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# Three-Phase Transformer (Two Windings)

Implement three-phase transformer with configurable winding connections

Elements

## Description

This block implements a three-phase transformer using three single-phase transformers. For a detailed description of the electrical model of a single-phase transformer, see the Linear Transformer block.

When activated, the saturation characteristic is the same as the one described for the Saturable Transformer block. If the fluxes are not specified, the initial values are automatically adjusted so that the simulation starts in steady state.

The leakage inductance and resistance of each winding are given in pu based on the transformer nominal power Pn and on the nominal voltage of the winding (V1 or V2). For a description of per units, refer to the Linear Transformer and to the Saturable Transformer.

The two windings of the transformer can be connected as follows:

• Y

• Y with accessible neutral

• Grounded Y

• Delta (D1), delta lagging Y by 30 degrees

• Delta (D11), delta leading Y by 30 degrees

If you select the Y connection with accessible neutral for winding 1, an input port labeled N is added to the block. If you ask for an accessible neutral on winding 2, an extra output port labeled n is generated.

The D1 and D11 notations refer to the clock convention that assumes that the reference Y voltage phasor is at noon (12) on a clock display. D1 and D11 refer respectively to 1:00 p.m. (delta voltages lagging Y voltages by 30 degrees) and 11:00 a.m. (delta voltages leading Y voltages by 30 degrees).

### Standard Notation for Winding Connections

The conventional notation for a two-winding three-phase transformer uses two letters followed by a number. The first letter (Y or D) indicates a high-voltage wye or delta winding connection. The second letter (y or d) indicates a low-voltage wye or delta winding connection. The number, an integer between 0 and 12, indicates the position of the low-voltage positive-sequence voltage phasor on a clock display when the high-voltage positive-sequence voltage phasor is at 12:00.

The following three figures are examples of standard winding connections. The dots indicate polarity marks, and arrows indicate the position of phase A-to-neutral voltage phasors on high-voltage and low-voltage windings. The phasors are assumed to rotate in a counterclockwise direction so that rising numbers indicate increasing phase lag.

• Yd1: The low-voltage winding (d) is lagging high-voltage winding (Y) by 30 degrees. The Winding 2 connection parameter is set to D1.

• Dy11: The low-voltage winding (y) is leading high-voltage winding (D) by 30 degrees. The Winding 1 connection parameter is set to D1.

• Dy1: The low-voltage winding (y) is lagging high-voltage winding (D) by 30 degrees. The Winding 1 connection parameter is set to D11.

You can represent many other connections with phase shifts between 0 and 360 degrees (by steps of 30 degrees) by combining the +30- or –30-degree phase shift provided by the D1 and D11 block parameter settings and, in some cases, an additional +/–120-degree phase shift obtained by connecting the output terminals of delta winding to the appropriate phases of the network.

The table explains how to set up the Three-Phase Transformer block to obtain common connections.

Clock PositionPhase Shift (degrees)ConnectionWinding 1 ConnectionWinding 2 ConnectionTerminals of Delta Winding to Connect to Network ABC Phases
00Yy0YY
Dd0D1D1abc
1–30Yd1YD1abc
Dy1D11Yabc
2–60Dd2D11D1abc
5–150Yd5YD1bca
Dy5D11Ycab
7+150Yd7YD11cab
Dy7D1Ybca
10+60Dd10D1D11abc
11+30Yd11YD11abc
Dy11D1Yabc

For example, to obtain the Yd5 connection, set the Winding 1 connection parameter to Y and the Winding 2 connection parameter to D1, and connect the network phases to the winding 2 as follows:

For more details on conventional transformer winding notations, see International Standard IEC 60076-1 [1].

## Dialog Box and Parameters

### Configuration Tab

Winding 1 connection (ABC terminals)

The winding connections for winding 1.

Winding 2 connection (abc terminals)

The winding connections for winding 2.

Saturable core

If selected, implements a saturable three-phase transformer.

If you want to simulate the transformer in the phasor mode of the Powergui block, you must clear this parameter.

Simulate hysteresis

Select to model a saturation characteristic including hysteresis instead of a single-valued saturation curve. This parameter is visible only if the Saturable core parameter is selected.

If you want to simulate the transformer in the phasor mode of the Powergui block, you must clear this parameter.

Hysteresis Mat file

This parameter is visible only if the Simulate hysteresis parameter is selected.

Specify a .mat file containing the data for use in the hysteresis model. When you open the Hysteresis Design Tool of the Powergui block, the default hysteresis loop and parameters saved in the hysteresis.mat file are displayed. Use the Load button of the Hysteresis Design tool to load another .mat file. Use the Save button of the Hysteresis Design tool to save your model in a new .mat file.

Specify initial fluxes

If selected, the initial fluxes are defined by the Initial fluxes parameter on the Parameters tab. The Specify initial fluxes parameter is visible only if the Saturable core parameter is selected.

When the Specify initial fluxes parameter is not selected upon simulation, SimPowerSystems™ software automatically computes the initial fluxes to start the simulation in steady state. The computed values are saved in the Initial Fluxes parameter and will overwrite any previous values.

Measurements

Select Winding voltages to measure the voltage across the winding terminals.

Select Winding currents to measure the current flowing through the windings.

Select Fluxes and excitation currents (Im + IRm) to measure the flux linkage, in volt seconds (V.s), and the total excitation current including iron losses modeled by Rm.

Select Fluxes and magnetization currents (Im) to measure the flux linkage, in volt seconds (V.s), and the magnetization current, in amperes (A), not including iron losses modeled by Rm.

Select All measurements (V, I, Flux) to measure the winding voltages, currents, magnetization currents, and the flux linkages.

Place a Multimeter block in your model to display the selected measurements during the simulation. In the Available Measurements list box of the Multimeter block, the measurements are identified by a label followed by the block name.

If the Winding 1 connection (ABC terminals) parameter is set to Y, Yn, or Yg, the labels are as follows.

Measurement

Label

Winding 1 voltages

Uan_w1:, Ubn_w1:, Ucn_w1:

or

Uag_w1:, Ubg_w1:, Ucg_w1:

Winding 1 currents

Ian_w1:, Ibn_w1:, Icn_w1:

or

Iag_w1:, Ibg_w1:, Icg_w1:

Fluxes

Flux_A:, Flux_B:, Flux_C:

Magnetization currents

Imag_A:, Imag_B:, Imag_C:

Excitation currents

Iexc_A:, Iexc_B:, Iexc_C:

The same labels apply for winding 2, except that 1 is replaced by 2 in the labels.

If the Winding 1 connection (ABC terminals) parameter is set to Delta (D11) or Delta (D1), the labels are as follows.

Measurement

Label

Winding 1 voltages

Uab_w1:, Ubc_w1:, Uca_w1:

Winding 1 currents

Iab_w1:, Ibc_w1:, Ica_w1:

Flux_A:, Flux_B:, Flux_C:

Magnetization currents

Imag_A:, Imag_B:, Imag_C:

Excitation currents

Iexc_A:, Iexc_B:, Iexc_C:

### Parameters Tab

Units

Specify the units used to enter the parameters of this block. Select pu to use per unit. Select SI to use SI units. Changing the Units parameter from pu to SI, or from SI to pu, automatically converts the parameters displayed in the mask of the block. The per unit conversion is based on the transformer rated power Pn in VA, nominal frequency fn in Hz, and nominal voltage Vn, in Vrms, of the windings.

Nominal power and frequency

The nominal power rating, in volt-amperes (VA), and nominal frequency, in hertz (Hz), of the transformer. The nominal parameters have no impact on the transformer model when the Units parameter is set to SI.

Winding 1 parameters

The phase-to-phase nominal voltage in volts RMS, resistance, and leakage inductance in pu for winding 1.

Winding 2 parameters

The phase-to-phase nominal voltage in volts RMS, resistance, and leakage inductance in pu for winding 2.

Magnetization resistance Rm

The magnetization resistance Rm, in pu.

Magnetization inductance Lm

The magnetization inductance Lm, in pu, for a nonsaturable core. The Magnetization inductance Lm parameter is not accessible if the Saturable core parameter on the Configuration tab is selected.

Saturation characteristic

This parameter is available only if the Saturable core parameter on the Configuration tab is selected.

The saturation characteristic for the saturable core. Specify a series of current/ flux pairs (in pu) starting with the pair (0,0).

Initial fluxes

Specify initial fluxes for each phase of the transformer. This parameter is available only if the Specify initial fluxes and Saturable core parameters on the Configuration tab are selected.

When the Specify initial fluxes parameter is not selected upon simulation, SimPowerSystems software automatically computes the initial fluxes to start the simulation in steady state. The computed values are saved in the Initial Fluxes parameter and overwrite any previous values.

Break Algebraic loop in discrete saturation model

When you use the block in a discrete system, you get an algebraic loop. This algebraic loop, which is required in most cases to get an accurate solution, tends to slow down the simulation. To speed up the simulation, in some circumstances, you can disable the algebraic loop by selecting Break Algebraic loop in discrete saturation model. Be aware that disabling the algebraic loop introduces a one-simulation-step time delay in the model. This action can cause numerical oscillations if the sample time is too large.

## Example

The power_transfo3phpower_transfo3ph circuit uses the Three-Phase Transformer block where the saturable core is simulated. Both windings are connected in a Y grounded configuration. The neutral points of the two windings are internally connected to the ground.

The 500 kV/ 230 kV saturable transformer is energized on the 500 kV system. Remanent fluxes of 0.8 pu, −0.4 pu, and 0.4 pu have been specified respectively for phases A, B, and C. Run the simulation and observe inrush currents due to core saturation. See also the power_xfonotation model that shows four types of three-phase Yd and Dy transformer connections.

## References

[1] IEC. International Standard IEC 60076-1, Power Transformer - Part 1: General, Edition 2.1, 2000–04. "Annex D: Three-phase transformer connections." 2000.