Phase-Domain Synchronous Machine

Synchronous machine in phase coordinates with internal damage.

blockType: AcausalElectricPowerSystems.Electromechanical.Synchronous.PhaseDomain

Path in the library:

/Physical Modeling/Electrical/Electromechanical/Synchronous/Phase-Domain Synchronous Machine

Description

Block Phase-Domain Synchronous Machine simulates a synchronous machine in phase coordinates with internal damage. This machine can be used to simulate internal damage such as turn-to-turn short circuits, phase-to-phase short circuits, and ground faults in both the stator and field windings. The number of simultaneously selectable damage points is up to two for each of the machine windings.

To implement this model, the phase coordinate method [1] is used: the values of the machine’s inductors depend on the rotor position and saturation level. The mathematical model in phase coordinates allows you to simulate internal damage to synchronous machines. To simulate internal damage to a synchronous machine, it is necessary to calculate the self- and mutual induction of the machine windings, including faulty windings, as a function of rotor position and saturation.

The simulation of damage to the winding of the machine assumes access to the place of application of the damage. The damage point divides the winding into two parts — damaged and undamaged. Depending on the nature of the damage (short circuit to the housing, inter-turn short circuit, interphase short circuit, etc.) and the experimental conditions, the number of damage points may be several. Therefore, each damaged winding must be represented in the model by several parts — windings, as shown in the following figure.

Each one The I winding is represented in the machine as an equivalent sinusoidally distributed winding with its magnetic axis characterized by an angle , and an equivalent (effective) number of turns as shown in the picture below.

Ports

Output

# o — a port with a vector of the current values of the machine variables
vector

Details

A port with a vector of the current values of the machine variables. Connect it to the unit Synchronous Machine Measurement to output a variable as a signal.

Data types	`Float64`
Complex numbers support	No

Conserving

# ~1 — the beginning of the stator winding output
electricity

Details

Expandable three-phase port connected to the start of the stator winding output.

Program usage name

port1

# n — neutral
electricity

Details

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

Dependencies

To use this port, set the parameter Stator negative-end connections meaning Neutral point.

Program usage name

n

# A1, A2 — internal winding nodes of phase A
electricity

Details

Internal components of the phase winding .

Dependencies

To use this port, check the box Enable fault in phase A winding. Number of input ports A depends on the number of points specified in the parameter Percentage of phase A points of fault from the neutral. If a single point is specified (for example [50.0]), then only port A1 will be used; if two points are specified (for example [50.0, 75.0]), then two ports will be used: A1 and A2.

Program usage name

a1

# B1, B2 — internal winding nodes of phase B
electricity

Details

Internal components of the phase winding .

Dependencies

To use this port, check the box Enable fault in phase B winding. The number of input ports B depends on the number of points specified in the parameter Percentage of phase B points of fault from the neutral. If a single point is specified (for example [50.0]), then only port B1 will be used; if two points are specified (for example [50.0, 75.0]), then two ports will be used: B1 and B2.

Program usage name

b1

# C1, C2 — internal winding nodes of phase C
electricity

Details

Internal components of the phase winding .

Dependencies

To use this port, select the Enable fault in phase With winding checkbox. The number of input ports C depends on the number of points specified in the parameter Percentage of phase C points of fault from the neutral. If a single point is specified (for example [50.0]), then only port C1 will be used; if two points are specified (for example [50.0, 75.0]), then two ports will be used: C1 and C2.

Program usage name

c1

# F1, F2 — internal components of the excitation winding
electricity

Details

Internal components of the excitation winding.

Dependencies

To use this port, set the parameter Field excitation type meaning Electrical input port and check the box Enable fault in excitation winding. The number of input ports F depends on the number of points specified in the parameter Percentage of excitation winding points of fault from the terminal. If a single point is specified (for example [50.0]), then only port F1 will be used; if two points are specified (for example [50.0, 75.0]), then two ports will be used: F1 and F2.

Program usage name

f1

# ~2 — the end of the stator winding output
electricity

Details

Expandable three-phase port connected to the terminal end of the stator winding.

Dependencies

To use this port, set the parameter Stator negative-end connections meaning Three-phase port.

Program usage name

port2

# R — the rotor of the machine
rotational mechanics

Details

The port of mechanical rotation of the rotor.

Dependencies

To use this port, set the parameter Mechanical input type meaning Mechanical input ports.

Program usage name

rod_flange

# C — machine body
rotational mechanics

Details

The port of mechanical rotation of the machine body.

Dependencies

To use this port, set the parameter Mechanical input type meaning Mechanical input ports.

Program usage name

case_flange

# fd+ — positive port of the excitation circuit
electricity

Details

The positive port of the excitation circuit.

Dependencies

To use this port, set the parameter Field excitation type meaning Electrical input ports.

Program usage name

fd_p

# fd– — negative port of the excitation circuit
electricity

Details

The negative port of the excitation circuit.

Dependencies

To use this port, set the parameter Field excitation type meaning Electrical input ports.

Program usage name

fd_n

Input

# Efd — excitation voltage from the control system
scalar

Details

Input port for the excitation voltage from the control system in relative units.

Dependencies

To use this port, set the parameter Field excitation type meaning Signal control port.

Data types	`Float64`
Complex numbers support	No

# w — speed depends on the control system
scalar

Details

Input port for the speed from the control system in rad/s.

Dependencies

To use this port, set the parameter Mechanical input type meaning Signal input (speed).

Data types	`Float64`
Complex numbers support	No

# Pm — mechanical power from the control system
scalar

Details

Input port for mechanical power from the control system in relative units.

Dependencies

To use this port, set the parameter Mechanical input type meaning Signal input (power).

Data types	`Float64`
Complex numbers support	No

Parameters

Main

# Rated apparent power — rated power of the machine
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

Rated power of the machine.

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 — nominal RMS value of the line voltage
V | uV | mV | kV | MV

Details

The nominal RMS value of the line voltage.

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

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

Details

The nominal frequency.

Units	`Hz` \| `kHz` \| `MHz` \| `GHz`
Default value	`50.0 Hz`
Program usage name	`f_rated`
Evaluatable	Yes

# Field excitation type — control of arousal
Signal control port | Electrical input ports

Details

Selection of excitation control:

Signal control port — directional signal, O.E.;
Electrical input ports — electrical signal, V.

Values	`Signal control port` \| `Electrical input ports`
Default value	`Signal control port`
Program usage name	`field_excitation_input`
Evaluatable	No

# Specify field circuit input required to produce rated terminal voltage at no load by — the basic variable of the excitation circuit
Field circuit voltage | Field circuit current

Details

Selection of a preset base variable of the excitation circuit that determines the rated voltage of the machine in idle mode:

Field circuit voltage — the current of the excitation circuit;
Field circuit current — voltage of the excitation circuit.

Dependencies

To use this parameter, set for the parameter Field excitation type meaning Electrical input ports.

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

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

Details

The value of the excitation voltage required to generate the rated voltage at the rated idle speed.

Dependencies

To use this parameter, set for the parameter Field excitation type meaning Electrical input ports, and for the parameter Specify field circuit input required to produce rated terminal voltage at no load by meaning Field circuit voltage.

Units	`V` \| `uV` \| `mV` \| `kV` \| `MV`
Default value	`100.0 V`
Program usage name	`E_fd_base`
Evaluatable	Yes

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

Details

The value of the excitation circuit current required to generate the rated voltage at the rated idle speed.

Dependencies

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

# Mechanical input type — the type of control of the mechanical movement of the machine
Signal input (speed) | Signal input (power) | Mechanical input ports

Details

Choosing to control the mechanical movement of the machine:

Signal input (speed) — directional speed setting signal, O.E.;
Signal input (power) — directional signal setting the power, O.E.;
Mechanical input ports — a mechanical signal from a source of torque or speed.

Values	`Signal input (speed)` \| `Signal input (power)` \| `Mechanical input ports`
Default value	`Signal input (speed)`
Program usage name	`mechanical_input`
Evaluatable	No

# Rotor type — type of rotor
Salient pole | Round

Details

Explicit or implicit pole machine:

Salient pole — single-pole type of rotor, one damping winding along the axis ;
Round — implicit pole type of rotor, two damping windings along the axis .

Values	`Salient pole` \| `Round`
Default value	`Round`
Program usage name	`rotor_type`
Evaluatable	No

# Stator negative-end connections — access to the end of the stator winding
Neutral point | Three-phase port

Details

Selecting the port for the end of the stator winding:

Neutral point — access to a neutral point;
Three-phase port — access to three phase ends.

Values	`Neutral point` \| `Three-phase port`
Default value	`Neutral point`
Program usage name	`stator_negative_end_connections`
Evaluatable	No

Impedances

# Stator resistance Ra — active resistance of the stator

Details

The active resistance of the stator in relative units.

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

# Stator leakage reactance Xl — inductive scattering resistance of the stator winding

Details

The inductive scattering resistance of the stator winding in relative units.

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

# d-axis synchronous reactance Xd — synchronous inductive resistance along the axis

Details

Synchronous inductive resistance along the axis in relative units.

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

# q-axis synchronous reactance Xq — synchronous inductive resistance along the axis

Details

Synchronous inductive resistance along the axis in relative units.

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

# d-axis transient reactance Xd' — transient inductive resistance along the axis

Details

Transient inductive resistance along the axis in relative units.

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

# q-axis transient reactance Xq' — transient inductive resistance along the axis

Details

Transient inductive resistance along the axis in relative units.

Dependencies

To use this parameter, set for the parameter Number of q-axis damper circuits meaning 2.

Default value	`0.65`
Program usage name	`X_p_q`
Evaluatable	Yes

# d-axis subtransient reactance Xd" — superconductive inductive resistance along the axis

Details

Superconductive inductive resistance along the axis in relative units.

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

# q-axis subtransient reactance Xq" — superconductive inductive resistance along the axis

Details

superconductive inductive resistance along the axis in relative units.

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

Time Constants

# Specify d-axis time constant — selecting the setting of time constants along the axis
Open circuit | Short circuit

Details

Selecting the setting of time constants along the axis :

Open circuit — when the stator winding is open;
Short circuit — when the stator winding is short-circuited.

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

# d-axis transient open-circuit Td0' — the time transition constant along the axis when the stator winding is open
s | ns | us | ms | min | hr | d

Details

The transitional time constant along the axis when the stator winding is open.

Dependencies

To use this parameter, set for the parameter Specify d-axis time constant meaning 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" — the super-transient time constant along the axis when the stator winding is open
s | ns | us | ms | min | hr | d

Details

The super-transient time constant along the axis when the stator winding is open.

Dependencies

To use this parameter, set for the parameter Specify d-axis time constant meaning 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' — the time transition constant along the axis when the stator winding is short-circuited
s | ns | us | ms | min | hr | d

Details

The transitional time constant along the axis when the stator winding is short-circuited.

Dependencies

To use this parameter, set for the parameter Specify d-axis time constant meaning 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" — the super-transient time constant along the axis when the stator winding is short-circuited
s | ns | us | ms | min | hr | d

Details

The super-transient time constant along the axis when the stator winding is short-circuited.

Dependencies

To use this parameter, set for the parameter Specify d-axis time constant meaning 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 — selecting the setting of time constants along the axis
Open circuit | Short circuit

Details

Selecting the setting of time constants along the axis :

Open circuit — when the stator winding is open;
Short circuit — when the stator winding is short-circuited.

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

# q-axis transient open-circuit Tq0' — the time transition constant along the axis when the stator winding is open
s | ns | us | ms | min | hr | d

Details

The transitional time constant along the axis when the stator winding is open.

Dependencies

To use this parameter, set for the parameter Specify q-axis time constant meaning Open circuit.

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`1 s`
Program usage name	`T_p_q0`
Evaluatable	Yes

# q-axis subtransient open-circuit Tq0" — the super-transient time constant along the axis when the stator winding is open
s | ns | us | ms | min | hr | d

Details

The super-transient time constant along the axis when the stator winding is open.

Dependencies

To use this parameter, set for the parameter Specify q-axis time constant meaning 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 transient short-circuit Tq' — the time transition constant along the axis when the stator winding is short-circuited
s | ns | us | ms | min | hr | d

Details

The transitional time constant along the axis when the stator winding is short-circuited.

Dependencies

To use this parameter, set for the parameter Specify q-axis time constant meaning Short circuit.

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`0.3693 s`
Program usage name	`T_p_q`
Evaluatable	Yes

# q-axis subtransient short-circuit Tq" — the super-transient time constant along the axis when the stator winding is short-circuited
s | ns | us | ms | min | hr | d

Details

The super-transient time constant along the axis when the stator winding is short-circuited.

Dependencies

To use this parameter, set for the parameter Specify q-axis time constant meaning 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

# Terminal voltage magnitude — the initial value of the generator voltage
V | uV | mV | kV | MV

Details

The initial value of the generator voltage.

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

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

Details

The initial value of the voltage angle of the generator.

Units	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`0.0 deg`
Program usage name	`V_ang_start`
Evaluatable	Yes

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

Details

The initial value of the generated active power.

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 — the initial value of the generated reactive power
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

The initial value of the generated reactive power.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`0.0 V*A`
Program usage name	`Q_t_start`
Evaluatable	Yes

Mechanical

# Inertia constant, H — the inertial constant
s | ns | us | ms | min | hr | d | W*s/(A*V)

Details

The inertial constant.

Dependencies

To use this parameter, set for the parameter Mechanical input type meaning Signal input (power).

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d` \| `Ws/(AV)`
Default value	`0.2 Ws/(AV)`
Program usage name	`H`
Evaluatable	Yes

# Friction factor — coefficient of frictional damping

Details

Coefficient of frictional damping.

Dependencies

To use this parameter, set for the parameter Mechanical input type meaning Signal input (power).

Default value	`0.0`
Program usage name	`friction_factor`
Evaluatable	Yes

# Specify friction type — type of accounting for the moment of friction
Zero | Rated

Details

Choose how to account for the moment of friction in the equation of motion of the machine:

Zero — regarding the speed;
Rated — regarding the speed deviation.

Dependencies

To use this parameter, set for the parameter Mechanical input type meaning Signal input (power).

Values	`Zero` \| `Rated`
Default value	`Zero`
Program usage name	`friction_type`
Evaluatable	No

Faulted windings

# Enable fault in phase A winding — the winding of phase A is being damaged

Details

Check this box if the phase winding it is being damaged.

Default value	`false (switched off)`
Program usage name	`faulted_winding_A`
Evaluatable	No

# Percentage of phase A points of fault from the neutral — positions of the damage points of the phase A winding

Details

Position vector of the points of damage of the phase winding as a percentage of the neutral point.

Number of input ports A is equal to the number of elements of this vector.

Dependencies

To use this option, check the box Enable fault in phase A winding.

Default value	`[50.0]`
Program usage name	`A_winding_fault_points`
Evaluatable	Yes

# Enable fault in phase B winding — The winding of phase B is being damaged

Details

Check this box if the phase winding it is being damaged.

Default value	`false (switched off)`
Program usage name	`faulted_winding_B`
Evaluatable	No

# Percentage of phase B points of fault from the neutral — positions of the damage points of the phase B winding

Details

Position vector of the points of damage of the phase winding as a percentage of the neutral point.

The number of input ports B is equal to the number of elements of this vector.

Dependencies

To use this option, check the box Enable fault in phase B winding.

Default value	`[50.0]`
Program usage name	`B_winding_fault_points`
Evaluatable	Yes

# Enable fault in phase C winding — The phase C winding is being damaged

Details

Check this box if the phase winding it is being damaged.

The number of input ports C is equal to the number of elements of this vector.

Dependencies

To use this option, check the box Enable fault in phase C winding.

Default value	`false (switched off)`
Program usage name	`faulted_winding_C`
Evaluatable	No

# Percentage of phase C points of fault from the neutral — positions of the damage points of the phase C winding

Details

Position vector of the points of damage of the phase winding as a percentage of the neutral point.

Default value	`[50.0]`
Program usage name	`C_winding_fault_points`
Evaluatable	Yes

# Enable fault in excitation winding — the excitation winding is damaged

Details

Check this box if the field winding is damaged.

The number of input ports F is equal to the number of elements of this vector.

Dependencies

To use this parameter, set for the parameter Field excitation type meaning Electrical input port.

Default value	`false (switched off)`
Program usage name	`faulted_winding_F`
Evaluatable	No

# Percentage of excitation winding points of fault from the terminal — positions of the damage points of the excitation winding

Details

The position vector of the fault points of the excitation winding as a percentage of the negative output.

Dependencies

To use this parameter, set for the parameter Field excitation type meaning Electrical input port and check the box Enable fault in excitation winding.

Default value	`[50.0]`
Program usage name	`F_winding_fault_points`
Evaluatable	Yes

Saturation

# Specification of saturation curve — selecting a saturation curve setting
Linear | Points | Factors

Details

Selecting a saturation curve setting:

Linear — linear function;
Points — table of points;
Factors — linear-quadratic function.

Values	`Linear` \| `Points` \| `Factors`
Default value	`Linear`
Program usage name	`saturation_curve`
Evaluatable	No

# Magnetizing current calculate by — axes along which the magnetization current is calculated to account for saturation
D-axis | DQ-axes

Details

Axes along which the magnetization current is calculated to account for saturation ( or ).

Values	`D-axis` \| `DQ-axes`
Default value	`DQ-axes`
Program usage name	`magnetization_axes`
Evaluatable	No

# Vector of coordinates of saturation curve points along excitation current (abscissa axis), pu — coordinates of the saturation curve points along the abscissa axis

Details

The vector of coordinates of the saturation curve points along the abscissa axis (excitation current in relative units).

Dependencies

To use this parameter, set for the parameter Specification of saturation curve meaning Points.

Default value	`[0.0, 0.48, 0.76, 1.38, 1.79]`
Program usage name	`ifd_data`
Evaluatable	Yes

# Vector of coordinates of saturation curve points along the generator voltage at idle speed (ordinate axis), pu — coordinates of the saturation curve points along the ordinate axis

Details

The vector of coordinates of the saturation curve points along the ordinate axis ( generator voltage at nominal idle speed in relative units).

Dependencies

To use this parameter, set for the parameter Specification of saturation curve meaning Points.

Default value	`[0.0, 0.80, 1.08, 1.31, 1.40]`
Program usage name	`Vag_data`
Evaluatable	Yes

# Coefficient that specifies the shift of the curve to the right relative to the unsaturated curve at ordinate 1.0 SE10. — the coefficient that defines the shift of the curve to the right relative to the unsaturated curve at ordinate 1.0

Details

The coefficient that defines the shift of the curve to the right relative to the unsaturated curve at ordinate 1.0.

Dependencies

To use this parameter, set for the parameter Specification of saturation curve meaning Factors.

Default value	`0.0609`
Program usage name	`SE10`
Evaluatable	Yes

# Coefficient that specifies the shift of the curve to the right relative to the unsaturated curve at ordinate 1.2 SE12. — the coefficient that defines the shift of the curve to the right relative to the unsaturated curve at ordinate 1.2

Details

The coefficient that defines the displacement of the curve to the right relative to the unsaturated curve at ordinate 1.2.

Dependencies

To use this parameter, set for the parameter Specification of saturation curve meaning Factors.

Default value	`0.1292`
Program usage name	`SE12`
Evaluatable	Yes

Main

# Display Associated Initial Conditions — displaying the initial conditions

Details

Display the corresponding initial conditions in the diagnostic window of the model.

Default value	`None`
Program usage name	`display_initial_conditions`
Evaluatable	No

Literature

A. B. Dehkordi, P. Neti, A.M Gole, and T.L. Maguire, «Development and Validation of a Comprehensive Synchronous Machine Model for a Real‐Time Environment», IEEE Trans. Energy Conversion, Vol. 25, No. 1, March 2010.