# Multi-Winding Transformer

Implement multi-winding transformer with taps

## Library

Simscape / Electrical / Specialized Power Systems / Fundamental Blocks / Elements

## Description

The Multi-Winding Transformer block implements a transformer where the number of windings can be specified for both the primary (left side windings) and the secondary (right side windings).

The equivalent circuit of the Multi-Winding Transformer block is similar to the one of the Linear Transformer blocks and the saturation characteristic of the core can be specified or not. See the Saturable Transformer block reference pages for more details on how the saturation and the hysteresis characteristic are implemented.

The equivalent circuit of a Multi-Windings Transformer block with two primary windings and three secondary windings is shown in the next figure.

You can add equally spaced taps to the first primary winding (the upper-left winding) or to the first secondary winding (the upper-right winding). The equivalent circuit of a Multi-Winding Transformer block with one primary winding and eight taps on the first of the two secondary windings is shown in the next figure.

The winding terminals are identified by the corresponding winding number. The first winding is the first one on the primary side (upper-left side) and the last winding is the last one on the secondary side (bottom-right side). The polarities of the windings are defined by a plus sign.

The tap terminals are identified by their winding number followed by a dot character and the tap number. Taps are equally spaced so that voltage appearing at no load between two consecutive taps is equal to the total voltage of the winding divided by (number of taps +1). The total winding resistance and leakage inductance of a tapped winding is equally distributed along the taps.

## Parameters

### Configuration Tab

Number of windings on left side

Specifies the number of windings on the primary side (left side) of the transformer. Default is `1`.

Number of windings on right side

Specifies the number of windings on the secondary side (right side) of the transformer. Default is `3`.

Tapped winding

Select `no taps` (default) if you don't want to add taps to the transformer. Select `taps on upper left winding` to add taps to the first winding on the primary side of the transformer. Select ```taps on upper right winding``` to add taps to the secondary winding on the right side of the transformer. The number of taps is specified by the Number of taps (equally spaced) parameter.

Number of taps (equally spaced)

This parameter is not enabled if the Tapped winding parameter is set to `no taps`. Default is `2`.

If theTapped winding parameter is set to ```taps on upper left winding```, you specify the number of taps to add to the first winding on the left side.

If theTapped winding parameter is set to ```taps on upper right winding```, you specify the number of taps to add to the first winding on the right side.

Saturable core

If selected, implements a saturable transformer. See also the Saturation characteristic parameter on the Parameters tab. Default is cleared.

Simulate hysteresis

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

Hysteresis Mat file

The Hysteresis Mat file parameter is enabled only if the Simulate hysteresis parameter is selected.

Specify a `.mat` file containing the data to be used for the hysteresis model. When you open the Hysteresis Design Tool of the Powergui, 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.

Measurements

Select `Winding voltages` to measure the voltage across the winding terminals of the Saturable Transformer block.

Select `Winding currents` to measure the current flowing through the windings of the Saturable Transformer block.

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

Select `Flux and magnetization current (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 measurement (V, I, Flux)` to measure the winding voltages, currents, magnetization currents, and the flux linkage.

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.

Measurement

Label

Winding voltages

`U_LeftWinding_1:`
`U_TapWinding_2.1:``U_RightWinding_1:`

Winding currents

`I_LeftWinding_1:`
`I_TapWinding_2.1:``I_RightWinding_1:`

Excitation current

`Iexc:`

Magnetization current

`Imag:`

`Flux:`

### Parameters Tab

Units

Specify the units used to enter the parameters of the Multi-Winding 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. Default is `pu`.

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 `[75e3 60]`.

Winding nominal voltages

Specify a vector containing the nominal RMS voltages, in Vrms, of the windings on the left side, followed by the nominal RMS voltages of the windings on the right side. You don't have to specify the individual tap nominal voltages. Default is ```[ 14400 120 120 120 ]```.

Winding resistances

Specify a vector containing the resistance values of the windings on the left side, followed by the resistance values of the windings on the right side. You don't have to specify the individual tap resistances. Default is ```[ 0.005 0.005 0.005 0.005]``` when the Units parameter is `pu` and `[13.824 0.00096 0.00096 0.00096]` when the Units parameter is `SI`.

Winding leakage inductances

Specify a vector containing the leakage inductance values of the windings on the left side, followed by the leakage inductance values of windings on the right side. You don't have to specify the individual tap leakage inductances. Default is ```[ 0.02 0.02 0.02 0.02 ]``` when the Units parameter is `pu` and ```[0.14668 1.0186e-05 1.0186e-05 1.0186e-05]``` when the Units parameter is `SI`.

Magnetization resistance Rm

The magnetization resistance Rm, in ohms or in pu. Default is `50` when the Units parameter is `pu` and `1.3824e+05` when the Units parameter is `SI`.

Magnetization inductance Lm

The Magnetization inductance Lm parameter is not accessible if the Saturable core parameter on the Configuration tab is selected.

The magnetization inductance Lm, in Henry or in pu, for a nonsaturable core. Default is `50` when the Units parameter is `pu` and `366.69` when the Units parameter is `SI`.

Saturation characteristic

This parameter is accessible only if the Saturation 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). Default is ```[ 0,0 ; 0.0024,1.2 ; 1.0,1.52 ]``` when the Units parameter is `pu` and `[0 0;0.017678 64.823;7.3657 82.109]` when the Units parameter is `SI`.

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, the 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 discretization method of the saturation model is specified by the Discrete solver model parameter.

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.

## Examples

The `power_OLTCregtransformer` example uses three Multi-Winding Transformer blocks to implement a three-phase On Load Tap Changer (OLTC) transformer.

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