Synchronous Machine Model 2.1

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

blockType: AcausalElectricPowerSystems.Electromechanical.Synchronous.MachineModel2p1

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/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:

where

and — stresses along the axes and for hyper-transient reactivity;
— stator resistance;
and — stator currents along the axes and , defined by the formula:

;
, and — stator currents flowing from port ~ to neutral n;
and — hyperconversion reactivity along the axes and ;
and — stator voltage along the axes and , defined 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:

where

and — superconvertible reactants along the axes and ;
and — the superconvertible time constant of the open excitation circuit along the axes and ;
— 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 axis ;
— voltage behind transient reactivity;
— the time constant of the excitation circuit along the 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.

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

# R — the rotor of the machine
rotational mechanics

Details

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

Program usage name

rod_flange

# C — machine body
rotational mechanics

Details

A mechanical rotation port connected to the machine body.

Program usage name

case_flange

# ~ — stator windings
electricity

Details

Expandable three-phase port connected to the stator windings.

Program usage name

port

# n — neutral
electricity

Details

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.

Program usage name

n

# fd+ — positive contact of the excitation winding
electricity

Details

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

Program usage name

fd_p

# fd− — negative contact of the excitation winding
electricity

Details

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

Program usage name

fd_n

Output

# o — machine measurements in relative units
vector

Details

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.

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 power.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`555e6 V*A`
Program usage name	`S_rated`
Evaluatable	Yes

# Rated voltage — Rated line voltage
V | uV | mV | kV | MV

Details

The nominal RMS line voltage.

Units	`V` \| `uV` \| `mV` \| `kV` \| `MV`
Default value	`24e3 V`
Program usage name	`V_rated`
Evaluatable	Yes

# Rated electrical frequency — rated electrical frequency, Hz
Hz | kHz | MHz | GHz

Details

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

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

# 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 a load
Field circuit voltage | Field circuit current

Details

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 parameters Field circuit voltage and Field circuit current.

Values	`Field circuit voltage` \| `Field circuit current`
Default value	`Field circuit current`
Program usage name	`field_circuit_parameterization`
Evaluatable	No

# Field circuit current — excitation circuit current
A | pA | nA | uA | mA | kA | MA

Details

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

Dependencies

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

Units	`A` \| `pA` \| `nA` \| `uA` \| `mA` \| `kA` \| `MA`
Default value	`1300.0 A`
Program usage name	`I_fd_base`
Evaluatable	Yes

# Field circuit voltage — voltage of the excitation circuit
V | uV | mV | kV | MV

Details

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

Dependencies

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

Units	`V` \| `uV` \| `mV` \| `kV` \| `MV`
Default value	`92.95 V`
Program usage name	`E_fd_base`
Evaluatable	Yes

# Rotor angle definition — a reference point for measuring the rotation angle of the rotor
Angle between the a-phase magnetic axis and the q-axis | Angle between the a-phase magnetic axis and the d-axis

Details

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.

Values	`Angle between the a-phase magnetic axis and the q-axis` \| `Angle between the a-phase magnetic axis and the d-axis`
Default value	`Angle between the a-phase magnetic axis and the d-axis`
Program usage name	`axes_parameterization`
Evaluatable	No

# Specify parameterization type by — parameterization method
Fundamental parameters | Standard parameters

Details

The parameterization method. The following options are possible:

Fundamental parameters — the fundamental parameters are visible in the section Impedances (impedance), but the settings are Time Constants (time constants) are not visible.
Standard parameters — the standard parameters are also visible in Impedances, and in Time Constants.

This parameter affects the visibility of the settings. Time Constants and the parameters in Impedances.

Values	`Fundamental parameters` \| `Standard parameters`
Default value	`Fundamental parameters`
Program usage name	`parameterization_option`
Evaluatable	No

Impedances

# Stator d-axis mutual inductance (unsaturated) Ladu — mutual inductance of the d axis of the stator (unsaturated)

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Fundamental parameters.

Default value	`1.66`
Program usage name	`L_ad`
Evaluatable	Yes

# Stator q-axis mutual inductance (unsaturated) Laqu — mutual inductance of the q axis of the stator (unsaturated)

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Fundamental parameters.

Default value	`1.61`
Program usage name	`L_aq`
Evaluatable	Yes

# Stator leakage inductance Ll — stator scattering inductance

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Fundamental parameters.

Default value	`0.15`
Program usage name	`L_l`
Evaluatable	Yes

# Stator resistance Ra — stator resistance

Details

Stator resistance. This parameter should be higher. 0.

Default value	`0.003`
Program usage name	`R_a`
Evaluatable	Yes

# Rotor field circuit inductance Lfd — inductance of the rotor excitation circuit

Details

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

Default value	`0.165`
Program usage name	`L_fd`
Evaluatable	Yes

# Rotor field circuit resistance Rfd — resistance of the rotor excitation circuit

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Fundamental parameters.

Default value	`0.0006`
Program usage name	`R_fd`
Evaluatable	Yes

# Rotor d-axis damper winding 1 inductance L1d — the winding inductance of one damper along the d axis of the rotor

Details

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 for the parameter Specify parameterization type by the value is set Fundamental parameters.

Default value	`0.1713`
Program usage name	`L_1d`
Evaluatable	Yes

# Rotor d-axis damper winding 1 resistance R1d — winding resistance of one damper along the d axis of the rotor

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Fundamental parameters.

Default value	`0.0284`
Program usage name	`R_1d`
Evaluatable	Yes

# Rotor q-axis damper winding 1 inductance L1q — the winding inductance of one damper along the q axis of the rotor

Details

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 for the parameter Specify parameterization type by the value is set Fundamental parameters.

Default value	`0.1066`
Program usage name	`L_1q`
Evaluatable	Yes

# Rotor q-axis damper winding 1 resistance R1q — winding resistance of one damper along the q axis of the rotor

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Fundamental parameters.

Default value	`0.065`
Program usage name	`R_1q`
Evaluatable	Yes

# Stator leakage reactance Xl — reactive scattering of the stator

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Standard parameters.

Default value	`0.15`
Program usage name	`X_l`
Evaluatable	Yes

# d-axis synchronous reactance Xd — synchronous reactivity on the d axis

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Standard parameters.

Default value	`1.81`
Program usage name	`X_d`
Evaluatable	Yes

# q-axis synchronous reactance Xq — synchronous reactivity along the q axis

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Standard parameters.

Default value	`1.76`
Program usage name	`X_q`
Evaluatable	Yes

# d-axis transient reactance Xd' — transient reactivity along the d axis

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Standard parameters.

Default value	`0.3`
Program usage name	`X_p_d`
Evaluatable	Yes

# d-axis subtransient reactance Xd" — hyperconversion reactivity along the d axis

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Standard parameters.

Default value	`0.23`
Program usage name	`X_pp_d`
Evaluatable	Yes

# q-axis subtransient reactance Xq" — hyperconversion reactivity along the q axis

Details

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

Dependencies

This parameter is used if for the parameter Specify parameterization type by the value is set Standard parameters.

Default value	`0.25`
Program usage name	`X_pp_q`
Evaluatable	Yes

Time Constants

# Specify d-axis time constant — the method of setting the time constant of the d axis
Open circuit | Short circuit

Details

Choose between Open circuit and Short circuit.

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

Values	`Open circuit` \| `Short circuit`
Default value	`Open circuit`
Program usage name	`option_d`
Evaluatable	No

# d-axis transient open-circuit Td0' — transient time constant of an open excitation circuit along the d axis
s | ns | us | ms | min | hr | d

Details

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

More 0.
More than d-axis transient open-circuit Td0".

Dependencies

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

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`8.0 s`
Program usage name	`T_p_d0`
Evaluatable	Yes

# d-axis transient open-circuit Td0" — hyper-transient time constant of an open excitation circuit along the d axis
s | ns | us | ms | min | hr | d

Details

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

Dependencies

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

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`0.03 s`
Program usage name	`T_pp_d0`
Evaluatable	Yes

# d-axis transient short-circuit Td' — transient time constant of a closed excitation circuit along the d axis
s | ns | us | ms | min | hr | d

Details

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

More 0.
More than d-axis transient short-circuit Td".

Dependencies

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

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`1.326 s`
Program usage name	`T_p_d`
Evaluatable	Yes

# d-axis transient short-circuit Td" — hyperconversion time constant of a closed excitation circuit along the d axis
s | ns | us | ms | min | hr | d

Details

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 for the parameter Specify d-axis time constant the value is set Short circuit.

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`0.023 s`
Program usage name	`T_pp_d`
Evaluatable	Yes

# Specify q-axis time constant — adjust the time constant along the q axis
Open circuit | Short circuit

Details

Choose between Open circuit and Short circuit.

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

Values	`Open circuit` \| `Short circuit`
Default value	`Open circuit`
Program usage name	`option_q`
Evaluatable	No

# q-axis subtransient open-circuit Tq0" — hyper-transient time constant of an open excitation circuit along the q axis
s | ns | us | ms | min | hr | d

Details

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 for the parameter Specify q-axis time constant the value is set Open circuit.

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`0.07 s`
Program usage name	`T_pp_q0`
Evaluatable	Yes

# q-axis subtransient short-circuit Tq" — the hyper-transient time constant of a closed excitation circuit along the q axis
s | ns | us | ms | min | hr | d

Details

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 for the parameter Specify q-axis time constant the value is set Short circuit.

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`0.0269 s`
Program usage name	`T_pp_q`
Evaluatable	Yes

Initial Conditions

# Initialization option — choosing initialization
Set targets for rotor angle and Park’s transform variables | Set real power, reactive power, terminal voltage, and terminal phase

Details

The method of setting parameter and variable values at the beginning of the simulation:

Set real power, reactive power, terminal voltage, and terminal phase — nominal parameters are set independently of the connected network.
Set targets for rotor angle and Park’s transform variables — priority and initial target values for block variables are set before simulation using settings Initial Targets.

Dependencies

If you set this parameter to:

Set targets for rotor angle and Park’s transform variables — the parameter settings section becomes visible Initial Targets.
Set real power, reactive power, terminal voltage, and terminal phase — the parameter settings section becomes visible Initial Conditions.

Values	`Set targets for rotor angle and Park’s transform variables` \| `Set real power, reactive power, terminal voltage, and terminal phase`
Default value	`Set real power, reactive power, terminal voltage, and terminal phase`
Program usage name	`initialization_option`
Evaluatable	No

# Terminal voltage magnitude — the initial voltage amplitude at the terminals
V | uV | mV | kV | MV

Details

The initial voltage amplitude at the terminals.

Dependencies

To use this parameter, set for the parameter Initialization option meaning Set real power, reactive power, terminal voltage, and terminal phase.

Units	`V` \| `uV` \| `mV` \| `kV` \| `MV`
Default value	`24e3 V`
Program usage name	`V_mag_start`
Evaluatable	Yes

# Terminal voltage angle — the initial phase of terminal voltage
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

The initial phase of the terminal voltage.

Dependencies

To use this parameter, set for the parameter Initialization option meaning Set real power, reactive power, terminal voltage, and terminal phase.

Units	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`0 deg`
Program usage name	`V_ang_start`
Evaluatable	Yes

# Active power generated — generated active power
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

Generated active power.

Dependencies

To use this parameter, set for the parameter Initialization option meaning Set real power, reactive power, terminal voltage, and terminal phase.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`500e6 V*A`
Program usage name	`P_t_start`
Evaluatable	Yes

# Reactive power generated — generated reactive power
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

Generated reactive power.

Dependencies

To use this parameter, set for the parameter Initialization option meaning Set real power, reactive power, terminal voltage, and terminal phase.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`0 V*A`
Program usage name	`Q_t_start`
Evaluatable	Yes