Engee documentation

Synchronous Machine Round Rotor

Synchronous machine with implicit pole rotor with basic or standard parameterization.

synchronous machine round rotor

Description

The Synchronous Machine Round Rotor block models a synchronous machine with a round rotor using fundamental or standard parameters.

Initialisation of the synchronous machine using load flow targets

If the unit is on a network compatible with the time-frequency simulation mode, a load flow analysis can be performed on the network. The load flow analysis introduces steady-state values that can be used to initialise the machine.

Synchronous machine equations

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

θθ ,

where:

  • θ - electric angle.

  • - number of pole pairs.

  • θ - rotor angle (mechanical angle).

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

θθπθπθθπθπ .

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

ωψω ,

ωψω ,

ω ,

Where:

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

    .

  • , and are the stator currents flowing from port ~ to normal n.

  • ω - base velocity.

  • ψψ and ψс are the d, q, and zero-sequence axis flux-couplings.

  • ω - rotor speed in o.u.

  • - stator active resistance.

  • and - stator winding currents along 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:

ω ,

ω ,

ω ,

ω ,

Where:

  • - excitation voltage.

  • and are 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.

  • - excitation circuit voltages in relative units using the synchronous machine model in the reciprocal o.c. system.

  • ψψψ and ψ are the magnetic fluxes connecting the excitation circuit, the damped winding on the d axis, the damped winding on the q axis, and the two damped windings on the q axis.

  • and - 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.

  • and - 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:

ψψ ,

ψψ ,

ψψψ ,

(If saturation is disabled),

ψ (If saturation is enabled),

,

,

Where:

  • ψ - d axis air gap or mutual flux.

  • ψ - air gap along the q axis or mutual flux.

  • ψ - air gap flux-coupling.

  • - saturation coefficient.

  • - unsaturated stator mutual inductance in the d axis.

  • - stator mutual inductance in the d axis.

  • - unsaturated stator mutual inductance in the q axis.

  • - stator mutual inductance in the q axis.

The saturation coefficient is calculated using the open circuit interpolation table in o.u. as:

ψ ,

,

,

where is the air gap voltage in o.u.

In relative units:

и

ψ

can be rebuilt in:

ψ .

Then the stator flux-coupling equations are defined by:

,

,

,

Where:

  • - stator dissipation inductance.

  • - mutual stator inductances in the d and q axes.

Then the rotor flux-coupling equations are defined:

ψ ,

ψ ,

ψ ,

ψ ,

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.

  • - self-induction of the excitation circuit of two damping windings along 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. It represents a vector of several elements:

  • Excitation voltage (the base of the excitation circuit, ),

  • Field current (field 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 Simplified 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 parameter to Include.

Parameters

Main

Rated apparent power, VA - rated apparent power
`555e6 V*A (by default)

Rated power.

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

Nominal RMS line voltage.

Rated electrical frequency, Hz - 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
1 (By default).

Number of pole pairs of the machine.

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

Method of block parameterization. The following options are possible:

  • Fundamental parameters - adjust impedance using fundamental parameters.

  • Standard parameters - adjust impedance using standard parameters and specify time constants on d and q axes. This parameter affects the visibility of the Time Constant and Impedances parameter settings.

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 (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, V - field circuit voltage
`95.95 V (by default).

The field circuit voltage that produces the nominal voltage at the machine terminals.

Dependencies

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

Field circuit current, A - field circuit current
1300 A (By default).

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

Dependencies

This parameter is used when Specify field circuit input required to produce rated terminal voltage at no load by 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 using Partitioning solving errors occur.

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

Dependencies

If this parameter is set to:

  • Include and Specify parameterization by is set to Fundamental parameters, the parameter Stator zero-sequence inductance, in the Impedances settings will be visible.

  • Include and Specify parameterization by is set to Standart parameters, then the zero-sequence inductance parameter, in the Impedances settings will be visible.

  • Exclude - the zero-sequence parameter is not visible in the Impedances settings.

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.

By default, the rotor axis and the а -phase magnetic axis of the stator are aligned when the rotor rotation 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 а -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)
1.66 (by default) | `positive scalar'.

Unsaturated mutual inductance in the stator axis. This parameter must be greater than 0.

Dependencies

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

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

Unsaturated mutual inductance along the stator axis. This parameter must be greater than 0.

Dependencies

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

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

Stator resistance. This parameter must be greater than 0.

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

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

Rotor 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 when Specify parameterization by is set to Fundamental parameters.

Rotor d-axix damper winding 1 inductance L1d, pu - inductance of one damper winding in the d-axis of the rotor
0.1713 (by default) | positive scalar

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

Dependencies

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

Rotor d-axix damper winding 1 resistance R1d, pu - resistance of one damper winding on rotor d-axis
0.0284 (by default) | positive scalar

Resistance of one damper winding in the rotor axis . This parameter must be greater than 0.

Dependencies

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

Rotor q-axis damper winding 1 inductance L1q, pu - inductance of one damper winding on rotor q-axis
0.7252 (by default) | positive scalar

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

Dependencies

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

Rotor q-axix damper winding 1 resistance R1q, pu - resistance of one damper winding on rotor q-axis
0.00619 (by default) | positive scalar

Resistance of one damper winding in the rotor axis . This parameter must be greater than 0.

Dependencies

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

Rotor q-axix damper winding 2 inductance L2q, pu - winding inductance of two dampers on rotor q-axis
0.125 (by default) | positive scalar

Winding inductance of the two dampers in the rotor axis . This parameter must be greater than 0.

Dependencies

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

Rotor q-axix damper winding 2 resistance R2q, pu - resistance of the winding of two dampers on rotor q-axis
0.02368 (by default) | positive scalar

Resistance of the winding of the two dampers in the axis of the rotor. This parameter must be greater than 0.

Dependencies

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

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

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

Dependencies

This parameter is used when Specify parameterization by is set to Standart parameters.

d-axis synchronous reactance Xd, pu - d-axis synchronous reactance
1.81 (by default) | `positive scalar'.

Synchronous reactance on the d axis. This parameter must be greater than 0.

Dependencies

This parameter is used when Specify parameterization by is set to Standart parameters.

q-axis synchronous reactance Xq, pu - q-axis synchronous reactance
1.76 (by default) | `positive scalar'.

Synchronous reactance on the q axis. This parameter must be greater than 0.

Dependencies

This parameter is used when Specify parameterization by is set to Standart parameters.

zero-sequence reactance X0, pu - zero-sequence reactance
0.15 (by default) | `positive scalar'.

Zero sequence reactance. This parameter must be greater than 0.

Dependencies

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

d-axis transient reactance Xd', pu - d-axis transient reactance
0.3 (by default) | `positive scalar'.

Transient reactance on the d axis. This parameter must be greater than 0.

Dependencies

This parameter is used when Specify parameterization by is set to Standart parameters.

q-axis transient reactance Xq', pu - q-axis transient reactance
0 (By default) | `positive scalar'.

Transient reactance on the q axis. This parameter must be greater than 0.

Dependencies

This parameter is used when Specify parameterization by is set to Standart parameters.

d-axis subtransient reactance Xd", pu - d-axis subtransient reactance
0.23 (By default) | `positive scalar'.

The d-axis subtransient reactance. This parameter must be greater than 0.

Dependencies

This parameter is used when Specify parameterization by is set to Standart parameters.

q-axis subtransient reactance Xq", pu - q-axis subtransient reactance
0.25 (by default) | `positive scalar'.

Super transient reactance on the q axis. This parameter must be greater than 0.

Dependencies

This parameter is used when Specify parameterization by is set to Standart parameters.

Time Constants

Specify d-axis time constant - set d-axis time constant
Open circuit (default) | Short circuit

Select between Open circuit and Short circuit.

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

d-axis transient open-circuit time constant Td0', s is the transient open-circuit time constant of the d-axis excitation circuit
8 (By default) | `positive scalar'.

Transient open-circuit excitation transient time constant. This parameter must be:

  • Greater than 0.

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

Dependencies

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

d-axis transient short-circuit Td' is the d-axis transient time constant of the closed excitation circuit
1.3260 (by default) | `positive scalar'.

Transient time constant of the closed excitation circuit in the d axis. This parameter must be:

  • Greater than 0.

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

Dependencies

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

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

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

Dependencies

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

d-axis subtransient short-circuit Td", s is the super transient time constant of the d-axis closed excitation circuit
0.0230 (by default) | `positive scalar'.

The 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 Specify d-axis transient time constant is set to `Short circuit'.

Specify q-axis time constant - set the q-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 time constant parameters on the q axis.

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

Transient open-circuit transient time constant on the q axis. This parameter should be:

  • Greater than 0.

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

Dependencies

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

q-axis transient short-circuit Tq', s - transient time constant of closed circuit on q-axis
0.3693 (by default) | `positive scalar'.

The transient time constant of the closed circuit on the q axis. This parameter should be:

  • Greater than 0.

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

Dependencies

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

q-axis subtransient open-circuit Tq0", s is the q-axis transient open-circuit open-circuit time constant
0.07 (by default) | `positive scalar'.

The super transient time constant of the open-circuit excitation circuit in the q axis. This parameter must be greater than 0.

Dependencies

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

q-axis subtransient short-circuit Tq", s - super transient time constant of closed excitation circuit on q-axis
0.0269 (by default) | `positive scalar'.

The super transient time constant of the closed excitation circuit in the q axis. This parameter must be greater than 0.

Dependencies

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

Examples