Induction Machine Squirrel Cage

Squirrel cage induction machine with parameterization in the relative unit system or in the SI system.

induction machine squirrel cage

Description

The Induction Machine Squirrel Cage simulates a squirrel cage induction machine whose basic parameters are expressed in relative units or in the International System of Units (SI). A squirrel cage induction machine is a type of asynchronous machine. All stator and rotor connections are available on the unit. It is therefore possible to simulate soft-start modes by switching between Y (star connection) and Δ (delta connection) configurations or by increasing the rotor resistance.

Initialising the induction machine using power flow targets

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

Asynchronous machine equations

To realise the SI parameters, the unit converts the entered SI values into o.c. The converted values are based on the delta connection of the machine windings.

To realise the measurement in relative units, it is necessary to set resistances and inductances on the resistance tab, assuming that the machine windings are connected in delta.

The asynchronous machine equations are expressed with respect to the synchronous reference frame defined as follows

where is the nominal frequency of the electric current.

The Park-Gorev transformation translates the stator equations into a reference frame that is stationary with respect to the rated frequency of the electric current. It is written as follows:

where is the electric angle.

The rotor equations are mapped to another reference frame defined by the difference between the electric angle and the product of the rotor angle and the number of pole pairs :

The Park-Gorev transformation is used to define the equations of an induction machine in relative units. The equations for the stator voltage are defined as follows:

Where:

and - zero sequence stator voltages along the axes and , determined by the formula:

, and are the stator voltages at ports ~1 and ~2.
- base velocity in relative units.
and - zero-sequence stator flux-couplings along the axes and _ .
- stator resistance.
and - stator currents along the axes , and zero-sequence stator currents defined as:

where , and are the stator currents flowing from port ~1 to port ~2.

The rotor voltage equation is determined by the formula:

Where:

and are the rotor voltages along the axis and and the zero-sequence rotor voltage defined through the expression:

and are the rotor voltages at ports ~1r' and ~2r'.
- rotor flux-circuit coefficients along the axes , and zero sequence.
- synchronous speed in relative units. For synchronous reference frame the value is 1.
- mechanical rotational speed in relative units.
- rotor resistance in relation to the stator.
- rotor currents along the axis , and zero sequence, defined through the expression:

- rotor currents flowing from port ~1r' to port ~2r'.

The stator flux-current equations are defined as follows:

where is the stator self-inductance and is the magnetising inductance.

The rotor flux-coupling equations are defined as follows:

where is the self-inductance of the rotor relative to the stator.

The rotor torque is determined by

The stator self-inductance , stator dissipation inductance and magnetising inductance are related as follows

Rotor self-inductance , rotor dissipation inductance and magnetising inductance are related as follows.

In the presence of a saturation curve, the equations for determining the saturated magnetising inductance as a function of the magnetising flux are as follows:

For no saturation the equation reduces to

Ports

Output

o - output port for outputting measurement results in relative units
vector

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

Non-directional

R - machine rotor
`rotational mechanics

A mechanical port associated with the rotor of a machine.

C - the machine housing
`rotational mechanics

A mechanical port associated with the machine housing.

~1 is the beginning of the stator winding output
electricity

Expandable three-phase port associated with the beginning of the stator winding lead.

~2 is the end of the stator winding lead
electricity

Expandable three-phase port associated with the end of the stator winding lead.

Parameters

All parameter values by default are based on delta connection of the stator windings.

Main

Rated apparent power - rated apparent power
15e3 V*A (by default)

Rated total electrical power.

Rated voltage - effective voltage
`220 V (by default).

RMS line voltage.

Rated electrical frequency - rated electrical frequency
50 Hz (By default).

The rated electrical frequency corresponding to the rated full power.

Number of pole pairs - machine pole pairs
1 (By default).

Number of pole pairs of the machine.

parameterization unit - unit system for the parameterization of units
SI (By default) | Per unit.

Unit system for the parameterization of the blocks. Select one of the options: SI - international unit system and Per unit - relative unit system.

Dependencies

Choose:

SI reveals the SI measurement parameters in the Impedances and Saturation settings.
Relative Units options reveal the relative units in the Impedances and Saturation settings.

Squirrel cage is a short squirrel cage setting option
Single squirrel cage (By 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 cage.

Zero sequence - zero sequence
On (By default) | Off.

Zero sequence model:

On - prioritises the accuracy of the model.

Disabled - model speed priority for desktop modelling or real-time deployment.

Dependencies

When this parameter is set to:

On and parameterization unit is set to CI - the parameter Stator zero-sequence reactance, X0 in the resistance settings will be visible.
On and parameterization unit is set to Relative units - the parameter Stator zero-sequence inductance, pu_L0 (pu) will be visible in the resistance settings.
Disabled - the stator zero-sequence inductance parameter is not visible in the resistance settings.

Impedances

For parameterization unit and in Main settings, select SI to display parameters in SI system or Per unit to display parameters in relative units.

SStator resistance Rs, Ohm - stator resistance
0.25 Ohm (by default).

Stator resistance.

Dependencies

This parameter is used when parameterization unit is set to SI.

Stator leakage reactance Xls, Ohm - stator leakage reactance
0.4 Ohm (by default).

Stator leakage reactance.

Dependencies

This parameter is used when parameterization unit is set to SI.

Referred rotor resistance Rr', Ohm - reduced rotor resistance
0.14 Ohm (By default).

Rotor resistance reduced to the stator.

Dependencies

This parameter is used when parameterization unit is set to SI and Squirrel cage is set to Single squirrel cage.

Referred rotor leakage reactance Xlr', Ohm - reduced rotor leakage reactance
0.41 Ohm (by default).

Induced rotor leakage reactance.

Dependencies

This parameter is used when parameterization unit is set to SI and Squirrel cage is set to Single squirrel cage.

Referred rotor resistance in cage 1 Rr1', Ohm is the reduced resistance of the first squirrel cage
0.28 Ohm (By default).

The reduced resistance of the first squirrel cage.

Dependencies

This parameter is used when parameterization unit is set to SI and Squirrel cage is set to Double squirrel cage.

Referred rotor leakage reactance in cage 1 Xlr1', Ohm is the reduced reactance of the first squirrel cage
0.82 Ohm (by default).

The reduced reactance of the first squirrel cage.

Dependencies

This parameter is used when parameterization unit is set to SI and Squirrel cage is set to Double squirrel cage.

Referred rotor resistance in cage 2 Rr2', Ohm is the reduced resistance of the second squirrel cage
0.28 Ohm (By default).

The reduced resistance of the second squirrel cage.

Dependencies

This parameter is used when parameterization unit is set to SI and Squirrel cage is set to Double squirrel cage.

Referred rotor leakage reactance in cage 2 Xlr2', Ohm is the reduced reactance of the second squirrel cage
0.82 Ohm (by default).

The reduced reactance of the second squirrel cage.

Dependencies

This parameter is used when parameterization unit is set to SI and Squirrel cage is set to Double squirrel cage.

Magnetising reactance Xm, Ohm - magnetizing reactance
0.17 Ohm (By default).

Magnetising reactance.

Dependencies

This parameter is used when parameterization unit is set to SI.

Stator zero-sequence reactance X0, Ohm - stator zero-sequence reactance
0.4 Ohm (by default).

Stator zero-sequence reactance.

Dependencies

This parameter is used when parameterization unit is set to SI and Zero sequence is set to On.

Stator resistance Rs, pu - stator resistance in relative units
0.0258 (by default).

Stator resistance in relative units.

Dependencies

This parameter is used when the parameterization unit in the Main setting is set to Per unit.

Stator leakage inductance Lls, pu - stator leakage inductance in relative units
0.0413 (By default).

Stator leakage inductance in relative units.

Dependencies

This parameter is used when the parameterization unit in the Main setting is set to Per unit.

Referred rotor resistance Rr', pu - reduced rotor resistance in relative units
0.0145 (By default).

Referred rotor resistance in relative units.

Dependencies

This parameter is used when parameterization unit is set to `Relative units' and Zero sequence is set to `Single squirrel cage'.

Referred rotor leakage inductance Llr', pu - reduced rotor leakage inductance in relative units
0.0424 (By default).

Induced rotor leakage inductance in relative units.

Dependencies

This parameter is used when parameterization unit is set to `Relative units' and Zero sequence is set to `Single squirrel cage'.

Referred rotor resistance in cage 1 Rr1', pu is the reduced rotor resistance of the first squirrel cage, o.u.
0.0290 (By default).

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

Dependencies

This parameter is used when parameterization unit is set to Double squirrel cage.

Referred rotor leakage reactance in cage 1 Llr1', pu is the reduced scattering inductance of the first squirrel cage, o.u.
0.0848 (By default).

The reduced scattering inductance of the first squirrel cage, o.u.

Dependencies

This parameter is used when parameterization unit is set to Double squirrel cage.

Referred rotor resistance in cage 2 Rr2', pu - reduced rotor resistance of the second squirrel cage, o.u.
0.0290 (By default).

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

Dependencies

This parameter is used when parameterization unit is set to Double squirrel cage.

Referred rotor leakage reactance in cage 2 Llr2', pu is the reduced scattering inductance of the second squirrel cage, o.u.
0.0848 (By default).

The reduced scattering inductance of the second squirrel cage, o.u.

Dependencies

This parameter is used when parameterization unit is set to `Relative units' and Zero sequence is set to `Double squirrel cage'.

Magnetising inductance Lm, pu - magnetizing inductance in relative units
1.7562 (By default).

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

Dependencies

This parameter is used when parameterization unit is set to `Relative units' and Zero sequence is set to `Double squirrel cage'.

Stator zero-sequence inductance L0, pu - relative stator zero-sequence inductance in relative units
0.0413 (by default)

Stator zero-sequence inductance in relative units.

Dependencies

This parameter is used when parameterization unit is set to on.

Examples

Star-delta starting of induction motor