Engee documentation

Three-Winding Transformer (Three-Phase)

A three-phase linear non-ideal three-winding transformer with a Star and Triangle windings connection and saturation consideration.

blockType: AcausalElectricPowerSystems.Passive.Transformers.ThreePhase

three winding transformer three phase

Three-Winding Transformer (Three-Phase)

Path in the library:

/Physical Modeling/Electrical/Passive/Transformers/Three-Winding Transformer (Three-Phase)

two winding transformer three phase

Two-Winding Transformer (Three-Phase)

Path in the library:

/Physical Modeling/Electrical/Passive/Transformers/Two-Winding Transformer (Three-Phase)

Description

Block Three-Winding Transformer (Three-Phase) It is a linear non-ideal three-phase three-winding transformer that transfers electrical energy between two or more circuits by means of electromagnetic induction. The block includes the effects of linear leakage of the windings and linear magnetization of the core. The block resistance can be parameterized in relative units. The connections of the primary, secondary and tertiary windings, the triangle-star phase angle and the types of cores are adjusted.

The configuration options for the primary and secondary windings are as follows:

  • Wye with floating neutral — a star with a floating three-phase neutral.

  • Wye with neutral port — a star with a three-phase neutral.

  • Wye with grounded neutral — a star with a grounded three-phase neutral.

  • Delta 1 o’clock — a triangle 30 degrees behind the star.

  • Delta 11 o’clock — a triangle with a 30-degree advance of the star.

For more information about the operating modes of a three-phase system connected according to the Triangle scheme, see the article Recommendations for delta connection of transformer windings.

Core type Options:

  • Three-phase five-limb — three-phase five-rod core.

  • Three-phase three-limb — three-phase three-core core.

Although a three-core is usually cheaper, a five-core has the following advantages:

  • Lower resistance for the zero sequence current component, that is, between the line and the neutral, in the case of an unbalanced load.

  • Greater heat dissipation.

The equations

The three- core core

This block is implemented in the magnetic field using blocks Nonlinear Reluctance, Winding and Eddy Current (Physical Modeling Electrical Passive).

two winding transformer (three phase) 1 s

It is important to determine the relationship between the parameters of the electrical region from the block mask and the parameters of the magnetic region used in the model.:

  • — the number of turns of the primary winding;

  • — the number of turns of the secondary winding;

  • — the number of turns of the tertiary winding;

  • — shunt magnetizing inductance;

  • — zero-sequence inductance;

  • — the scattering inductance of the primary winding;

  • — the scattering inductance of the secondary winding;

  • — the scattering inductance of the tertiary winding;

  • — shunting magnetizing resistance;

  • — magnetizing resistance between phases:

  • — zero sequence resistance coefficient:

  • — leakage resistance of the primary winding:

  • — leakage resistance of the secondary winding:

  • — leakage resistance of the tertiary winding:

  • — the conductivity of the eddy current loop:

For three-winding three-phase transformers, the connection between the different windings in each phase is the same.

The five - core core

In the case of a transformer with a five-rod core, the additional magnetic flux paths provided by the additional rods can be represented using zero-sequence magnetic resistances, which were originally developed for magnetic paths through the air in a transformer with a three-rod core.

two winding transformer (three phase) 2 s

In the five-core model, the magnetic resistances from the phases to the additional windings should be equal to the magnetic resistances between the phases.:

The conclusion follows from this:

Variables

Use the parameter group Initial Targets to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

Ports

Conserving

# ~1 — terminals of the primary winding
electricity

Details

Three-phase electrical port corresponding to the phase terminals , and the primary winding.

Program usage name

port1

# ~2 — secondary winding terminals
electricity

Details

Three-phase electrical port corresponding to the phase terminals , and secondary winding.

Program usage name

port2

# ~3 — terminals of the tertiary winding
electricity

Details

Three-phase electrical port corresponding to the phase terminals , and the tertiary winding.

Program usage name

port3

# n2 — neutral
electricity

Details

The electrical port connected to the neutral of the secondary winding.

Dependencies

To use this port, set the parameter Secondary winding connection type meaning Wye with neutral port.

Program usage name

n2

# n1 — neutral
electricity

Details

The electrical port connected to the neutral of the primary winding.

Dependencies

To use this port, set the parameter Primary winding connection type meaning Wye with neutral port.

Program usage name

n1

# n3 — neutral
electricity

Details

An electrical port connected to the neutral conductor of the tertiary winding.

Dependencies

To use this port, set the parameter Tertiary winding connection type meaning Wye with neutral port.

Program usage name

n3

Input

# Tap — RPN branch position signal
scalar

Details

An input signal indicating the current position of the RPN branch.

Dependencies

To use this port, check the box Tap control.

Data types

Float64
Complex numbers support

No

Parameters

Main

# Number of windings — switching between a two- and three-winding transformer
Two | Three

Details

Switching between a two- and three-winding transformer.

  • Two — the unit simulates a two-winding transformer.

  • Three — the unit simulates a three-winding transformer.

Values

Two | Three
Default value

—
Program usage name

N_windings
Evaluatable

No

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

Details

The rated power passing through the transformer. The value must be higher 0.

Units

W | uW | mW | kW | MW | GW | V*A | HP_DIN
Default value

100e6 V*A
Program usage name

S_rated
Evaluatable

Yes

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

Details

The nominal or nominal frequency of the AC network to which the transformer is connected. The value must be higher 0.

Units

Hz | kHz | MHz | GHz
Default value

50 Hz
Program usage name

f_rated
Evaluatable

Yes

# Primary winding connection type — primary winding configuration
Wye with floating neutral | Wye with neutral port | Wye with grounded neutral | Delta 1 o’clock | Delta 11 o’clock

Details

The type of primary winding.

Values

Wye with floating neutral | Wye with neutral port | Wye with grounded neutral | Delta 1 o’clock | Delta 11 o’clock
Default value

Wye with floating neutral
Program usage name

winding1_connection
Evaluatable

No

# Primary rated voltage — RMS mains voltage applied to the primary winding
V | uV | mV | kV | MV

Details

RMS linear voltage applied to the primary winding under normal operating conditions. The value must be higher 0.

Units

V | uV | mV | kV | MV
Default value

4160 V
Program usage name

V1_rated
Evaluatable

Yes

# Secondary winding connection type — secondary winding configuration
Wye with floating neutral | Wye with neutral port | Wye with grounded neutral | Delta 1 o’clock | Delta 11 o’clock

Details

The type of secondary winding.

Values

Wye with floating neutral | Wye with neutral port | Wye with grounded neutral | Delta 1 o’clock | Delta 11 o’clock
Default value

Wye with floating neutral
Program usage name

winding2_connection
Evaluatable

No

# Secondary rated voltage — RMS mains voltage applied to the secondary winding
V | uV | mV | kV | MV

Details

RMS linear voltage applied to the secondary winding under normal operating conditions. The value must be higher 0.

Units

V | uV | mV | kV | MV
Default value

24e3 V
Program usage name

V2_rated
Evaluatable

Yes

# Tertiary winding connection type — configuration of the tertiary winding
Wye with floating neutral | Wye with neutral port | Wye with grounded neutral | Delta 1 o’clock | Delta 11 o’clock

Details

The type of tertiary winding.

Values

Wye with floating neutral | Wye with neutral port | Wye with grounded neutral | Delta 1 o’clock | Delta 11 o’clock
Default value

Wye with floating neutral
Program usage name

winding3_connection
Evaluatable

No

# Tertiary rated voltage — RMS mains voltage applied to the tertiary winding
V | uV | mV | kV | MV

Details

RMS linear voltage applied to the tertiary winding under normal operating conditions. The value must be higher 0.

Units

V | uV | mV | kV | MV
Default value

24e3 V
Program usage name

V3_rated
Evaluatable

Yes

# Core type — core type
Three-phase three-limb | Three-phase five-limb

Details

The type of core.

Values

Three-phase three-limb | Three-phase five-limb
Default value

Three-phase three-limb
Program usage name

number_of_limbs
Evaluatable

No

Impedances

# Primary winding resistance, pu — resistance of the primary winding, O.E.

Details

The resistance of the primary winding, i.e. the value must be greater 0.

Default value

0.01
Program usage name

R_1_pu
Evaluatable

Yes

# Secondary winding resistance, pu — resistance of the secondary winding, O.E.

Details

The resistance of the secondary winding, i.e. the value should be greater 0.

Default value

0.01
Program usage name

R_2_pu
Evaluatable

Yes

# Tertiary winding resistance, pu — resistance of the tertiary winding, O.E.

Details

The resistance of the tertiary winding, i.e. the value must be greater 0.

Default value

0.01
Program usage name

R_3_pu
Evaluatable

Yes

# Leakage reactance — accounting for magnetic flux losses

Details

Enabling the simulation of magnetic flux losses.

Default value

false (switched off)
Program usage name

include_leakage_reactance
Evaluatable

No

# Primary leakage reactance, pu — magnetic resistance of the primary winding, O.E.

Details

Magnetic flux loss in the primary winding, i.e. the value should be greater 0.

Dependencies

To use this option, check the box Leakage reactance.

Default value

0.05
Program usage name

X_1_pu
Evaluatable

Yes

# Secondary leakage reactance, pu — magnetic resistance of the secondary winding, O.E.

Details

Magnetic flux loss in the secondary winding, i.e. the value should be greater 0.

Dependencies

To use this option, check the box Leakage reactance.

Default value

0.05
Program usage name

X_2_pu
Evaluatable

Yes

# Tertiary leakage reactance, pu — magnetic resistance of the tertiary winding, O.E.

Details

Magnetic flux losses in the tertiary winding, i.e. the value should be greater 0.

Dependencies

To use this option, check the box Leakage reactance.

Default value

0.05
Program usage name

X_3_pu
Evaluatable

Yes

# Magnetizing resistance — consideration of magnetization resistance

Details

Enabling the simulation of the magnetization resistance in the transformer core.

Default value

false (switched off)
Program usage name

include_magnetizing_resistance
Evaluatable

No

# Shunt magnetizing resistance, pu — active resistance of the magnetization branch, O.E.

Details

The active resistance of the magnetization branch, i.e. the value should be greater 0.

Dependencies

To use this option, check the box Magnetizing resistance.

Default value

500
Program usage name

R_m_pu
Evaluatable

Yes

# Magnetizing reactance — accounting for magnetic effects

Details

Enabling the simulation of the magnetic effects of the transformer core.

Default value

false (switched off)
Program usage name

include_magnetizing_reactance
Evaluatable

No

# Magnetic saturation — representation of magnetic saturation

Details

Select this option to use magnetic saturation.

Dependencies

To use this option, check the box Magnetizing reactance.

Default value

false (switched off)
Program usage name

include_saturation
Evaluatable

No

# Shunt magnetizing reactance, pu — reactivity of the magnetization branch, O.E.

Details

The reactance of the magnetization branch during operation of the linear domain, i.e. the value should be greater 0.

Dependencies

To use this option, check the box Magnetizing reactance and check the box Magnetic saturation.

Default value

500
Program usage name

X_m_pu
Evaluatable

Yes

# Current vector, pu — vector of current values, O.E.

Details

The vector of current values, i.e. the first value should be 0 the rest are strictly in ascending order.

Dependencies

To use this option, check the box Magnetizing reactance and check the box Magnetic saturation.

Default value

[0, 0.002, 1, 2]
Program usage name

i_vector_pu
Evaluatable

Yes

# Magnetic flux vector, pu — vector of flow values, O.E.

Details

The vector of magnetic flux values, i.e. the first value should be 0 the rest are strictly in ascending order.

Dependencies

To use this option, check the box Magnetizing reactance and check the box Magnetic saturation.

Default value

[0, 1.2, 1.5, 1.51]
Program usage name

Phi_vector_pu
Evaluatable

Yes

# Zero sequence reactance, pu — zero-sequence reactance

Details

The reactance of the zero sequence in the O.E. Value must be greater than or equal to the magnetic flux losses of the primary winding.

Dependencies

To use this parameter, set for the parameter Core type meaning Three-phase three-limb.

Default value

0.5
Program usage name

X_0_pu
Evaluatable

Yes

Tap control

# Tap control — managing the positions of the RPN branches

Details

Select this checkbox to switch the positions of the RPN branch using the Tap input signal.

Default value

false (switched off)
Program usage name

include_tap_control
Evaluatable

No

# Minimum tap position — minimum position of the RPN branch

Details

The minimum allowable position of the RPN branch.

The value of this parameter is usually in the range of −20 before +20. In the minimum position of the switch, the voltage transformation coefficient is:

U2/U1 = 1/(1 + Minimum tap position × Voltage step per tap, pu)

For example, the value of the voltage step per position 0.015 and the minimum position of the switch −20 The voltage transformation coefficient will be given:

U2/U1 = 1/(1 + (−20) × 0.015) = 1.428 pu.

Dependencies

To use this option, check the box Tap control.

Default value

-10
Program usage name

tap_min
Evaluatable

Yes

# Maximum tap position — the maximum position of the RPN branch

Details

The maximum allowable position of the RPN branch.

The value of this parameter is usually in the range of −20 before +20. At the maximum position of the switch, the voltage transformation coefficient is:

U2/U1 = 1/(1 + Maximum tap position × Voltage step per tap, pu)

For example, the value of the voltage step per position 0.015 and the maximum position of the switch +20 The voltage transformation coefficient will be given:

U2/U1 = 1/(1 + 20 × 0.015) = 0.769 pu.

Dependencies

To use this option, check the box Tap control.

Default value

10
Program usage name

tap_max
Evaluatable

Yes

# Voltage step per tap, pu — voltage step between two switch positions

Details

The voltage step between the two positions of the transformer switch in relative units. The value of this parameter is usually from 0.01 before 0.05 O.E.

The voltage transformation coefficient is determined by the formula:

U2/U1 = 1 /(1 + Tap position × Voltage step per tap, pu).

For example, the value of the voltage step per position 0.015 and the position of the switch −20 The voltage transformation coefficient will be given:

U2/U1 = 1/(1 + (−20) × 0.015) = 1.428 pu.

Parameter value Voltage step per tap, pu must be selected according to the value specified for the parameter. Minimum tap position. Follow this constraint according to the equation above:

Minimum tap position × Voltage step per tap, pu > −1.

For example, if the value Voltage step per tap, pu equally 0.05 O.E., the minimum value that can be specified for the parameter Minimum tap position, amounts to −19. Meaning −20 gives an infinite voltage ratio, but the value is less −20 leads to a negative voltage ratio, which is not applicable.

Default value

0.015
Program usage name

n_per_tap_pu
Evaluatable

Yes

Examples