Synchronous machine with simplified transformation, simplified representation, fundamental or standard parameterization.
Description
Unit Synchronous Machine Model 2.1 represents a synchronous machine with one field winding and a damper on the axes (longitudinal) and (transverse). Fundamental or standard parameters are used to characterise the machine. This block contains a Park-Gorev transformation, so use it only for balanced operation.
Synchronous machine equations
The equations of a synchronous machine are written relative to a rotating reference frame, which is defined as follows:
,
where:
- electric angle.
- number of pole pairs.
- rotor angle (mechanical angle).
The Park-Gorev transformation maps the equations of a synchronous machine into a rotating coordinate system with respect to the electric angle. It is written as follows:
.
The Park-Gorev transformation is written in relative units. The stator stress equations are as follows:
и
Where:
and are the voltages along the d and q axes behind the supertransient reactance.
- of the stator resistance.
and - stator currents along the d and q axes, determined by the formula:
.
, and are the stator currents flowing from port ~ to neutral n.
and are the supertransient reactances along the d and q axes.
and - stator voltages along the d and q axes, determined by the formula:
.
where , and are the stator voltages measured between port ~ and neutral n.
The rotor voltage equation is defined by the formula:
,
where:
- resistance of the rotor excitation circuit.
- field circuit current in relative units usage of the synchronous machine model in the reciprocal system of relative units.
- field circuit voltage in relative units usage of the synchronous machine model in reciprocal relative units.
The voltage behind the transient reactance is described by the formula:
,
,
и
,
Where:
and are the supertransient reactances along the d and q axes.
and is the transient time constant of the open-circuit excitation circuit along the d and q axes.
- excitation circuit voltage in relative units with usage of the exciter model in a non-reciprocal system of relative units.
- transient reactance on the d axis.
- voltage behind the transient reactance.
- time constant of the excitation circuit on the d axis.
The rotor torque is determined by the expression:
These equations do not describe the parameters that can be set in the dialogue box.
Ports
Output
o - machine measurements in relative units vector
A port that outputs the current values of machine variables; a vector of multiple elements. The elements of a vector are:
Field winding voltage, .
Field winding current, .
Electromagnetic torque, .
Rotor speed, .
Stator axis voltage, , .
Stator axis voltage , .
Stator zero sequence voltage, - this element is provided for compatibility with other machine models. Its value is always zero.
Stator axis current , .
Stator axis current, .
Stator zero sequence current - this element is provided for compatibility with other machine models. Its value is always zero.
fd+ - positive contact of the field winding electricity
Electrical port associated with the positive contact of the field winding.
fd- is the negative contact of the field winding electricity
Electrical port associated with the negative contact of the field winding.
R is the rotor of the machine `rotational mechanics
A mechanical port of rotation associated with the rotor of a machine.
C - the machine housing `rotational mechanics
A mechanical port of rotation associated with the machine housing.
~ - stator windings electricity
Expandable three-phase port connected to the stator windings.
n - neutral electricity
An electrical port associated with the neutral of a star-connected winding. This port is provided to ensure interface compatibility with existing machine models. Voltage and current on this port are ignored.
Parameters
Main
Rated apparent power, VA - rated apparent power `555e6 V*A (by default)
Rated power.
Rated voltage, V - rated line voltage 24e3 V (by default).
The rated electrical frequency for which the rated total power is specified.
Number of pole pairs - number of pole pairs 1 (By default).
Number of pole pairs of the machine.
Specify field circuit input required to produce rated terminal voltage at no load by - method of specifying the field circuit excitation required to produce rated terminal voltage at no load by Field circuit current (default) | Field circuit voltage
Field circuit parameterization method. The following options are possible:
Field circuit voltage - specifying the field circuit voltage.
Field circuit current to set the field circuit current. 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 - field circuit current `1300 A (by default).
The field circuit current that produces the rated voltage across the machine contacts.
Dependencies
This parameter is used if the Specify field circuit input required to produce rated terminal voltage at no load by parameter is set to Field circuit current.
Field circuit voltage, V - field circuit voltage 92.9 V (By default).
The field circuit voltage that produces the rated voltage across the machine contacts.
Dependencies
This parameter is used when the Specify field circuit input required to produce rated terminal voltage at no load by parameter is set to Field circuit voltage.
Rotor angle definition - reference point for rotor angle measurement Angle between the a-phase magnetic axis and the d-axis (By default)| Angle between the a-phase magnetic axis and the q-axis.
The reference point for measuring the rotor angle.
By default, the rotor axis and the stator phase magnetic axis coincide when the rotor rotation angle is zero.
Another value that can be selected for this parameter is Angle between the a-phase magnetic axis and the q-axis. When this value is selected, the rotor axis and the a-phase magnetic axis of the stator coincide when the rotor rotation angle is zero.
Specify parameterization type by - parameterization method Fundamental parameters (By default) | Standard parameters.
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 - standard parameters are visible in both Impedances and Time Constants.
This parameter affects the visibility of Time Constant settings and parameters in Impedances.
Super transient reactance on the axis . This parameters must be greater than 0.
Dependencies
This parameter is used if the Specify parameterization by parameter is set to Standard parameters.
Time Constants
Specify d-axis time constant - method of specifying the d-axis time constant Open circuit (default) | Short circuit
Select between Open circuit and Short circuit.
Setting this parameter affects the visibility of the time constant parameters of the axis .
d-axis transient open-circuit time constant Td0', s is the transient open-circuit time constant of the d-axis excitation circuit 8 s (by default) | positive scalar
Transient open-circuit excitation transient time constant. This parameters should be:
Greater than 0.
Greater 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 - transient time constant of the closed excitation circuit in the d-axis 1.3260 s (by default) | `positive scalar'.
Transient time constant of the closed-loop excitation circuit in the axis . This parameters should be:
Greater than 0.
Greater than d-axis subtransient short-circuit, .
Dependencies
This parameter is used when the Specify d-axis transient time constant parameter is set to Short circuit.
d-axis subtransient open-circuit Td0", s is the d-axis transient open-circuit open-circuit time constant 0.03 s (by default) | `positive scalar'.
Super transient time constant of the open-circuit excitation circuit in the axis . This parameter must be greater than 0.
Dependencies
This parameter is used if the Specify d-axis transient time constant parameters are set to Open circuit.
d-axis subtransient short-circuit Td", s is the super transient time constant of the d-axis closed excitation circuit 0.0230 s (by default) | `positive scalar'.
Super transient time constant of the closed-loop excitation circuit in the axis . This parameter must be greater than 0.
Dependencies
This parameter is used if the Specify d-axis transient time constant parameters are set to Short circuit.
Specify q-axis transient time constant - set the q-axis transient time constant Open circuit (by default)| Short circuit.
Select between Open circuit and Short circuit.
The setting of this parameter affects the visibility of the time constant parameters in the axis.
q-axis subtransient open-circuit Tq0", s - super transient open-circuit time constant in q-axis excitation circuit 0.07 s (by default) | positive scalar
Super transient time constant of the open-circuit excitation circuit in the axis . This parameter must be greater than 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 - super transient time constant of closed excitation circuit on q-axis 0.0269 s (by default) | `positive scalar'.
Super transient time constant of the closed excitation circuit in the axis . This parameter must be greater than 0.
Dependencies
This parameter is used if the Specify q-axis transient time constant parameters are set to Short circuit.