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

The Induction Machine Wound Rotor block models 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 Phase Permute block 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 unit converts the machine parameters you set in SI into a system of relative units. The parameters are entered into the equations in relative units. The parameter values are calculated assuming that the machine windings are connected in delta.

To model the parameters in relative units, it is necessary to set the 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 parameter.

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 Enable thermal port. 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 Enable thermal port.

HB - thermal port of phase b
`heat

Thermal port associated with the stator winding b.

Dependencies

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

HC - thermal port of the c phase
`heat

Thermal port associated with the stator winding c.

Dependencies

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

HAr - rotor phase a thermal port
heat

Thermal port associated with the rotor winding a.

Dependencies

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

HBr - rotor phase b thermal port
heat

Thermal port associated with the rotor winding b.

Dependencies

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

HCr - rotor phase c thermal port
heat

Thermal port associated with the c rotor winding.

Dependencies

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

Parameters

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

Thermal Port

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

The value of the parameter determines whether the thermal ports of the unit 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 - measurement parameters in the SI system in the Impedances settings.
Relative units - measurement options in relative units in the 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

When this parameter 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