# Zigzag Phase-Shifting Transformer

Implement zigzag phase-shifting transformer with configurable secondary winding connection

## Library

Simscape / Electrical / Specialized Power Systems / Power Grid Elements

## Description

The Zigzag Phase-Shifting Transformer block implements a three-phase transformer with a primary winding connected in a zigzag configuration and a configurable secondary winding. The model uses three single-phase, three- winding transformers. The primary winding connects the windings 1 and 2 of the single-phase transformers in a zigzag configuration. The secondary winding uses the windings 3 of the single phase transformers, and they can be connected in one of the following ways:

Y

Y with accessible neutral

Grounded Y

Delta (D1), delta lagging Y by 30 degrees

Delta (D11), delta leading Y by 30 degrees

**Note**The D1 and D11 notations refer to the following clock convention. It assumes that the reference Y voltage phasor is at noon (12) on a clock display. D1 and D11 refer respectively to 1 PM (lagging Y by 30 degrees) and 11 AM (leading Y by 30 degrees).

If the secondary winding is connected in Y, the secondary phase voltages are leading or lagging the primary voltages by the Phi phase angle specified in the parameters of the block. If the secondary winding is connected in delta (D11), an additional phase shift of +30 degrees is added to the phase angle. If the secondary winding is connected in delta (D1), a phase shift of −30 degrees is added to the phase angle.

The block takes into account the connection type you have selected and the icon of the block is automatically updated. An output port labeled N is added to the block if you select the Y connection with accessible neutral for the secondary winding.

The saturation characteristic, when activated, is the same as the one described for the Saturable Transformer block.

## Parameters

### Configuration Tab

**Secondary winding (abc) connection**The winding connection for the secondary winding. Choices are

`Y`

,`Yn`

,`Yg`

(default),`Delta (D1)`

, and`Delta (D11)`

.**Saturable core**If selected, implements a saturable core. Default is cleared.

**Specify initial fluxes**If selected, the initial fluxes are defined by the

**Initial fluxes**parameter on the Parameters tab. This parameter is available only if the**Saturable core**parameter is selected. Default is cleared.When the

**Specify initial fluxes**parameter is not selected upon simulation, Simscape™ Electrical™ Specialized Power Systems 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 of the Three-Phase Transformer block.Select

`Winding currents`

to measure the current flowing through the windings of the Three-Phase Transformer block.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.Default is

`None`

.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.The labels used in the Multimeter are as follows.

Measurement

Label

Winding voltages of primary (zigzag)

`Uprim_A:`

Winding currents of primary (zigzag)

`Iprim_A:`

Winding voltages of secondary

(Y, Yn, or Yg)`Usec_A:`

Winding voltages of secondary

(delta)`Usec_AB:`

Winding currents of secondary

(Y, Yn, or Yg)`Isec_A:`

Winding currents of secondary

(delta)`Isec_AB:`

Fluxes

(windings 1 of zigzag)`Flux_A:`

Excitation currents

(windings 1 of zigzag)`Iexc_A:`

Magnetization currents

(windings 1 of zigzag)`Imag_A:`

### Parameters Tab

**Units**Specify the units used to enter the parameters of the Zigzag Phase-Shifting Transformer 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`

, will automatically convert 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. Note that the nominal parameters have no impact on the transformer model when the

**Units**parameter is set to`SI`

. Default is`[ 100e6 60]`

.**Primary (zigzag) nominal voltage Vp**The phase-to-phase nominal voltage in volts RMS, for the primary winding of the transformer. Default is

`10e3`

.**Secondary nom. voltage phase shift**The phase-to-phase nominal voltage, in volts RMS, and the phase shift, in degrees, for the secondary winding of the transformer. Default is

`[ 30e3 +15]`

.**Winding 1 zig-zag [R1 L1]**The resistance and leakage inductance of the windings 1 of the single-phase transformers used to implement the primary winding of the Zigzag Phase-Shifting Transformer. Default is

`[ 0.002 0.08 ]`

when the**Units**parameter is`pu`

and`[0.002488 0.00026399]`

when the**Units**parameter is`SI`

.**Winding 2 zig-zag [R2 L2]**The resistance and leakage inductance of the windings 2 of the single-phase transformers used to implement the primary winding of the Zigzag Phase-Shifting Transformer. Default is

`[ 0.002 0.08 ]`

when the**Units**parameter is`pu`

and`[0.00017863 1.8954e-05]`

when the**Units**parameter is`SI`

.**Winding 3 secondary [R3 L3]**The resistance and leakage inductance of the windings 3 of the single-phase transformers used to implement the secondary winding of the Zigzag Phase-Shifting Transformer. Default is

`[ 0.002 0.08 ]`

when the**Units**parameter is`pu`

and`[0.018 0.0019099]`

when the**Units**parameter is`SI`

.**Magnetizing branch [Rm Lm]**The

**Magnetizing branch**parameter is not accessible if the**Saturable core**check box is selected. Default is`[ 500 500 ]`

when the**Units**parameter is`pu`

and`[622.01 622.01]`

when the**Units**parameter is`SI`

.The magnetization resistance Rm and inductance Lm, in pu, when the saturation is not simulated.

**Magnetization resistance Rm**This parameter is accessible only if the

**Saturable core**parameter on the**Configuration**tab is selected. Default is`500`

when the**Units**parameter is`pu`

and`622.01`

when the**Units**parameter is`SI`

.The magnetization resistance Rm, in pu, when the saturation is simulated.

**Saturation characteristic**This parameter is accessible only if the

**Saturable core**parameter on the**Configuration**tab is selected. Default is`[ 0,0 ; 0.0024,1.2 ; 1.0,1.52 ]`

when the**Units**parameter is`pu`

and`[0 0;17.569 28.988;7320.5 36.718]`

when the**Units**parameter is`SI`

.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 accessible only if the

**Specify initial fluxes**parameter on the**Configuration**tab is selected. Default is`[0,0,0]`

.When the

**Specify initial fluxes**parameter is not selected upon simulation, Simscape Electrical Specialized Power Systems 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.

### Advanced Tab

The **Advanced** tab of the block is not visible when you set the
**Simulation type** parameter of the powergui block to
`Continuous`

, or when you select the **Automatically handle
discrete solver** parameter of the powergui block. The tab is visible
when you set the **Simulation type** parameter of the powergui
block to `Discrete`

, and when the **Automatically handle
discrete solver** parameter of the powergui block is cleared.

**Break Algebraic loop in discrete saturation model**When selected, a delay is inserted at the output of the saturation model computing magnetization current as a function of flux linkage (the integral of input voltage computed by a Trapezoidal method). This delay eliminates the algebraic loop resulting from trapezoidal discretization methods and speeds up the simulation of the model. However, this delay introduces a one simulation step time delay in the model and can cause numerical oscillations if the sample time is too large. The algebraic loop is required in most cases to get an accurate solution.

When cleared (default), the

**Discrete solver model**parameter specifies the discretization method of the saturation model.**Discrete solver model**Select one of these methods to resolve the algebraic loop.

`Trapezoidal iterative`

—Although this method produces correct results, it is not recommended because Simulink^{®}tends to slow down and may fail to converge (simulation stops), especially when the number of saturable transformers is increased. Also, because of the Simulink algebraic loop constraint, this method cannot be used in real time. In R2018b and previous releases, you used this method when the**Break Algebraic loop in discrete saturation model**parameter was cleared.`Trapezoidal robust`

—This method is slightly more accurate than the`Backward Euler robust`

method. However, it may produce slightly damped numerical oscillations on transformer voltages when the transformer is at no load.`Backward Euler robust`

—This method provides good accuracy and prevents oscillations when the transformer is at no load.

The maximum number of iterations for the robust methods is specified in the

**Preferences**tab of the powergui block, in the**Solver details for nonlinear elements**section. For real time applications, you may need to limit the number of iterations. Usually, limiting the number of iterations to 2 produces acceptable results. The two robust solvers are the recommended methods for discretizing the saturation model of the transformer.For more information on what method to use in your application, see Simulating Discretized Electrical Systems.

## Examples

See the help text of the `power_48pulsegtoconverter`

example.

In this model, a 48-pulse GTO converter is built with four Three-Level Bridge blocks and four Zigzag Phase-Shifting Transformer blocks. Harmonic neutralization is obtained by use of appropriate phase shifts introduced by the Zigzag connections (+7.5/−7.5 degrees) and of secondary winding connections (Y or Delta).

**Introduced before R2006a**