Synchronous Machine Round Rotor

A synchronous machine with an implicit-pole rotor with basic or standard parameterization.

blockType: AcausalElectricPowerSystems.Electromechanical.Synchronous.RoundRotor

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/Physical Modeling/Electrical/Electromechanical/Synchronous/Synchronous Machine Round Rotor

Description

Block Synchronous Machine Round Rotor simulates a synchronous machine with a circular rotor using fundamental or standard parameters.

Initializing a synchronous machine using target load flow values

If the unit is located in a network compatible with the time-frequency simulation mode, then you can analyze the load flow in the network. Load flow analysis introduces steady-state values that can be used to initialize the machine.

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;
— number of pairs of poles;
— the angle of the rotor (mechanical angle).

Park’s 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 transformation of the Park is written in relative units (oe). The stator stress equations are as follows:

where

, and — stator voltage along the axes and and the zero sequence, respectively, determined by the formula:

,

where , and — stator voltages measured from port ~ to neutral port n;
— base speed in relative units;
, and — flow coupling along the axes and and the zero sequence;
— the speed of rotation of the rotor in relative units;
— active resistance of the stator;
and — stator winding currents along the axes , and the zero-sequence stator current, defined as:

,

where , and — currents on the stator from the port ~ to the neutral port n.

Rotor voltage equations:

where

— arousal voltage;
, and — voltage on one damping winding along the axis , on one damping winding along the axis and on two damping windings along the axis . They are all equal 0;

, , and — magnetic fluxes connecting the excitation circuit, the damping winding along the axis , damping winding along the axis and two damping windings along the axis ;
, , and — resistance of the rotor excitation circuit, one damper winding along the axis , one damping winding along the axis and two damping windings along the axis ;
, , and — currents flowing in the excitation circuit of one damper winding along the axis , one damping winding along the axis and two damping windings along the axis .

The saturation equations are described as follows:

(If saturation is disabled),

(If saturation is enabled),

where

— flow coupling in the air gap along the axis or mutual flow coupling;
— flow coupling in the air gap along the axis or mutual flow coupling;
— flow coupling in the air gap;
— saturation coefficient;
— unsaturated mutual inductance of the stator along the axis ;
— mutual inductance of the stator along the axis ;
— unsaturated mutual inductance of the stator along the axis ;
— mutual inductance of the stator along the axis .

Saturation coefficient function it is calculated using the open circuit interpolation table in relative units as:

where — air gap voltage in relative units.

In relative units:

and

can be converted to:

Then the stator flow coupling equations:

where

— stator scattering inductance;
, — mutual inductors of the stator along the axes and .

Then the flow coupling equations of the rotor look like this:

where

— self-induction of the rotor excitation circuit;
— self-induction of the excitation circuit of one damper winding along the axis ;
— self-induction of the excitation circuit of one damper winding along the axis ;
— self-induction of the excitation circuit of two damper windings along the axis ;
— the excitation circuit of the rotor and the mutual inductance of one winding of the damper along the axis .

Inductors are described by the following equations:

The inductance equations assume that the mutual inductances are in relative units hence, the currents of the stator and rotor in the axis they are connected into a single mutual stream, represented by .

Then the torque of the rotor is:

Ports

Conserving

# fd+ — positive terminal of the field winding
electricity

Details

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

Program usage name

fd_p

# fd− — negative terminal of the field winding
electricity

Details

An electrical port connected to the negative terminal of the field winding.

Program usage name

fd_n

# R — the rotor of the machine
rotational mechanics

Details

A mechanical port connected to the rotor of the machine.

Program usage name

rod_flange

# C — machine body
rotational mechanics

Details

A mechanical 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 at the winding point to a neutral wire of the Star type.

Dependencies

To use this port, set the parameter Zero sequence meaning Include.

Program usage name

n

Output

# o — machine measurements in relative units
vector

Details

The port that outputs the current values of the machine variables. It is a vector of several elements.:

Excitation voltage (base of the excitation circuit, ), .
Excitation current (base of the excitation circuit, ), .
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 axis the stator, .
Current along the axis 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

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	`1`
Program usage name	`N_pole_pairs`
Evaluatable	Yes

# Specify parameterization type by — parameterization of the block
Fundamental parameters | Standard parameters

Details

The block parameterization method. The following options are possible:

Fundamental parameters — Adjust the impedance using the fundamental parameters.
Standard parameters — adjust the impedance using standard parameters and specify time constants along the axes and .

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

# Specify field circuit input required to produce rated terminal voltage at no load by — specify the excitation circuit 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 — adjust the voltage of the excitation circuit.
Field circuit current — adjust the current of the excitation circuit. This method is the default method of parameterization of the excitation circuit.

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

# 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 terminals of the machine.

Dependencies

To use this parameter, set 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	`92.95 V`
Program usage name	`E_fd_base`
Evaluatable	Yes

# 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 terminals of the machine.

Dependencies

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

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

# Zero sequence — the zero sequence model
Exclude | Include

Details

The zero-sequence model:

Include — priority is given to the accuracy of the model. It is the default zero sequence model. When zero sequence conditions are enabled for simulations using Partitioning solving, errors occur.
Exclude — Priority is given to simulation speed for desktop simulation or real-time deployment.

Values	`Exclude` \| `Include`
Default value	`Include`
Program usage name	`zero_sequence`
Evaluatable	No

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

Details

A reference point for measuring the rotation angle of the rotor.

When selecting a value Angle between the a-phase magnetic axis and the d-axis the axis the rotor and -the phase magnetic axis of the stator is aligned when the rotation angle of the rotor is zero.

When selecting a value Angle between the a-phase magnetic axis and the q-axis the axis the rotor and -the phase magnetic axis of the stator is aligned when the rotation angle of the rotor is zero.

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

Impedances

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

Details

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

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Fundamental parameters.

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

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

Details

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

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Fundamental parameters.

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

# Stator zero-sequence inductance L0 — inductance of the zero sequence of the stator

Details

The inductance of the zero sequence of the stator. This parameter should be higher. 0.

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Fundamental parameters, and for the parameter Zero sequence set the value Include.

Default value	`0.15`
Program usage name	`L_0`
Evaluatable	Yes

# Stator leakage inductance Ll — stator scattering inductance

Details

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

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning 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

To use this parameter, set for the parameter Specify parameterization type by meaning Fundamental parameters.

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

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

Details

The inductance of the winding of one damper along the axis the rotor. This parameter should be higher. 0.

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning 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 axis the rotors

Details

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

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Fundamental parameters.

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

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

Details

The inductance of the winding of one damper along the axis the rotor. This parameter should be higher. 0.

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Fundamental parameters.

Default value	`0.7252`
Program usage name	`L_1q`
Evaluatable	Yes

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

Details

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

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Fundamental parameters.

Default value	`0.00619`
Program usage name	`R_1q`
Evaluatable	Yes

# Rotor q-axis damper winding 2 inductance L2q — the inductance of the winding of the two dampers along the axis the rotors

Details

The inductance of the winding of the two dampers along the axis the rotor. This parameter should be higher. 0.

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Fundamental parameters.

Default value	`0.125`
Program usage name	`L_2q`
Evaluatable	Yes

# Rotor q-axis damper winding 2 resistance R2q — the winding resistance of the two dampers along the axis the rotors

Details

The winding resistance of the two dampers along the axis the rotor. This parameter should be higher. 0.

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Fundamental parameters.

Default value	`0.02368`
Program usage name	`R_2q`
Evaluatable	Yes

# Stator leakage reactance Xl — stator scattering reactance

Details

The reactive resistance of the stator scattering. This parameter should be higher. 0.

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Standard parameters.

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

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

Details

Synchronous reactance along the axis . This parameter should be higher. 0.

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Standard parameters.

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

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

Details

Synchronous reactance along the axis . This parameter should be higher. 0.

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Standard parameters.

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

# zero-sequence reactance X0 — zero-sequence reactance

Details

Zero-sequence reactance. This parameter should be higher. 0.

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Standard parameters, and for the parameter Zero sequence meaning Include.

Default value	`0.15`
Program usage name	`X_0`
Evaluatable	Yes

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

Details

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

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Standard parameters.

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

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

Details

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

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Standard parameters.

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

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

Details

Superconductive reactance along the axis . This parameter should be higher. 0.

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Standard parameters.

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

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

Details

Superconductive reactance along the axis . This parameter should be higher. 0.

Dependencies

To use this parameter, set for the parameter Specify parameterization type by meaning Standard parameters.

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

Time Constants

# Specify d-axis time constant — setting the time constant of the 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 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

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

Details

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

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' — transient time constant of a closed excitation circuit along the 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

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 of a closed excitation circuit along the 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

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 — setting the time constant along the 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 transient open-circuit Tq0' — the transient time constant of an open circuit along the axis
s | ns | us | ms | min | hr | d

Details

The transient time constant of an open circuit along the axis . This parameter should be:

More 0.
More than q-axis subtransient open-circuit Tq0".

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 hyper-transient time constant of an open circuit along the 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

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	`0.07 s`
Program usage name	`T_pp_q0`
Evaluatable	Yes

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

Details

The transient time constant of a closed circuit along the axis . This parameter should be:

More 0.
More than q-axis subtransient short-circuit Tq".

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 of a closed excitation circuit along the 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

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

# Initialization option — initialization option
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 the values of parameters and variables at the beginning of the simulation.

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

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

Details

Specify the voltage on 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 — voltage angle at the terminals
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

Specify the voltage angle 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	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`0 deg`
Program usage name	`V_ang_start`
Evaluatable	Yes

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

Details

Specify the 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 — reactive power
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

Specify the 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

An implicit pole generator without regulators