Simplified Synchronous Machine

A simplified synchronous machine with an EMF.

blockType: AcausalElectricPowerSystems.Electromechanical.Synchronous.SimplifiedMachine

Path in the library:

/Physical Modeling/Electrical/Electromechanical/Synchronous/Simplified Synchronous Machine

Description

Block Simplified Synchronous Machine simulates a simplified synchronous machine with a voltage source that represents an electromotive force (EMF). You can specify the internal active resistance and inductance with parameters in relative units or in SI units.

Equivalent circuits of a simplified synchronous machine for the longitudinal axis, transverse axis, and zero sequence:

simplified synchronous machine 1 1

simplified synchronous machine 2 1

simplified synchronous machine 3 1

Flow coupling

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

where

— electric angle;
— 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 frame of reference relative to an electric angle. It is written as follows:

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

where

, , and — stresses along the axes , and null sequences, defined as:

;
, , and — internal voltage sources in relative units, defined as:

,

,

;
— the amplitude of the EMF in O.E.;
, , and are defined as follows:

;
, , and — stator voltages measured from port ~ to neutral n;
— base frequency in radians;
, , and — flow coupling of axes , and the zero sequence;
— the speed of rotation of the rotor in oe.;
— active resistance of the stator;
, , and — stator winding currents along the axis , and zero-sequence stator currents, defined as:

;
, , and — stator currents flowing out of port ~.

The flow couplings of the stator are equal:

where — stator scattering inductance.

The power equation of a simplified synchronous machine in OE is as follows:

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

Mechanical rotary port, corresponds to the rotor of the machine.

Program usage name

rod_flange

# C — machine body
rotational mechanics

Details

Mechanical rotary port, corresponds to the machine body.

Program usage name

case_flange

# ~ — stator winding
electricity

Details

Three-phase electrical port, corresponds to the stator windings.

Program usage name

port

# n — neutral
electricity

Details

The electrical port corresponds to the neutral point of the stator winding.

Program usage name

n

Output

# o — current values of variables, O.E.
vector

Details

An output port that outputs the current values of the machine’s variables in OE; a vector of several elements. Vector elements:

EMF of phase A,
EMF of phase b,
EMF of phase C,
The electromagnetic moment,
Rotor speed,
Stator voltage along the axis ,
Stator voltage along the axis ,
Voltage of the zero sequence of the stator,
Current along the d axis of the stator,
Current along the q axis of the stator,
Stator zero sequence current
Electric angle of the rotor,

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

Data types	`Float64`
Complex numbers support	No

Input

# E_si — amplitude of the internal generated voltage (phase-neutral)
vector

Details

The input port of the signal associated with the amplitude of the internal generated voltage (phase-neutral); a vector of three elements.

Dependencies

To use this port, set the parameter Parameterization unit meaning SI.

Data types	`Float64`
Complex numbers support	No

# E_pu — the amplitude of the internal generated voltage in relative voltage units
vector

Details

The port is associated with the amplitude in relative units of the internal generated voltage in the form of a vector.

Dependencies

To use this port, set the parameter Parameterization unit meaning Per unit.

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 — RMS 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 | kHz | MHz | GHz

Details

The rated electrical frequency at which the rated total power is indicated.

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	`2`
Program usage name	`N_pole_pairs`
Evaluatable	Yes

# Parameterization unit — units of measurement for block parameters
Per unit | SI

Details

Units of measurement for block parameters:

SI;
Per unit.

Values	`Per unit` \| `SI`
Default value	`SI`
Program usage name	`parameter_units`
Evaluatable	No

# Internal resistance, pu — internal active resistance

Details

Internal resistance.

Dependencies

To use this parameter, set for the parameter Parameterization unit meaning Per unit.

Default value	`0.05`
Program usage name	`R_pu`
Evaluatable	Yes

# Internal inductance, pu — internal inductance

Details

Internal inductance.

Dependencies

To use this parameter, set for the parameter Parameterization unit meaning Per unit.

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

# Internal resistance — internal active resistance
Ohm | mOhm | kOhm | MOhm | GOhm

Details

Internal active resistance.

Dependencies

To use this parameter, set for the parameter Parameterization unit meaning SI.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.0519 Ohm`
Program usage name	`R_si`
Evaluatable	Yes

# Internal inductance — internal inductance
H | nH | uH | mH

Details

Internal inductance.

Dependencies

To use this parameter, set for the parameter Parameterization unit meaning SI.

Units	`H` \| `nH` \| `uH` \| `mH`
Default value	`0.00082589 H`
Program usage name	`L_si`
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

Examples

Speed control of a simplified synchronous generator