Engee documentation

Induction Machine Wound Rotor

Phase rotor induction machine with parameterization in the relative unit system or in the SI system.

induction machine wound rotor

Description

Unit Induction Machine Wound Rotor simulates a phase rotor induction machine whose basic parameters are expressed in relative units or in the International System of Units (SI). A phase rotor induction machine is a type of induction machine. The starts and ends of the stator and rotor windings are brought out as ports and are flexibly configurable. To connect the stator in delta, connect a block Phase Permute between ports ~1 and ~2. To star the stator, connect port ~2 to a Grounded Neutral or Floating Neutral block. If you do not need access to the rotor windings, use the Induction Machine Squirrel Cage block.

If you do not need to change the rotor resistance, connect port ~1r' to the Floating Neutral (Three-Phase) block and port ~2r' to the Grounded Neutral (Three-Phase) block.

The rotor circuit parameters are referenced to the stator circuit parameters, which are taken as reference.

Equations of induction machine

The SI parameters you set for the machine are converted into relative units. The parameters are entered into the equations in relative units. The parameters are calculated assuming that the machine windings are connected in delta.

To model parameters in relative units, it is necessary to set resistance and inductance values in the Impedances tab, assuming that the machine windings are connected in delta.

The equations of the asynchronous machine in the synchronous reference frame are defined as follows:

,

where is the rated electrical frequency set in the Rated electrical frequency parameters.

The Park-Gorev transformation converts the stator equations to a reference frame fixed with respect to the rated electrical frequency. 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 are stator voltages along the axes , and zero sequence, respectively, defined as:

,

where , and are the stator voltages at ports ~1 and ~2.

  • - is the basic electric angular velocity in relative units.

  • and - stator flux-couplings along the axes , and zero sequence, respectively.

  • - stator resistance.

  • and - stator currents along the axes , and zero sequence, respectively, defined as:

,

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

The equations for the rotor voltage are defined as follows:

,

,

,

Where:

  • and are rotor voltages along the axes , and zero sequence, respectively, defined as:

,

where and are rotor voltages at ports ~1r' and ~2r'.

  • - are rotor flux-circuit coefficients along the axes , and zero sequence, respectively.

  • - 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 axes , and zero sequence respectively, defined as:

,

where are the rotor currents flowing from port ~1r' to port ~2r'.

The stator flux-current equations are defined as follows:

,

,

,

where is the stator inductance and is the magnetising inductance.

The rotor flux-coupling equations are defined as follows:

,

,

,

where is the rotor inductance relative to the stator.

The rotor torque is determined by

.

The stator natural inductance , stator dissipation inductance and magnetising inductance are related to each other as follows:

.

The rotor natural inductance , rotor dissipation inductance and magnetising inductance are related as follows:

.

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

,

.

In the absence of saturation, the equation reduces to

.

Modelling of thermal effects

When this option is enabled, thermal ports for each rotor and stator winding will appear in the block. In this way you can control the motor temperature and influence the motor with external heat sources. Tick the checkbox for the Enable thermal port parameters. The winding resistance is assumed to be linearly dependent on temperature and is defined as:

,

where:

  • - resistance at temperature ;

  • - initial resistance at initial temperature ;

  • - temperature coefficient. The value for copper is 3.93e-3 1/K.

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:

  • pu_torque

  • pu_velocity

  • pu_vds

  • pu_vqs

  • pu_v0s

  • pu_ids

  • pu_iqs

  • pu_i0s

To display measurement results, connect the Induction Machine Measurement unit to this port.

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.

~1r' is the beginning of the rotor winding lead
electricity

Expandable three-phase port bound by the beginning of the rotor winding lead.

~2r' is the end of the rotor winding lead
electricity

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

HA - heat port of phase a
heat

Thermal port associated with the stator winding a.

Dependencies

To use this port, select the checkbox for the Enable thermal port parameters.

HB - thermal port of phase b
`heat

Thermal port associated with the stator winding b.

Dependencies

To use this port, select the checkbox for the Enable thermal port parameters.

HC - thermal port of the c phase
`heat

Thermal port associated with the stator winding c.

Dependencies

To use this port, select the check box for the Enable thermal port parameters.

HAr - rotor phase a thermal port
heat

Thermal port associated with the rotor winding a.

Dependencies

To use this port, select the checkbox for the Enable thermal port parameters.

HBr - rotor phase b thermal port
heat

Thermal port associated with the rotor winding b.

Dependencies

To use this port, select the checkbox for the Enable thermal port parameters.

HCr - rotor phase c thermal port
heat

Thermal port associated with the c rotor winding.

Dependencies

To use this port, select the checkbox for the Enable thermal port parameters.

Parameters

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

Thermal Port

Enable thermal port - Enable thermal ports
Off (By default) | On

The parameters value determines whether the block thermal ports are available and whether heat generation and temperature modelling will be performed.

Main

Rated apparent power - rated apparent power
`15e3 A*B (By default)

Rated total electrical power.

Rated voltage - rated 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 - number of pole pairs
1 (By default).

Number of pole pairs of the machine.

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

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

Dependencies

Select:

  • SI - parameters of measurements in the SI system in the Impedances settings.

  • Relative units - parameters of measurement in relative units in Impedances settings.

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

If this parameters is set to:

  • On and Parameterization unit is set to CI - the parameter Stator zero-sequence reactance X0 in the Impedances settings will be visible.

  • On and Parameterization unit is set to Relative units - the parameter Stator zero-sequence inductance pu_L0, pu in the Impedances settings will be visible.

  • Disabled - stator zero-sequence inductance parameter is not visible in Impedances settings.

Initialisation option - initialisation method
Set targets for flux variables (by default).

Initialisation method.

Impedances

For Parameterization unit under Main in the settings, select SI to display parameters in SI system or Per unit to display parameters in relative units.

Stator resistance Rs - stator resistance
`0.25 Ohm (by default)'.

Stator resistance.

Dependencies

This parameter is used when the Parameterization unit parameter is set to SI.

Stator leakage reactance Xls - stator dissipation reactance
`0.4 Ohm (by default)'.

Stator leakage reactance.

Dependencies

This parameter is used when the Parameterization unit parameters are set to SI.

Referred rotor resistance Rr' - reduced rotor resistance
`0.14 Ohm (by default)'.

Rotor resistance reduced to the stator.

Dependencies

This parameter is used when the Parameterization unit parameter is set to SI.

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

Induced rotor leakage reactance.

Dependencies

This parameter is used when the Parameterization unit parameters are set to SI.

Magnetising reactance Xm - magnetizing reactance
`0.17 Ohm (by default)'.

Magnetising reactance.

Dependencies

This parameter is used when the Parameterization unit parameters are set to SI.

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

Stator zero-sequence reactance.

Dependencies

This parameter is used when the Parameterization unit parameters are set to SI.

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 parameter 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 parameter 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 the Parameterization unit parameters are set to `Relative units'.

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 the Parameterization unit parameter is set to `Relative units'.

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 the Parameterization unit parameter is set to `Relative units'.

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 Relative units' and Zero sequence parameters are set to `On.

Thermal

These parameters appear only when the thermal ports option is enabled.

Measurement temperature - nominal temperature
298.15 K (By default) | scalar

The temperature for which the machine parameters are specified.

Resistance temperature coefficient - resistance temperature coefficient
0.00393 1/K (by default) | scalar

Resistance temperature coefficient in the resistance-temperature equation for all three windings. The by default value, 3.93e-3 1/K, for copper.

Thermal mass for each stator winding - heat capacity of the winding
100 J/K (by default) | scalar.

Value of heat capacity for each stator winding. Heat capacity is the energy required to raise the temperature by one degree.

Rotor thermal mass - rotor heat capacity
200 J/K (by default) | scalar.

Rotor heat capacity. Heat capacity is the energy required to raise the temperature by one degree.

References

  1. Kundur, P. Power System Stability and Control. New York, NY: McGraw Hill, 1993.

  2. Lyshevski, S. E. Electromechanical Systems, Electric Machines and Applied Mechatronics. Boca Raton, FL: CRC Press, 1999.

  3. Ojo, J. O., Consoli, A.,and Lipo, T. A., "An improved model of saturated induction machines," IEEE Transactions on Industry Applications. Vol. 26, no. 2, pp. 212-221, 1990.