Induction Machine Wound Rotor

Asynchronous machine with a phase rotor with parameterization in the system of relative units or in the SI system.

blockType: AcausalElectricPowerSystems.Electromechanical.Asynchronous.InductionMachineWoundRotor

Path in the library:

/Physical Modeling/Electrical/Electromechanical/Asynchronous/Induction Machine Wound Rotor

Description

Block Induction Machine Wound Rotor simulates an asynchronous machine with a phase rotor, the main parameters of which are expressed in relative units (OE) or in the International System of Units (SI). A phase rotor asynchronous machine is a type of asynchronous machine. The beginnings and ends of the stator and rotor windings are output as ports and are flexibly configured. To connect the stator to «triangle», connect the unit between ports ~1 and ~2 Phase Permute. To connect the stator to «A star» connect port ~2 to the Grounded Neutral or Floating Neutral unit. If you do not need access to the rotor windings, use the block Induction Machine Squirrel Cage.

If it is not necessary to change the rotor resistance, connect the port ~1r' to the unit Floating Neutral (Three-Phase), and the port ~2r' is to the block Grounded Neutral (Three-Phase).

The parameters of the rotor circuit are reduced to the parameters of the stator circuit, which are taken as basic.

Asynchronous machine equations

The SI block translates the machine parameters you set into a system of relative units. The parameters are entered into the equations in relative units. The parameter values are calculated based on the fact that the machine windings are connected «a triangle».

To model the parameters in relative units, it is necessary to set the values of resistance and inductance in the tab Impedances based on the fact that the machine windings are connected «a triangle».

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

where — the rated frequency of the electric current set in the parameter Rated electrical frequency.

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 — stator voltage along the axes , and the zero sequence, respectively, defined as:

,

where , and — stator voltages at ports ~1 and ~2;
— basic electrical angular velocity in relative units;
and — flow coupling of the stator along the axes , and the zero sequence , respectively;
— stator resistance;
and — stator currents along the axes , and the zero sequence, respectively, defined as:

,

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

The equations for the rotor voltage are defined as follows:

where

and — rotor stresses along the axes , and the zero sequence, respectively, defined as:

,

where and — rotor voltages at ports ~1r' and ~2r';
— flow coupling of the rotor along the axes , and the zero sequence , respectively;
— 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 axes , and the zero sequence, respectively, defined as:

,

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

The stator flow coupling equations are defined as follows:

where — the stator’s own inductance, and — magnetization inductance.

The rotor flow coupling equations are defined as follows:

where — the intrinsic inductance of the rotor relative to the stator.

The rotor torque is defined as

Stator intrinsic inductance , stator scattering inductance and the magnetization inductance they are related as follows:

Rotor’s own inductance , rotor scattering inductance and the magnetization inductance they are related as follows:

In the presence of a saturation curve, the equations for determining the magnetization inductance, depending on the flow coupling, have the form:

In the absence of saturation, the equation reduces to

Modeling of thermal effects

When the option is enabled, thermal ports for each rotor and stator winding will appear in the unit. This way you can control the temperature of the engine and influence it with external heat sources. Check the box for the parameter Enable thermal port. It is assumed that the winding resistance is linearly dependent on temperature and is defined as:

where

— resistance at temperature ;
— initial resistance at the initial temperature ;
— temperature coefficient. Value for copper — 3.93e−3 1/K.

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

# ~1r' — the beginning of the output of the rotor winding
electricity

Details

Expandable three-phase port connected by the start of the rotor winding output.

Program usage name

rotor_port1

# ~2r' — the end of the rotor winding output
electricity

Details

Expandable three-phase port connected to the end of the rotor winding output.

Program usage name

rotor_port2

# 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

stator_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

stator_port2

# HA — thermal port of phase a
warm

Details

The thermal port connected to the stator winding a.

Dependencies

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

Program usage name

stator_thermal_port_a

# HB — thermal port of phase b
warm

Details

The thermal port connected to the stator winding b.

Dependencies

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

Program usage name

stator_thermal_port_b

# HC — thermal port of phase c
warm

Details

The thermal port connected to the stator winding c.

Dependencies

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

Program usage name

stator_thermal_port_c

# HAr — thermal port of the rotor phase a
warm

Details

The thermal port connected to the rotor winding a.

Dependencies

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

Program usage name

rotor_thermal_port_a

# HBr — thermal port of the rotor phase b
warm

Details

The thermal port connected to the rotor winding b.

Dependencies

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

Program usage name

rotor_thermal_port_b

# HCr — thermal port of the rotor phase c
warm

Details

The thermal port connected to the rotor winding c.

Dependencies

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

Program usage name

rotor_thermal_port_c

Output

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

Details

The vector of the output port 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 the measurement results, connect the unit to this port Induction Machine Measurement.

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 — Rated 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 — number of pairs of poles

Details

The number of pairs of poles of the machine.

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

# Parameterization unit — unit system for parameterization of a block
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 — a system of relative units.

Dependencies

Choose:

SI — measurement parameters in the SI system in the settings Impedances.
Per unit — measurement parameters in relative units in the settings Impedances.

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

# Zero sequence — the zero sequence

Details

The zero-sequence model:

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:

Enabled and Parameterization unit installed in SI — the parameter will be visible Stator zero-sequence reactance X0 in the settings Impedances.
Enabled and Parameterization unit installed on Per unit — the parameter Stator zero-sequence induction pu_L0, pu will be visible in the settings Impedances.
Turned off — the inductance parameter of the zero sequence of the stator in the settings Impedances not visible.

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

# Initialization option — initialization method
Set targets for flux variables

Details

Initialization method.

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