Phase-Domain Synchronous Machine

Synchronous machine in phase coordinates with internal faults.

blockType: AcausalElectricPowerSystems.Electromechanical.Synchronous.PhaseDomain

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

Description

The Phase-Domain Synchronous Machine block simulates a synchronous machine in phase coordinates with internal faults. You can use this machine to simulate internal faults such as inter-turn faults, phase-to-phase faults, earth faults in both stator and field windings. The number of simultaneously selectable fault points is up to two per machine winding.

The phase coordinate method [1] is used to realise this model: the values of the machine inductances depend on the rotor position and saturation level. The mathematical model in phase coordinates allows to simulate the internal damage of synchronous machines. To simulate the internal damage of a synchronous machine, it is necessary to calculate the self and mutual inductance of the machine windings, including faulty windings, as functions of the rotor position and saturation.

Modelling a machine winding fault involves accessing the point of fault application. The fault point divides the winding into two parts - damaged and undamaged. Depending on the nature of the fault (chassis fault, inter-turn fault, phase-to-phase fault, etc.) and the experimental conditions, the number of fault points can be several. Consequently, each damaged winding should be represented in the model by several parts - sub-windings, as shown in Figure 1.

Each -subwinding is represented in the machine by an equivalent sinusoidal-distributed winding with its magnetic axis characterised by the angle , and the equivalent (effective) number of turns , as shown in Figure 2.

Ports

Output

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

Details

Port with a vector of current values of machine variables. Connect it to the block Synchronous Machine Measurement, to output the variable as a signal.

Data types	`Float64`.
Complex numbers support	No

Conserving

# ~1 — start of stator winding lead
electricity

Details

Expandable three-phase port associated with the beginning of the stator winding lead.

Program usage name

port1

# n — neutral
electricity

Details

Electrical port, corresponds to the neutral point of the stator winding.

Dependencies

To use this port, set the parameters Stator negative-end connections to . Neutral point.

Program usage name

n

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

Details

Internal phase winding assemblies .

Dependencies

To use this port, select the check box Enable fault in phase A winding. The number of input ports A depends on the number of points specified in the parameters Percentage of phase A points of fault from the neutral. If one point is specified (e.g. [50.0]), only port A1 will be used, if two points are specified (e.g. [50.0, 75.0]), two ports will be used: A1 and A2.

Program usage name

a1

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

Details

Internal phase winding assemblies .

Dependencies

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

Program usage name

b1

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

Details

Internal phase winding assemblies .

Dependencies

To use this port, select the Enable fault in phase C winding checkbox. The number of C input ports depends on the number of points specified in the parameters Percentage of phase C points of fault from the neutral. If one point is specified (e.g. [50.0]), only port C1 will be used, if two points are specified (e.g. [50.0, 75.0]), two ports will be used: C1 and C2.

Program usage name

c1

# F1, F2 — field winding internals
electricity

Details

Internal assemblies of the field winding.

Dependencies

To use this port, set the parameters Field excitation type to Electrical input port and tick the checkbox Enable fault in excitation winding. The number of input ports F depends on the number of points set in the parameter Percentage of excitation winding points of fault from the terminal. If one point is specified (e.g. [50.0]), only port F1 will be used, if two points are specified (e.g. [50.0, 75.0]), two ports will be used: F1 and F2.

Program usage name

f1

# ~2 — end of stator winding lead
electricity

Details

An expandable three-phase port connected to the end of the stator winding lead.

Dependencies

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

Program usage name

port2

# R — machine rotor
`rotational mechanics

Details

Port of mechanical rotation of the rotor.

Dependencies

To use this port, set the parameters Mechanical input type to Mechanical input ports.

Program usage name

rod_flange

# C — machine housing
`rotational mechanics

Details

A mechanical rotation port of a machine body.

Dependencies

To use this port, set the parameters Mechanical input type to Mechanical input ports.

Program usage name

case_flange

# fd+ — positive port of the field circuit
electricity

Details

Positive port of the excitation circuit.

Dependencies

To use this port, set the parameters Field excitation type to Electrical input ports.

Program usage name

fd_p

# fd- — negative excitation port
electricity

Details

Negative port of the excitation circuit.

Dependencies

To use this port, set the parameters Field excitation type to 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 parameters Field excitation type to . Signal control port.

Data types	`Float64`.
Complex numbers support	No

# w — speed from the control system
scalar

Details

Input port for velocity from the control system in rad/c.

Dependencies

To use this port, set the parameters Mechanical input type to 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 parameters Mechanical input type to Signal input (power)

Data types	`Float64`
Complex numbers support	No

Parameters

Main

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

Details

Rated machine power.

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

# Rated voltage — nominal rms value of line voltage
V | MV | kV | mV

Details

Nominal RMS value of the line voltage.

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

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

Details

Rated frequency.

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

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

Details

Excitation control selection:

Signal control port - directional signal, o.u;
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 — excitation circuit reference variable
Field circuit voltage | Field circuit current

Details

Selects the field circuit reference variable that determines the machine’s rated no-load voltage:

Field circuit voltage - field circuit current;
Field circuit current - field circuit voltage.

Dependencies

To use this parameter, set the parameters Field excitation type to . 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 | MV | kV | mV

Details

The value of the excitation voltage required to generate the rated voltage at rated speed at idle speed. the rated voltage at rated speed in no-load mode.

Dependencies

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

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

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

Details

The value of field circuit current required to produce the rated voltage at rated speed at idle speed. voltage at rated speed at idle speed.

Dependencies

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

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

Details

Selection of the mechanical motion control of the machine:

Signal input (speed) - directional signal that sets the speed, o.c.;
Signal input (power) - directional signal setting power, o.u;
Mechanical input ports - mechanical signal from a torque or velocity source.

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

# Rotor type — rotor type
Salient pole | Round

Details

Explicitly pole or implicitly pole machine:

Salient pole - explicitly pole rotor type, one damping winding in the axis ;
Round - implicit pole rotor type, two damping windings in 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

Selects the port for the stator winding end:

Neutral point - Neutral point access;
Three-phase port - access to the 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 — stator active resistance

Details

Stator active resistance in relative units.

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

# Stator leakage reactance Xl — stator winding inductive dissipation resistance

Details

Inductive dissipation 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 impedance along the d-axis

Details

Synchronous inductive impedance in the axis in relative units.

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

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

Details

Synchronous inductive impedance in the axis in relative units.

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

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

Details

Transient inductive impedance in 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 in the q axis

Details

Transient inductive impedance along the axis in relative units.

Dependencies

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

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

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

Details

Super transient inductive impedance along the axis in relative units.

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

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

Details

super transient 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 — selection of the time constant setting in the d-axis
Open circuit | Short circuit

Details

Selects the time constant reference for 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' — transient time constant in the d-axis with open stator winding
d | s | hr | ms | ns | us | min

Details

Transient time constant in the axis when the stator winding is open.

Dependencies

To use this parameter, set the parameter Specify d-axis time constant to the value of Open circuit.

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

# d-axis transient open-circuit Td0" — super transient time constant along the d-axis at open-circuited stator winding
d | s | hr | ms | ns | us | min

Details

Super transient time constant in the axis when the stator winding is open.

Dependencies

To use this parameter, set the parameter Specify d-axis time constant to the value of Open circuit.

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

# d-axis transient short-circuit Td' — transient time constant in the d-axis with short-circuited stator winding
d | s | hr | ms | ns | us | min

Details

Transient time constant in the axis with short-circuited stator winding.

Dependencies

To use this parameter, set the parameter Specify d-axis time constant to the value of Short circuit.

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

# d-axis transient short-circuit Td" — super transient time constant along the d-axis at short-circuited stator winding
d | s | hr | ms | ns | us | min

Details

Super transient time constant in the axis with short-circuited stator winding.

Dependencies

To use this parameter, set the parameter Specify d-axis time constant to the value of Short circuit.

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

# Specify q-axis time constant — selection of the time constant setting on the q axis
Open circuit | Short circuit

Details

Selection of the time constant setting in 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' — transient time constant in the q-axis with open stator winding
d | s | hr | ms | ns | us | min

Details

Transient time constant in the axis when the stator winding is open.

Dependencies

To use this parameter, set the parameter Specify q-axis time constant to the value of Open circuit.

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

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

Details

Super transient time constant in the axis when the stator winding is open.

Dependencies

To use this parameter, set the parameter Specify q-axis time constant to the value of Open circuit.

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

# q-axis transient short-circuit Tq' — transient time constant in q axis with short-circuited stator winding
d | s | hr | ms | ns | us | min

Details

Transient time constant in the axis with short-circuited stator winding.

Dependencies

To use this parameter, set the parameter Specify q-axis time constant to the value of Short circuit.

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

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

Details

Super transient time constant in the axis with short-circuited stator winding.

Dependencies

To use this parameter, set the parameter Specify q-axis time constant to the value of Short circuit.

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

Initial Conditions

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

Details

The initial value of the generator voltage.

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

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

Details

Initial value of the generator voltage angle.

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

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

Details

Initial value of the generated active power.

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

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

Details

Initial value of generated reactive power.

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

Mechanical

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

Details

Inertial constant.

Dependencies

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

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

# Friction factor — friction damping coefficient

Details

Friction damping coefficient.

Dependencies

To use this parameter, set the parameters Mechanical input type to . Signal input (power).

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

# Specify friction type — type of friction torque accounting
Zero | Rated

Details

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

Zero - relative to the velocity;
Rated - relative to velocity deviation.

Dependencies

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

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

Faulted windings

# Enable fault in phase A winding — phase A winding is damaged

Details

Select this check box if the winding of phase is 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 fault points of the A phase winding

Details

Phase winding fault point position vector as a percentage of the neutral point.

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

Dependencies

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

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

# Enable fault in phase B winding — phase B winding is damaged

Details

Select this check box if the winding of phase is 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 fault points of the B phase winding

Details

Phase winding fault point position vector 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 parameters, select the checkbox 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 — phase C winding is damaged

Details

Select this check box if the winding of phase is damaged.

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

Dependencies

To use this parameters, select the checkbox 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 fault points of the C phase winding

Details

Phase winding fault point position vector 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 field winding is damaged

Details

Select this check box if the field winding is subject to damage.

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

Dependencies

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

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 field winding fault points

Details

Vector of the field winding fault point positions in per cent of the negative terminal.

Dependencies

To use this parameter, set the parameter Field excitation type to Electrical input port and tick the checkbox Enable fault in excitation winding.

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

Saturation

# Specification of saturation curve — selection of saturation curve setting
Linear | Points | Factors

Details

Selects the saturation curve setting:

Linear - linear function;
Points - point table;
Factors - linear-quadratic function.

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

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

Details

Axes used to calculate the magnetising current 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 saturation curve points on the abscissa axis

Details

Vector of coordinates of saturation curve points on the abscissa axis (excitation current in relative units).

Dependencies

To use this parameter, set the parameter Specification of saturation curve to . 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 saturation curve points on the ordinate axis

Details

Vector of coordinates of saturation curve points on the ordinate axis (generator voltage at nominal speed at idle speed in relative units). generator voltage at rated speed at idle speed in relative units).

Dependencies

To use this parameter, set the parameter Specification of saturation curve to . 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. — coefficient, specifying the curve shift to the right relative to the unsaturated curve curve at ordinate 1.0

Details

Coefficient specifying the curve shift to the right relative to the unsaturated curve at an ordinate of 1.0. curve at ordinate 1.0.

Dependencies

To use this parameter, set the Specification of saturation curve parameters to . 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. — coefficient, specifying the shift of the curve to the right relative to the unsaturated curve curve at ordinate 1.2

Details

The coefficient specifying the curve shift to the right relative to the unsaturated curve at ordinate 1.2. curve at ordinate 1.2.

Dependencies

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

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

Literature

[1] 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.