unit and in the Main settings, select |
Stator resistance Rs, Ohm — stator resistance
0.25 Ohms (default)
Stator resistance.
Dependencies
This parameter is used if the Parameterization unit parameter is set to SI.
Stator leakage reactance Xls, Ohm — stator scattering reactance
0.4 Ohms (default)
The reactive resistance of the stator scattering.
Dependencies
This parameter is used if the Parameterization unit parameter is set to SI.
Referred rotor resistance Rr', Ohm — reduced rotor resistance
0.14 Ohms (default)
The resistance of the rotor, brought to the stator.
Dependencies
This parameter is used if the Parameterization unit parameter is set to SI, and the Squirrel cage parameter is set to Single squirrel cage.
Referred rotor leakage reactance Xlr', Ohm — reduced reactance of the rotor scattering
0.41 ohms (default)
The reduced reactance of the rotor scattering.
Dependencies
This parameter is used if the Parameterization unit parameter is set to SI, and the Squirrel cage parameter is set to Single squirrel cage.
Referred rotor resistance in cage 1 Rr1', Ohm — reduced resistance of the first squirrel cage
0.28 ohms (default)
The reduced resistance of the first squirrel cage.
Dependencies
This parameter is used if the Parameterization unit parameter is set to SI, and the Squirrel cage parameter is set to Double squirrel cage.
Referred rotor leakage reactance in cage 1 Xlr1', Ohm — reduced reactance of the first squirrel cage
0.82 ohms (default)
The reduced reactance of the first squirrel cage.
Dependencies
This parameter is used if the Parameterization unit parameter is set to SI, and the Squirrel cage parameter is set to Double squirrel cage.
Referred rotor resistance in cage 2 Rr2', Ohm — reduced resistance of the second squirrel cage
0.28 ohms (default)
The reduced resistance of the second squirrel cage.
Dependencies
This parameter is used if the Parameterization unit parameter is set to SI, and the Squirrel cage parameter is set to Double squirrel cage.
Referred rotor leakage reactance in cage 2 Xlr2', Ohm — reduced reactance of the second squirrel cage
0.82 ohms (default)
The reduced reactance of the second squirrel cage.
Dependencies
This parameter is used if the Parameterization unit parameter is set to SI, and the Squirrel cage parameter is set to Double squirrel cage.
Magnetizing reactance Xm, Ohm — magnetization reactance
0.17 ohms (default)
The reactance of magnetization.
Dependencies
This parameter is used if the Parameterization unit parameter is set to SI.
Stator zero-sequence reactance X0, Ohm — reactance of the zero sequence of the stator
0.4 Ohms (default)
The reactance of the zero sequence of the stator.
Dependencies
This parameter is used if the Parameterization unit parameter is set to SI, and the Zero sequence parameter is set to Enabled.
Stator resistance Rs, pu — stator resistance in relative units of
0.0258 (default)
Stator resistance in relative units.
Dependencies
This parameter is used if the Parameterization unit parameter in the Main setting is set to Per unit.
Stator leakage induction Lls, pu — stator leakage inductance in relative units of
0.0413 (default)
Stator scattering inductance in relative units.
Dependencies
This parameter is used if the Parameterization unit parameter in the Main setting is set to Per unit.
Referred rotor resistance Rr', pu — reduced rotor resistance in relative units of
0.0145 (default)
The reduced resistance of the rotor in relative units.
Dependencies
This parameter is used if the Parameterization unit parameter is set to Relative units, and the Zero sequence parameter is set to Single squirrel cage.
Referred rotor leakage induction Llr', pu — reduced rotor leakage inductance in relative units of
0.0424 (default)
The reduced inductance of the rotor scattering in relative units.
Dependencies
This parameter is used if the Parameterization unit parameter is set to Relative units, and the Zero sequence parameter is set to Single squirrel cage.
Referred rotor resistance in cage 1 Rr1', pu — reduced resistance of the first squirrel cage, O.E.
0.0290 (default)
The reduced resistance of the first squirrel cage in relative units.
Dependencies
This parameter is used if the Parameterization unit parameter is set to Double squirrel cage.
Referred rotor leakage reactance in cage 1 Llr1', pu — reduced scattering inductance of the first squirrel cage, O.E.
0.0848 (default)
Reduced scattering inductance of the first squirrel cage, O.E.
Dependencies
This parameter is used if the Parameterization unit parameter is set to Double squirrel cage.
Referred rotor resistance in cage 2 Rr2', pu — reduced resistance of the second squirrel cage, O.E.
0.0290 (default)
The reduced resistance of the first squirrel cage in relative units.
Dependencies
This parameter is used if the Parameterization unit parameter is set to Double squirrel cage.
Referred rotor leakage reactance in cage 2 Llr2', pu — reduced scattering inductance of the second squirrel cage, O.E.
0.0848 (default)
Reduced scattering inductance of the second squirrel cage, O.E.
Dependencies
This parameter is used if the Parameterization unit parameter is set to Relative units, and the Zero sequence parameter is set to Double squirrel cage.
Magnetizing induction Lm, pu — magnetization inductance in relative units of
1.7562 (default)
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 the Parameterization unit parameter is set to Relative units, and the Zero sequence parameter is set to Double squirrel cage.
Stator zero-sequence induction L0, pu is the relative inductance of the zero sequence of the stator in relative units of
0.0413 (default)
The inductance of the zero sequence of the stator in relative units.
Dependencies
This parameter is used if the Parameterization unit parameter is set to Enabled.