Simplified Synchronous Machine
Simplified synchronous machine with EMF.
Description
The Simplified Synchronous Machine block models a simplified synchronous machine with a voltage source that represents the electromotive force (EMF). You can specify the internal active resistance and inductance with parameters in relative units or SI units.
Equivalent diagrams of a simplified synchronous machine for longitudinal axis, transverse axis and zero sequence:
Potococeles
The simplified equations of a synchronous machine are written with respect to a rotating reference frame, which is defined as follows:
,
where:
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- electric angle.
-
- number of pole pairs.
-
- rotor angle (mechanical angle).
The Park-Gorev transformation maps the equations of a synchronous machine into a rotating reference frame with respect to the electric angle. It is written as follows:
The Park-Gorev transformation is written in relative units. The stress equations are as follows:
Where:
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, , and are the d, q and zero-sequence axis voltages defined as:
-
, , and - internal voltage sources in relative units, defined as:
-
- EMF amplitude in o.u.
-
, , and are defined as follows:
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, , and are the stator voltages measured from port ~ to neutral n.
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- is the base frequency in radians.
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, , and - d, q and zero sequence axis flux-couplings.
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- rotor rotation speed in o.u.
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- stator active resistance.
-
, , and - stator winding currents along the d-axis, q and zero-sequence stator currents, defined as:
-
, , and are the stator currents flowing from the ~ port.
The stator potococircuit currents are equal to:
,
Where:
-
- stator dissipation inductance.
The power equation of the simplified synchronous machine in o.c. is as follows:
.
Ports
Input
E_si - amplitude of internal generated voltage (phase-neutral)
vector
The input port of the signal associated with the amplitude of the internally generated voltage (phase-neutral); a vector of three elements.
Dependencies
To use this port, set the parameterization unit parameter to SI.
E_pu - amplitude of the internal generated voltage in relative voltage units
vector
Port associated with the amplitude in relative units of the internally generated voltage in the form of a vector.
Dependencies
To use this port, set the parameterization unit parameter to Per unit.
Output
o - current values of variables, o.u.
vector
An output port that outputs the current values of machine variables, in o.u.; a vector of multiple elements. The elements of a vector are:
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Phase EMF a,
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phase EMF b,
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phase c EMF,
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Electromagnetic torque,
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Rotor speed,
-
Stator voltage in the axis ,
-
Stator axis voltage ,
-
Stator zero sequence voltage,
-
Stator d-axis current,
-
Stator q-axis current,
-
Stator zero sequence current
-
Electrical angle of the rotor,
To connect to this port, use the block Simplified Synchronous Machine Measurement.
Non-directional
R - machine rotor
`rotational mechanics
Mechanical rotational port, corresponds to the rotor of the machine.
C - machine housing
`rotational mechanics
Mechanical rotational port, corresponds to the machine housing.
~ - stator winding
electricity
Three-phase electrical port, corresponds to the stator windings.
n - neutral
electricity
Electrical port, corresponds to the neutral point of the stator winding.
Parameters
Main
Rated apparent power, VA - rated apparent power
555e6 V*A (by default) | scalar
Rated power.
Rated voltage, V - RMS line voltage
24e3 V (by default) | scalar
Rated RMS line voltage.
Rated electrical frequency, Hz - rated electrical frequency
50 Hz (by default) | scalar.
The rated electrical frequency at which the rated total power is indicated.
Number of pole pairs - number of pole pairs
2 (By default) | scalar.
Number of pole pairs of the machine.
parameterization units - parameterization of the unit
SI (By default) | Per unit
Parameterization method of the unit. Options:
-
SI. -
`Per unit
Internal resistance, pu - internal active resistance
0.05 (by default) | scalar
Internal resistance.
Dependencies
To use this parameter, set parameterization units to `Per unit'.
Internal inductance, pu - internal inductance
0.3 (By default) | scalar.
Internal inductance.
Dependencies
To use this parameter, set parameterization units to Per unit.
Internal resistance, Ohm - internal active resistance
0.0519 Ohm (by default) | scalar.
Internal active resistance.
Dependencies
To use this parameter, set parameterization units to SI.
Internal inductance, H - internal inductance
0.3 (By default) | scalar.
Internal inductance.
Dependencies
To use this parameter, set parameterization units to SI.
Initial Conditions
Initialisation option - Initialization option
Set real power, reactive power, terminal voltage, and terminal phase (by default) | `Set targets for rotor angle and Park’s transform variables `
A way of setting the values of parameters and variables at the beginning of the simulation:
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Set real power, reactive power, terminal voltage and terminal phase- the nominal parameters are set independently of the connected network. -
Set targets for rotor angle and Park’s transform variables- the priority and initial target values for the block variables are set before the simulation using the Initial Targets settings.
Dependencies
If you set this parameter to:
-
Set targets for rotor angle and Park’s transform variables- the Initial Targets section of the parameter settings becomes visible. -
If you set
Set real power, reactive power, terminal voltage, and terminal phase- the Initial Conditions section of the parameter settings becomes visible.
Terminal voltage magnitude, V - initial terminal voltage magnitude
24e3 (by default)
Initial terminal voltage magnitude.
Dependencies
To use this parameter, set the Initialisation option to `Set real power, reactive power, terminal voltage, and terminal phase'.
Terminal voltage angle, rad - initial terminal voltage phase
0.0 (By default).
Initial phase of terminal voltage.
Dependencies
To use this parameter, set the Initialisation option to `Set real power, reactive power, terminal voltage, and terminal phase'.
Active power generated, W - active power generated
500e6 W (By default).
Active power generated.
Dependencies
To use this parameter, set the Initialisation option to Set real power, reactive power, terminal voltage, and terminal phase.
Reactive power generated, VAR - reactive power generated
0.0 (By default).
Reactive power generated.
Dependencies
To use this parameter, set the Initialisation option to Set real power, reactive power, terminal voltage, and terminal phase.
Initial Targets
Rotor angle (mechanical), rad - initial mechanical rotor angle
`0.0 (by default)
Initial mechanical angle of the rotor.
Dependencies
To use this parameter, set the Initialisation option to `Set targets for rotor angle and Park’s transform variables'.
d-axis flux linkage Ψd, pu - initial stator flux linkage in d axis
0.0 (by default)
Initial stator flux in the axis .
Dependencies
To use this parameter, set the Initialisation option to `Set targets for rotor angle and Park’s transform variables'.
q-axis flux linkage Ψq, pu - initial stator flux linkage in q axis
0.0 (by default)
Initial stator flux coefficient in the axis .
Dependencies
To use this parameter, set the Initialisation option to `Set targets for rotor angle and Park’s transform variables'.
Zero-sequence flux linkage Ψ0, pu - initial zero-sequence stator flux linkage Ψ0, pu* - initial zero-sequence stator flux linkage
0.0 (by default).
Zero-sequence stator initial flux linkage.
Dependencies
To use this parameter, set the Initialisation option to `Set targets for rotor angle and Park’s transform variables'.