# Three-Winding Nonlinear Transformer

Single-phase nonlinear three-winding transformer

**Libraries:**

Simscape /
Electrical /
Passive /
Transformers

## Description

The Three-Winding Nonlinear Transformer block represents a single-phase, nonlinear, three-winding transformer with a nonideal core. A core may be nonideal due to its magnetic properties or dimensions. This figure shows the equivalent circuit topology,

where:

*R1*is the primary winding resistance.*L1*is the primary leakage inductance.*R2*is the first secondary winding resistance.*L2*is the first secondary leakage inductance.*R3*is the second secondary winding resistance.*L3*is the second secondary leakage inductance.*Rm*is the magnetization resistance.*Lm*is the magnetization inductance.

To parameterize the nonlinear magnetization inductance, set the
**Magnetization inductance parameterized by** parameter to one of
these options:

`Single inductance (linear)`

`Single saturation point`

`Magnetic flux versus current characteristic`

`Magnetic flux density versus magnetic field strength characteristic`

`Magnetic flux density versus magnetic field strength characteristic with hysteresis`

For more information about these parameterization options including the equations that the block uses to model nonlinear magnetization inductance, see the Nonlinear Inductor block reference page.

## Ports

### Conserving

**1+** — Line 1 positive terminal

electrical

Electrical conserving port associated with the positive terminal of line 1.

**1-** — Line 1 negative terminal

electrical

Electrical conserving port associated with the negative terminal of line 1.

**2+** — Line 2 positive terminal

electrical

Electrical conserving port associated with the positive terminal of line 2.

**2-** — Line 2 negative terminal

electrical

Electrical conserving port associated with the negative terminal of line 2.

**3+** — Line 3 positive terminal

electrical

Electrical conserving port associated with the positive terminal of line 3.

**3-** — Line 3 negative terminal

electrical

Electrical conserving port associated with the negative terminal of line 3.

## Parameters

### Main

**Primary number of turns** — Winding 1 primary turns number

`100`

(default) | positive scalar integer

Number of turns of wire on the first primary winding of the transformer.

**First secondary number of turns** — Winding 2 turns number

`200`

(default) | positive scalar integer

Number of turns of wire on the first secondary winding of the transformer.

**Second secondary number of turns** — Winding 3 turns number

`200`

(default) | positive scalar integer

Number of turns of wire on the second secondary winding of the transformer.

**Primary winding resistance** — Winding 1 resistance

`0.01`

`Ohm`

(default) | nonnegative scalar

Resistance for *R1*, which represents the power loss
of the primary winding.

**Primary leakage inductance** — Winding 1 leakage inductance

`0.0001`

`H`

(default) | nonnegative scalar

Inductance for *L1*, which represents the magnetic flux loss of the
primary winding.

**First secondary winding resistance** — Winding 2 resistance

`0.01`

`Ohm`

(default) | nonnegative scalar

Resistance for *R2*, which represents the power loss
of the first secondary winding.

**First secondary leakage inductance** — Winding 2 leakage inductance

`0.0001`

`H`

(default) | nonnegative scalar

Inductance for *L2*, which represents the magnetic flux loss of the
first secondary winding.

**Second secondary winding resistance** — Winding 3 resistance

`0.01`

`Ohm`

(default) | nonnegative scalar

Resistance for *R3*, which represents the power loss
of the second secondary winding.

**Second secondary leakage inductance** — Winding 3 leakage inductance

`0.0001`

`H`

(default) | nonnegative scalar

Inductance for *L3*, which represents the magnetic flux loss of the
second secondary winding.

### Magnetization

**Magnetization resistance** — Magnetization resistance

`100`

`Ohm`

(default)

Resistance for *Rm*, which represents the magnetic losses in the
transformer core.

**Magnetization inductance parameterized by** — Nonlinear magnetization inductance parameterization

```
Single saturation
point
```

(default) | `Single inductance (linear)`

| ```
Magnetic flux versus current
characteristic
```

| ```
Magnetic flux density versus field strength
characteristic
```

| ```
Magnetic flux density versus field strength
characteristic with hysteresis
```

Method of the nonlinear magnetization inductance parameterization:

`Single inductance (linear)`

— Provide the unsaturated inductance value.`Single saturation point`

— Provide the values for the unsaturated and saturated inductances, as well as saturation magnetic flux.`Magnetic flux versus current characteristic`

— Provide the current vector and the magnetic flux vector, and then populate the magnetic flux versus current lookup table.`Magnetic flux density versus field strength characteristic`

— Provide the values for effective core length, cross-sectional area, magnetic field strength vector and the magnetic flux density vector, and then populate the magnetic flux density versus magnetic field strength lookup table.`Magnetic flux density versus field strength characteristic with hysteresis`

— Define magnetic flux density as a function or both the current value and the history of the field strength by providing the number of turns, the effective core length and cross-sectional area, the initial anhysteretic B-H curve gradient, the magnetic flux density and field strength at a certain point on the B-H curve, the coefficient for the reversible magnetization, the bulk coupling coefficient, and the inter-domain coupling factor.

**Unsaturated inductance** — Unsaturated inductance

`4e-2`

`H`

(default)

Inductance when the magnetization inductance *Lm* operates in its
linear region.

#### Dependencies

To enable this parameter, set the **Magnetization inductance parameterized
by** parameter to ```
Single inductance
(linear)
```

or ```
Single saturation
point
```

.

**Saturated inductance** — Saturated inductance

`1e-2`

`H`

(default)

Inductance when the magnetization inductance *Lm* operates beyond its
saturation point.

#### Dependencies

To enable this parameter, set the **Magnetization
inductance parameterized by** parameter to
`Single saturation point`

.

**Saturation magnetic flux** — Saturation magnetic flux

`1.6e-04`

`Wb`

(default)

Magnetic flux at which the magnetization inductance *Lm*
saturates.

#### Dependencies

To enable this parameter, set the **Magnetization
inductance parameterized by** parameter to
`Single saturation point`

.

**Current vector, i** — Current data

`[0, .4, .8, 1.2, 1.6, 2]`

`A`

(default)

Current data that the block uses to populate the magnetic flux versus current lookup table.

#### Dependencies

To enable this parameter, set the **Magnetization
inductance parameterized by** parameter to
```
Magnetic flux versus current
characteristic
```

.

**Magnetic flux vector, phi** — Magnetic flux vector

```
[0, .161, .25, .284, .295, .299] .*
1e-3
```

`Wb`

(default)

Magnetic flux data that the block uses to populate the magnetic flux versus current lookup table.

#### Dependencies

To enable this parameter, set the **Magnetization
inductance parameterized by** parameter to
```
Magnetic flux versus current
characteristic
```

.

**Magnetic field strength vector, H** — Magnetic field strength vector

`[0, 200, 400, 600, 800, 1000]`

`A/m`

(default) | vector

Magnetic field intensity *H*, specified as a vector with the same
number of elements as the magnetic flux density vector
*B*.

#### Dependencies

To enable this parameter, set the **Magnetization
inductance parameterized by** parameter to
```
Magnetic flux density versus field strength
characteristic
```

.

**Magnetic flux density vector, B** — Magnetic flux density vector

`[0, .81, 1.25, 1.42, 1.48, 1.49]`

`T`

(default) | vector

Magnetic flux density *B*, specified as a vector with
the same number of elements as the magnetic field strength vector
*H*.

#### Dependencies

To enable this parameter, set the **Magnetization
inductance parameterized by** parameter to
```
Magnetic flux density versus field strength
characteristic
```

.

**Effective length** — Effective core length

`0.2`

`m`

(default) | positive finite scalar

Effective core length. This parameter represents the average length of the magnetic path around the core.

#### Dependencies

To enable this parameter, set the **Magnetization inductance parameterized
by** parameter to ```
Magnetic flux density versus field
strength characteristic
```

or ```
Magnetic flux density
versus field strength characteristic with hysteresis
```

.

**Effective cross-sectional area** — Effective core cross-sectional area

`2e-4`

`m^2`

(default) | positive finite scalar

Effective core cross-sectional area. This parameter represents the average area of the magnetic path around the core.

#### Dependencies

To enable this parameter, set the
**Magnetization inductance parameterized
by** parameter to ```
Magnetic
flux density versus field strength
characteristic
```

or
```
Magnetic flux density versus field
strength characteristic with
hysteresis
```

.

**Anhysteretic B-H gradient when H is zero** — Gradient of anhysteretic B-H curve around zero field strength

`0.005`

`m*T/A`

(default) | scalar

Gradient of the anhysteretic *B*-*H* curve around
zero field strength. Set this parameter to the average gradient of the ascending and
descending hysteresis curves.

#### Dependencies

To enable this parameter, set the **Magnetization inductance parameterized
by** parameter to ```
Magnetic flux density versus field
strength characteristic with hysteresis
```

.

**Flux density point on anhysteretic B-H curve** — Flux density point on anhysteretic B-H curve

`1.49`

`T`

(default) | scalar

Flux density of the point for field strength measurement. You must specify a point on the anhysteretic curve by providing its flux density value. To obtain accurate results, pick a point at high field strength where the ascending and descending hysteresis curves align.

#### Dependencies

To enable this parameter, set the **Magnetization inductance parameterized by** parameter to `Magnetic flux density versus field strength characteristic with hysteresis`

.

**Corresponding field strength** — Field strength at measurement point

`1000`

`A/m`

(default) | scalar

Field strength that corresponds to the point that you define using the **Flux density
point on anhysteretic B-H curve** parameter.

#### Dependencies

To enable this parameter, set **Magnetization inductance parameterized by** to `Magnetic flux density versus field strength characteristic with hysteresis`

.

**Coefficient for reversible magnetization, c** — Coefficient for reversible magnetization

`0.1`

(default) | scalar in the range [0,1]

Coefficient for reversible magnetization in the Jiles-Atherton
equations, *c*. This parameter represents the
proportion of the magnetization that you can reverse.

#### Dependencies

To enable this parameter, set **Magnetization
inductance parameterized by** to
```
Magnetic flux density versus magnetic
field strength characteristic with
hysteresis
```

.

**Bulk coupling coefficient, K** — Bulk coupling coefficient

`200`

`A/m`

(default) | finite positive scalar

Bulk coupling coefficient in the Jiles-Atherton equations, *K*. This
parameter primarily controls the field strength magnitude at which the
*B*-*H* curve crosses the zero flux density
line.

#### Dependencies

To enable this parameter, set **Magnetization inductance parameterized by** to `Magnetic flux density versus field strength characteristic with hysteresis`

.

**Inter-domain coupling factor, alpha** — Inter-domain coupling factor

`1e-4`

(default) | scalar

Inter-domain coupling factor in the Jiles-Atherton equations, *α*. This
parameter primarily affects the points at which the
*B*-*H* curves intersect the zero field strength
line. Typical values are in the range of `1e-4`

to
`1e-3`

.

#### Dependencies

To enable this parameter, set the **Magnetization inductance parameterized by** parameter to `Magnetic flux density versus field strength characteristic with hysteresis`

.

**Interpolation option** — Interpolation option

`Linear`

(default) | `Smooth`

Lookup table interpolation option. Select one of these interpolation methods:

`Linear`

— Select this option to get the best performance.`Smooth`

— Produce a continuous curve with continuous first-order derivatives.

For more information on interpolation algorithms, see the PS Lookup Table (1D) block reference page.

#### Dependencies

To enable this parameter, set the **Magnetization
inductance parameterized by** parameter to
```
Magnetic flux versus current
characteristic
```

or ```
Magnetic flux
density versus field strength characteristic
```

.

### Initial Conditions

**Primary leakage inductance initial current** — Primary leakage inductance initial current

`0`

`A`

(default)

Current through the primary leakage inductance *L1* at time
zero.

**First secondary leakage inductance initial current** — First secondary leakage inductance initial current

`0`

`A`

(default)

Current through the first secondary leakage inductance *L2* at time
zero.

**Second secondary leakage inductance initial current** — Second secondary leakage inductance initial current

`0`

`A`

(default)

Current through the second secondary leakage inductance *L3* at time
zero.

**Specify magnetization inductance initial state by** — Initial state specification option

`Current`

(default) | `Magnetic flux`

Initial state specification. Choose one of these options:

`Current`

— Specify the initial state of the magnetization inductance*Lm*by the initial current.`Magnetic flux`

— Specify the initial state of the magnetization inductance*Lm*by the magnetic flux.

#### Dependencies

To enable this parameter, on the
**Magnetization** setting, set the
**Magnetization inductance parameterized by**
parameter to:

`Single inductance (linear)`

`Single saturation point`

`Magnetic flux versus current characteristic`

`Magnetic flux density versus field strength characteristic`

**Magnetization inductance initial current** — Magnetization inductance initial current

`0`

`A`

(default)

Initial current value that the block uses to calculate the magnetic flux within the
magnetization inductance *Lm* at time zero. This
parameter is the current passing through the magnetization inductance
*Lm*. Total magnetization current consists of
current passing through the magnetization resistance
*Rm* and current passing through the magnetization
inductance *Lm*.

#### Dependencies

To enable this parameter, set the **Specify magnetization
inductance initial state by** parameter to
`Current`

**Magnetization inductance initial magnetic flux** — Magnetization inductance initial magnetic flux

`0`

`Wb`

(default)

Magnetic flux in the magnetization inductance *Lm* at time zero.

#### Dependencies

To enable this parameter, set the **Specify magnetization
inductance initial state by** parameter to
`Magnetic flux`

**Magnetization inductance initial magnetic flux density** — Magnetization inductance initial magnetic flux density

`0`

`T`

(default)

Magnetic flux density at time zero.

#### Dependencies

To enable this parameter, on the
**Magnetization** setting, set the
**Magnetization inductance parameterized by**
parameter to ```
Magnetic flux density versus field
strength characteristic with hysteresis
```

**Magnetization inductance initial field strength** — Magnetization inductance initial field strength

`0`

`A/m`

(default)

Magnetic field strength at time zero.

#### Dependencies

To enable this parameter, on the
**Magnetization** setting, set the
**Magnetization inductance parameterized by**
parameter to ```
Magnetic flux density versus field
strength characteristic with hysteresis
```

### Parasitics

**Primary leakage inductance parasitic parallel conductance** — Winding 1 leakage inductance parasitic parallel conductance

`1e-9`

`1/Ohm`

(default) | nonneagative scalar

Small parasitic effects in parallel to the primary leakage inductance
*L1*. To simulate some circuit topologies, you need
a small parallel conductance.

**First secondary leakage inductance parasitic parallel conductance** — Winding 2 leakage inductance parasitic parallel conductance

`1e-9`

`1/Ohm`

(default) | nonneagative scalar

Small parasitic effects in parallel to the first secondary leakage inductance
*L2*. To simulate some circuit topologies, you
need a small parallel conductance.

**Second secondary leakage inductance parasitic parallel conductance** — Winding 3 leakage inductance parasitic parallel conductance

`1e-9`

`1/Ohm`

(default) | nonneagative scalar

Small parasitic effects in parallel to the second secondary leakage inductance
*L3*. To simulate some circuit topologies, you
need a small parallel conductance.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

## Version History

**Introduced in R2019b**

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