Engee documentation

Synchronous Machine Model 2.1

Synchronous machine with simplified transformation, simplified representation, fundamental or standard parameterization.

synchronous machine model 2 1

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:

θθ ,

where:

  • θ - electric angle.

  • - number of pole pairs.

  • θ - 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:

θθπθπθθπθπ .

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.

  • Electrical 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

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).

Nominal RMS line voltage.

Rated electrical frequency, Hz - rated electrical frequency, Hz
50 Hz (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.

Impedances

Stator d-axis mutual inductance (unsaturated) Ladu, pu - stator d-axis mutual inductance (unsaturated)
1.66 (by default) | `positive scalar'.

Unsaturated mutual inductance in the stator axis. This parameters must be greater than 0.

Dependencies

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

Stator q-axis mutual inductance (unsaturated) Laqu, pu - stator q-axis mutual inductance (unsaturated)
1.61 (by default) | `positive scalar'.

Unsaturated mutual inductance along the stator axis. This parameters must be greater than 0.

Dependencies

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

Stator leakage inductance Ll, pu - stator leakage inductance
0.15 (by default) | `positive scalar'.

Stator leakage inductance. This parameter must be greater than 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 (by default) | `positive scalar'.

Stator resistance. This parameters must be greater than 0.

Rotor field circuit inductance Lfd, pu - rotor field circuit inductance
0.165 (by default) | `positive scalar'.

Rotor field circuit inductance. This parameters must be greater than 0.

Rotor field circuit resistance Rfd, pu - rotor field circuit resistance
0.0006 (by default) | `positive scalar'.

Rotor field circuit resistance. This parameter must be greater than 0.

Dependencies

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

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

Winding inductance of one damper winding in the rotor axis. This parameters must be greater than 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 - resistance of one damper winding on rotor d-axis
0.0284 (by default) | positive scalar

Resistance of one damper winding in the rotor axis . This parameters must be greater than 0.

Dependencies

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

Rotor q-axis damper winding 1 inductance L1q, pu - inductance of one damper winding on rotor q-axis
0.1066 (by default) | `positive scalar `

Winding inductance of one damper winding in the rotor axis . This parameters must be greater than 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 - resistance of one damper winding on rotor q-axis
0.0650 (by default) | positive scalar

Winding resistance of one damper winding in the rotor axis . This parameters must be greater than 0.

Dependencies

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

Stator leakage reactance Xl, pu - stator leakage reactance
0.15 (by default) | `positive scalar'.

Stator leakage reactance. This parameter must be greater than 0.

Dependencies

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

d-axis synchronous reactance Xd, pu - d-axis synchronous reactance
1.81 (by default) | `positive scalar'.

Synchronous reactance in the axis . This parameter must be greater than 0.

Dependencies

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

q-axis synchronous reactance Xq, pu - q-axis synchronous reactance
1.76 (by default) | `positive scalar'.

Synchronous reactance in the axis . This parameter must be greater than 0.

Dependencies

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

d-axis transient reactance Xd', pu - d-axis transient reactance
0.3 (by default) | `positive scalar'.

Transient reactance on axis . This parameters must be greater than 0.

Dependencies

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

d-axis subtransient reactance Xd", pu - d-axis subtransient reactance
0.23 (By default) | `positive scalar'.

Super transient reactance on axis . This parameter must be greater than 0.

Dependencies

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

q-axis subtransient reactance Xq", pu - q-axis subtransient reactance
0.25 (by default) | `positive scalar'.

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.