Synchronous Machine Salient Pole

Synchronous explicitly pole machine with fundamental or standard parameterization.

synchronous machine salient pole

Description

Block Synchronous Machine Salient Pole simulates an explicitly pole synchronous machine using fundamental or standard parameters.

Synchronous machine equations

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

where:

- electric angle.
- number of pole pairs.
- rotor angle (mechanical angle).

The Park-Gorev transformation maps the equations of a synchronous machine into a rotating reference frame with respect to the electric angle. It is written as follows:

The Park-Gorev transformation is written in relative units (r.u.). The stator stress equations are as follows:

Where:

and - stator voltages along the d, q and zero sequence axes, determined by the formula:

.
, and are the stator currents flowing from the port ~ to the normal n.
- base velocity.
, and - flux-couplings of d, q and zero sequence axes.
- rotor speed in o.u.
- stator active resistance.
, and - stator winding currents along the d, q axis and zero-sequence stator currents defined as:

,

where

, , and are the stator voltages measured from port ~ to neutral n.

The rotor voltage equation is determined by the formula:

Where:

- is the excitation voltage.
, are the voltages on one damping winding on the d axis, one damping winding on the q axis and two damping windings on the q axis. All of them are equal to 0.
, , are the magnetic fluxes connecting the field circuit, the damping winding in the d axis, the damping winding in the q axis and the two damping windings in the q axis.
, , - resistances of the rotor excitation circuit, one damping winding in the d axis, one damping winding in the q axis and two damping windings in the q axis.
, , - currents flowing in the excitation circuit, one damping winding in the d axis, one damping winding in the q axis and two damping windings in the q axis.

The saturation equations are described as follows:

(If saturation is disabled),

(If saturation is enabled),

where:

- air gap along the d axis or mutual flux-coupling.
- air gap in the q axis or mutual flux.
- air gap flux.
- saturation coefficient.
- unsaturated mutual inductance of the stator along the d axis.
- stator mutual inductance along the d axis.

The saturation factor is calculated using the open-circuit interpolation table in oh.e. as:

where is the air gap voltage in o.u.

In relative units:

can be rearranged into:

Then the stator flux-coupling equations are defined by:

Where:

- stator dissipation inductance.
, - mutual stator inductances along the d and q axes.

Then the rotor flux-coupling equations are defined:

Where:

- self-inductance of the rotor excitation circuit.
- self-inductance of the excitation circuit of one damping winding along the d axis.
- self-induction of the excitation circuit of one damping winding in the q axis.
- rotor excitation circuit and mutual inductance of one damper winding along the d axis.

The inductances are described by the following equations:

In the inductance equations it is assumed that the mutual inductance in o.e. hence the stator and rotor currents in the q axis couple into a single mutual flux represented by .

Then the rotor torque is equal to:

Ports

Output

o - machine measurements in relative units
vector

A port that outputs the current values of machine variables. Then for a vector of multiple elements:

Excitation voltage (base of the excitation circuit, ),
Excitation current (excitation circuit base, ),
Electromagnetic torque,
Rotor speed,
Stator voltage in the axis ,
Stator axis voltage ,
Stator zero sequence voltage,
Stator axis current
Stator axis current
Stator zero sequence current
Electrical angle of the rotor,

Use the Synchronous Machine Measurement block to connect to this port.

Non-directional

fd+ - positive terminal of field winding
electricity

Electrical port associated with the positive terminal of the field winding.

fd- is the negative terminal of the field winding
electricity

Electrical port associated with the negative terminal of the field winding.

R is the rotor of the machine
`rotational mechanics

A mechanical port associated with the rotor of a machine.

C - the machine housing
`rotational mechanics

A mechanical port associated with the machine housing.

~ - stator windings
electricity

Expandable three-phase port connected to the stator windings.

n - neutral
electricity

An electrical port connected at a winding point to the neutral in the Zvezda type.

Dependencies

To enable the port, set the Zero sequence parameters to `Include'.

Parameters

Main

Rated apparent power

 - rated apparent power 
 `300e6 V*A (by default)

Rated power.

Rated voltage - RMS line voltage
24e3 V (by default).

Nominal RMS line voltage.

Rated electrical frequency - rated electrical frequency
50 Hz (By default).

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

Number of pole pairs - number of pole pairs
10 (By default).

Number of pole pairs of the machine.

Specify parameterization type by - parameterization block
Fundamental parameters (by default) | Standard parameters.

Block parameterization method. The following options are possible:

Fundamental parameters - adjust impedance by usage of fundamental parameters.
Standard parameters - adjust impedance usage of standard parameters and specify time constants on and axes.

Dependencies

If this parameter is set to Fundamental parameters:

Fundamental parameters are visible in the *Impedances` settings.
The Time Constant settings are visible.

If this parameter is set to Standard parameters:

Standard parameters in the Impedances settings are visible.
The Time Constant parameters are not visible.

Specify field circuit input required to produce rated terminal voltage at no load by - specify field circuit input required to produce rated terminal voltage at no load by
Field circuit current (by default) | Field circuit voltage.

Field circuit parameterization method. The following options are possible:

Field circuit voltage - set the field circuit voltage.
Field circuit current - set the field circuit current. This method is the field circuit parameterization method by default.

This parameter affects the visibility of the Field circuit voltage and Field circuit current parameters.

Field circuit voltage - field circuit voltage
`216.54 V (by default).

The field circuit voltage that produces the rated voltage at the machine outputs.

Dependencies

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

Field circuit current - field circuit current
`1000 A (By default)'.

The field circuit current that produces the rated voltage at the machine outputs.

Dependencies

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

Zero sequence - zero sequence model
Include (by default) | Exclude.

Zero sequence model:

Include - prioritises the accuracy of the model. It is the zero-sequence model by default. When including zero-sequence conditions for simulations with usage of Partitioning solving, errors occur.

Exclude - priority is given to simulation speed for desktop simulation or real-time deployment.

Dependencies

If this parameters is set to:

Include and Specify parameterization by is set to Fundamental parameters, the parameter Stator zero-sequence inductance, L0 in the Impedances settings will be visible.
Include and Specify parameterization by is set to Standart parameters, then the parameter zero-sequence inductance, X0 in the Impedances settings will be visible.
Exclude - zero-sequence parameter is not visible in Impedances parameters.

Rotor angle definition - reference point for rotor angle measurement
Angle between the a-phase magnetic axis and the d-axis (by default)| Angle between the a-phase magnetic axis and the q-axis.

The reference point for measuring the rotor angle.

When the By default value is selected, the rotor axis and the a-phase magnetic axis of the stator axis are aligned when the rotor angle is zero.

Another value that can be selected for this parameter is Angle between the a-phase magnetic axis and the q-axis. When this value is selected, the rotor axis and the a-phase magnetic axis of the stator are aligned when the rotor rotation angle is zero.

Impedances

Stator d-axis mutual inductance (unsaturated) Ladu, pu - stator d axis mutual inductance (unsaturated)
0.9 (by default) | positive scalar

Unsaturated mutual inductance along the d axis of the stator. This parameters must be greater than 0.

Dependencies

This parameter is used if Specify parameterization by is set to Fundamental parameters.

Stator q-axis mutual inductance (unsaturated) Laqu, pu - stator q axis mutual inductance (unsaturated)
0.55 (by default) | `positive scalar'.

Unsaturated mutual inductance along the q axis of the stator. This parameters must be greater than 0.

Dependencies

This parameter is used if Specify parameterization by is set to Fundamental parameters.

Stator zero-sequence inductance L0, pu - stator zero-sequence inductance
0.15 (by default) | `positive scalar'.

Stator zero-sequence inductance. This parameters must be greater than 0.

Dependencies

This parameter is used when Specify parameterization by is set to Fundamental parameters and Zero Sequence is set to Include.

Stator leakage inductance Ll, pu - stator leakage inductance
0.15 (by default) | `positive scalar'.

Stator leakage inductance. This parameter must be greater than 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Stator resistance Ra, pu - stator resistance
0.011 (by default) | `positive scalar'.

Stator resistance. This parameters must be greater than 0.

Rotor field circuit inductance Lfd, pu - rotor field circuit inductance
0.2571 (by default) | `positive scalar'.

Rotor field circuit inductance. This parameter must be greater than 0.

RRotor field circuit resistance Rfd, pu - rotor field circuit resistance
0.0006 (by default) | `positive scalar'.

Rotor field circuit resistance. This parameter must be greater than 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Rotor d-axix damper winding 1 inductance L1d, pu - inductance of one damper winding along the d axis of the rotor
0.2 (by default) | `positive scalar'.

Winding inductance of one damper winding in the d axis of the rotor. This parameters must be greater than 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Rotor d-axix damper winding 1 resistance R1d, pu - resistance of one damper winding in the d axis of the rotor
0.0354 (by default) | positive scalar

Winding resistance of one damper winding in the d axis of the rotor. This parameters must be greater than 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

RRotor q-axis damper winding 1 inductance L1q, pu - inductance of one damper winding in the q axis of the rotor
0.2567 (by default) | `positive scalar `

Winding inductance of one damper winding in the q axis of the rotor. This parameters must be greater than 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

*Rotor q-axix damper winding 1 resistance R1q, pu - resistance of one damper winding in the q axis of the rotor
0.0428 (by default) | positive scalar

Winding resistance of one damper winding in the q axis of the rotor. This parameters must be greater than 0.

Dependencies

This parameter is used if the Specify parameterization by parameter is set to Fundamental parameters.

Time Constants

Specify d-axis time constant - setting of the d axis time constant.
Open circuit (by default) | Short circuit

Select between Open circuit and Short circuit.

The setting of this parameter affects the visibility of the d axis time constant parameters.

d-axis transient open-circuit time constant Td0', s - transient open-circuit time constant of the d-axis excitation circuit
5.25 c (by default) | `positive scalar'.

Transient time constant of the open-circuit excitation circuit. This parameters should be:

Greater than 0.
Greater than d-axis subtransient open-circuit, Td0''.

Dependencies

This parameter is used if the Specify d-axis transient time constant parameter is set to `Open circuit'.

d-axis transient short-circuit Td', s - transient time constant of the closed excitation circuit in the d axis
1.75 s (by default) | positive scalar quantity.

Transient time constant of the closed excitation circuit in the d axis. This parameters should be:

Greater than 0.
Greater than d-axis subtransient short-circuit, Td''.

Dependencies

This parameter is used when the Specify d-axis transient time constant parameter is set to `Short circuit'.

d-axis subtransient open-circuit Td0", s is the super transient open-circuit time constant of the excitation circuit on the d axis
0.03 s (by default) | `positive scalar'.

Super transient time constant of the open-circuit excitation circuit on the d axis. This parameter must be greater than 0.

Dependencies

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

d-axis subtransient short-circuit Td", s is the super transient time constant of the closed excitation circuit on the d axis
0.0214 s (by default) | `positive scalar'.

Super transient time constant of the closed excitation circuit in the d axis. This parameter must be greater than 0.

Dependencies

This parameter is used when the Specify d-axis transient time constant parameter is set to Short circuit.

Specify q-axis time constant - set the time constant on the q axis
Open circuit (by default)| Short circuit.

Select between Open circuit and Short circuit.

The setting of this parameter affects the visibility of the time constant parameters on the q axis.

q-axis transient open-circuit time constant, Tq0' - transient open-circuit time constant on the q axis
0.05 (by default)| `positive scalar'.

Select between Open circuit and Short circuit.

Transient time constant of the open circuit on the q axis. This parameters must be:

Greater than 0.
Greater than q-axis subtransient open-circuit, Tq0''.

Dependencies

This parameter is used if the Specify q-axis transient time constant parameter is set to `Open circuit'.

q-axis transient open-circuit, Tq' is the transient time constant of the closed circuit on the q axis
0.0232 s (by default) | positive scalar.

Select between Open circuit and Short circuit.

Transient time constant of the closed circuit on the q axis. This parameters must be:

Greater than 0.
Greater than q-axis subtransient short-circuit, Tq''.

Dependencies

This parameter is used when the Specify q-axis transient time constant parameter is set to `Short circuit'.

Initial Conditions

Initialisation option - Initialisation parameters
Set targets for rotor angle and Park’s transform variables (by default) | Set real power, reactive power, terminal voltage, and terminal phase

Model to set the values of certain parameters and variables at the beginning of the simulation.

To set the operating point independently of the connected network, set the Initialisation option parameters to Set real power, reactive power, terminal voltage and terminal phase.

To specify priority and initial targets for block variables before simulation using the Initial Targets parameters, set the Initialisation option to Set targets for rotor angle and Park’s transform variables.

Dependencies

If you set this parameter to:

Set targets for rotor angle and Park’s transform variables - the Initial Targets settings become visible.
Set real power, reactive power, terminal voltage, and terminal phase - the associated parameters become visible.