Synchronous Machine Model 2.1

A synchronous machine with simplified transformation, simplified representation, fundamental or standard parameterization.

blockType: AcausalElectricPowerSystems.Electromechanical.Synchronous.MachineModel2p1

Path in the library:

/Physical Modeling/Electrical/Electromechanical/Synchronous/Synchronous Machine Model 2.1

Description

Block Synchronous Machine Model 2.1 It is a synchronous machine with one excitation winding and a damper on the axes. (longitudinal) and (transverse). Fundamental or standard parameters are used to determine the characteristics of the machine. This block contains the Park–Gorev transformation, so use it only for balanced work.

Synchronous machine equations

The equations of a synchronous machine are written with respect to a rotating frame of reference, which is defined as follows:

where:

— electric angle.
— the number of pairs of poles.
— the angle of the rotor (mechanical angle).

The Park–Gorev transformation maps the equations of a synchronous machine into a rotating coordinate system relative to an electric angle. It is written as follows:

The Park–Gorev transformation is written in relative units. The stator stress equations are as follows:

and

where:

and — stresses along the d and q axes due to hyperconversion reactivity.
— stator resistance.
and — stator currents along the axes d and q, determined by the formula:

, and — stator currents flowing from port ~ to neutral n.
and — hyperconversion reactivity along the d and q axes.
and — stator voltages along the axes d and q, determined by the formula:

where , and — stator voltages measured between port ~ and neutral n.

The rotor voltage equation is determined by the formula:

where:

— resistance of the rotor excitation circuit.
— the current of the excitation circuit in relative units using a synchronous machine model in an inverse system of relative units.
— the voltage of the excitation circuit in relative units using a synchronous machine model in an inverse system of relative units.

The voltage behind the transient reactance is described by the formula:

and

where:

and — superconvertible reactants along the d and q axes.
and is the hyper—transient time constant of the open excitation circuit along the d and q axes.
— the voltage of the excitation circuit in relative units using the exciter model in a non-reciprocal system of relative units.
— transient reactivity along the d axis.
— the voltage behind the transient reactivity.
— the time constant of the excitation circuit along the d axis.

The torque of the rotor is determined by the expression:

These equations do not describe the parameters that can be set in the dialog box.

Ports

Output

o — machine measurements in relative units of
vector

A port that outputs the current values of the machine’s variables; a vector of several elements. Vector elements:

Voltage of the excitation winding, .
Field winding current, .
The electromagnetic moment, .
Rotor speed, .
Stator voltage along the axis , .
Stator voltage along the axis , .
Voltage of the zero sequence of the stator, — This element is provided for compatibility with other car models. Its value is always zero.
Current along the axis the stator, .
Current along the axis the stator, .
Stator zero sequence current — This element is provided for compatibility with other car models. Its value is always zero.
Electric angle of the rotor, .

To connect to this port, use the block Simplified Synchronous Machine Measurement.

Non-directional

fd+ — positive contact of the field winding
electricity

An electrical port connected to the positive contact of the excitation winding.

fd− — negative contact of the field winding
electricity

An electrical port connected to the negative contact of the excitation winding.

R — machine rotor
rotational mechanics

A mechanical rotation port connected to the machine’s rotor.

C — machine body
rotational mechanics

A mechanical rotation port connected to the machine body.

~ — stator windings
electricity

Expandable three-phase port connected to the stator windings.

n — neutral pass:Q[ ] electricity

An electrical port connected to the neutral of the winding connected by a star. This port is provided to ensure interface compatibility with existing machine models. The voltage and current on this port are ignored.

Parameters

Main

Rated apparent power, VA — rated total power
555e6 In*A (default)

Rated power.

Rated voltage, V — rated line voltage
24E3 V (default)

The nominal RMS line voltage.

Rated electrical frequency, Hz — rated electrical frequency, Hz
50 Hz (default)

The rated electrical frequency for which the rated total power is specified.

Number of pole pairs — number of pole pairs
1 (default)

The number of pairs of poles of the machine.

Specify field circuit input required to produce rated terminal voltage at no load by — a method for setting the excitation required to obtain the rated voltage in the absence of load
Field circuit current (default) | Field circuit voltage

Method of parameterization of the excitation circuit. The following options are possible:

Field circuit voltage — setting the voltage of the excitation circuit.
Field circuit current — setting the current of the excitation circuit. This method is used by default.

This parameter affects the visibility of the Field circuit voltage and Field circuit current parameters.

Field circuit current, A is the current of the pass excitation circuit:q[ ] 1300 A (default)

The current of the excitation circuit that creates the rated voltage at the contacts of the machine.

Dependencies

This parameter is used if the parameter Specify field circuit input required to produce rated terminal voltage at no load by is set to Field circuit current.

Field circuit voltage, V is the voltage of the pass excitation circuit:q[ ] 92.9 V (default)

The voltage of the excitation circuit that creates the rated voltage at the contacts of the machine.

Dependencies

This parameter is used if the parameter Specify field circuit input required to produce rated terminal voltage at no load by is set to Field circuit voltage.

Rotor angle definition is a reference point for measuring the rotation angle of the rotor
Angle between the a-phase magnetic axis and the d-axis (default)|Angle between the a-phase magnetic axis and the q-axis

A reference point for measuring the rotation angle of the rotor.

When selecting the default value, the axis rotors and magnetic phase axis The stators match when the rotation angle of the rotor is zero.

Another value that can be selected for this parameter, — Angle between the a-phase magnetic axis and the q-axis. When selecting this value, the axis rotors and magnetic phase axis The stators match when the rotation angle of the rotor is zero.

Specify parameterization type by — pass parameterization method:q[ ] Fundamental parameters (by default) | Standard parameters

The parameterization method. The following options are possible:

Fundamental parameters — The fundamental parameters are visible in the Impedances section, but the Time Constants settings are not visible.
Standard parameters — The standard parameters are visible in both Impedances and Time Constants.

This parameter affects the visibility of the Time Constant settings and the Impedances settings.

Impedances

Stator d-axis mutual induction (unsaturated) Ladu, pu — mutual inductance of the d-axis of the stator (unsaturated)
1.66 (default) | positive scalar

Unsaturated mutual inductance along the axis the stator. This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Stator q-axis mutual induction (unsaturated) Laqu, pu — mutual inductance of the q axis of the stator (unsaturated)
1.61 (default) | positive scalar

Unsaturated mutual inductance along the axis the stator. This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Stator leakage induction Ll, pu — stator leakage inductance
0.15 (default) | positive scalar

The stator scattering inductance. This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Stator resistance Ra, pu — stator resistance
0.003 (default) | positive scalar

Stator resistance. This parameter should be higher. 0.

Rotor field circuit induction Lfd, pu — inductance of the rotor excitation circuit
0.165 (default) | positive scalar

The inductance of the rotor excitation circuit. This parameter should be higher. 0.

Rotor field circuit resistance Rfd, pu — resistance of the rotor excitation circuit
0.0006 (default) | positive scalar

Resistance of the rotor excitation circuit. This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Rotor d-axix damper winding 1 induction L1d, pu — winding inductance of one damper along the d axis of the rotor
0.1713 (default) | positive scalar

The inductance of the winding of one damper along the axis the rotor. This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Rotor d-axix damper winding 1 resistance R1d, pu — winding resistance of one damper along the d axis of the rotor
0.0284 (default) | positive scalar

Winding resistance of one damper along the axis the rotor. This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Rotor q-axis damper winding 1 induction L1q, pu — winding inductance of one damper along the q axis of the rotor
0.1066 (default) | positive scalar

The inductance of the winding of one damper along the axis the rotor. This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Rotor q-axix damper winding 1 resistance R1q, pu — winding resistance of one damper along the q axis of the rotor
0.0650 (default) | positive scalar

Winding resistance of one damper along the axis the rotor. This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Stator leakage reactance Xl, pu — reactive scattering of the stator
0.15 (default) | positive scalar

Reactive scattering of the stator. This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Standard parameters.

d-axis synchronous reactivity Xd, pu — synchronous reactivity along the d-axis
1.81 (default) | positive scalar

Synchronous axis reactivity . This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Standard parameters.

q-axis synchronous reactivity Xq, pu — synchronous reactivity along the q axis
1.76 (default) | positive scalar

Synchronous axis reactivity . This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Standard parameters.

d-axis transient reactivity Xd', pu — transient reactivity along the d-axis
0.3 (default) | positive scalar

Transient reactivity along the axis . This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Standard parameters.

d-axis subtransient reactivity Xd", pu — hyper-transitive reactivity along the d-axis
0.23 (default) | positive scalar

Hyperconversion reactivity along the axis . This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Standard parameters.

q-axis subtransient reactivity Xq", pu — hyper-transitive reactivity along the q axis
0.25 (default) | positive scalar

Hyperconversion reactivity along the axis . This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Standard parameters.

Time Constants

Specify d-axis time constant — a way to set the time constant of the d-axis
Open circuit (default) | Short circuit

Choose between Open circuit and Short circuit.

Setting this parameter affects the visibility of the axis time constant parameters. .

d-axis transient open-circuit Td0', s is the transient time constant of the open-circuit excitation along the d pass axis:q[ ] 8 s (default) | positive scalar

The transient time constant of an open excitation circuit. This parameter should be:

More 0.
More than d-axis subtransient open-circuit, Td0".

Dependencies

This parameter is used if the Specify d-axis transient time constant parameter is set to Open circuit.

d-axis transient short-circuit Td', s is the transient time constant of a closed excitation circuit along the d pass axis:q[ ] 1.3260 s (default) | positive scalar

Transient time constant of a closed excitation circuit along the axis . This parameter should be:

More 0.
More than d-axis subtransient short-circuit, .

Dependencies

This parameter is used if the Specify d-axis transient time constant parameter is set to Short circuit.

d-axis subtransient open-circuit Td0", s is the super—transient time constant of the open-circuit excitation along the d pass axis:q[ ] 0.03 s (default) | positive scalar

The hyper-transient time constant of an open-circuit excitation along the axis . This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify d-axis transient time constant parameter is set to Open circuit.

d-axis subtransient short-circuit Td", s is the superconvertible time constant of a closed excitation circuit along the d pass axis:q[ ] 0.0230 s (default) | positive scalar

The super-transient time constant of a closed excitation circuit along the axis . This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify d-axis transient time constant parameter is set to Short circuit.

Specify q-axis time constant — adjust the time constant along the q pass axis:q[ ] Open circuit (by default)| Short circuit

Choose between Open circuit and Short circuit.

Setting this parameter affects the visibility of the time constant parameters along the axis .

q-axis subtransient open-circuit Tq0", s is the hyper—transitive time constant of the open-circuit excitation along the q pass axis:q[ ] 0.07 s (default) | positive scalar

The hyper-transient time constant of an open-circuit excitation along the axis . This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify q-axis transient time constant parameter is set to Open circuit.

q-axis subtransient short-circuit Tq", s is the hyper—transitive time constant of a closed excitation circuit along the q pass axis:q[ ] 0.0269 s (default) | positive scalar

The super-transient time constant of a closed excitation circuit along the axis . This parameter should be higher. 0.

Dependencies

This parameter is used if the Specify q-axis transient time constant parameter is set to Short circuit.