# Nonlinear Transformer

Transformer with nonideal core

**Libraries:**

Simscape /
Electrical /
Passive /
Transformers

## Description

The Nonlinear Transformer block represents a transformer with a nonideal core. A core may be nonideal due to its magnetic properties and dimensions. The equivalent circuit topology depends upon the option you choose to parameterize the winding leakage.

If you set **Winding parameterized by** to ```
Combined primary
and secondary values
```

, you use lumped resistance and inductance values to
represent the combined leakage in the primary and secondary windings.

In this diagram:

*Req*is the combined winding resistance.*Leq*is the combined leakage inductance.*L2*is the secondary leakage inductance.*Rm*is the magnetization resistance.*Lm*is the magnetization inductance.

If you set **Winding parameterized by** to ```
Separate primary
and secondary values
```

, you use separate resistances and inductances to
represent leakages in the primary and secondary windings.

In this diagram:

*R1*is the primary winding resistance.*L1*is the primary leakage inductance.*R2*is the secondary winding resistance.*L2*is the 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, see the Nonlinear Inductor block reference page.

## Examples

### Nonlinear Transformer Characteristics

Calculation and confirmation of a nonlinear transformer core magnetization characteristic. Starting with fundamental parameter values, the core characteristic is derived. This is then used in a Simscape™ model of an example test circuit which can be used to plot the core magnetization characteristic on an oscilloscope. Model outputs are then compared to the known values.

## Ports

### Conserving

**1+** — Primary winding positive polarity

electrical

Electrical conserving port associated with the primary winding positive polarity.

**1-** — Primary winding negative polarity

electrical

Electrical conserving port associated with the primary winding negative polarity.

**2+** — Secondary winding positive polarity

electrical

Electrical conserving port associated with the secondary winding positive polarity.

**2-** — Secondary winding negative polarity

electrical

Electrical conserving port associated with the secondary winding negative polarity.

## Parameters

### Main

**Primary number of turns** — Primary number of turns

`100`

(default)

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

**Secondary number of turns** — Secondary number of turns

`200`

(default)

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

**Winding parameterized by** — Winding leakage parameterization

```
Combined primary and secondary
values
```

(default) | `Separate primary and secondary values`

Parameterization option for winding leakage. Choose one of these methods:

`Combined primary and secondary values`

— Use the lumped resistance and inductance values to represent the combined leakage in the primary and secondary windings.`Separate primary and secondary values`

— Use separate resistances and inductances to represent leakages in the primary and secondary windings.

**Combined winding resistance** — Combined winding resistance

`0.01`

`Ohm`

(default)

Lumped equivalent resistance *Req*, which represents the combined
power loss of the primary and secondary windings.

#### Dependencies

To enable this parameter, set **Winding parameterized by** to
`Combined primary and secondary values`

.

**Combined leakage inductance** — Combined leakage inductance

`0.0001`

`H`

(default)

Lumped equivalent inductance *Leq*, which represents the combined
magnetic flux loss of the primary and secondary windings.

#### Dependencies

To enable this parameter, set **Winding parameterized by** to
`Combined primary and secondary values`

.

**Primary winding resistance** — Primary winding resistance

`0.01`

`Ohm`

(default)

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

#### Dependencies

To enable this parameter, set **Winding parameterized by** to
`Separate primary and secondary values`

.

**Primary leakage inductance** — Primary leakage inductance

`0.0001`

`H`

(default)

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

#### Dependencies

To enable this parameter, set **Winding parameterized by** to
`Separate primary and secondary values`

.

**Secondary winding resistance** — Secondary winding resistance

`0.01`

`Ohm`

(default)

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

#### Dependencies

To enable this parameter, set **Winding parameterized by** to
`Separate primary and secondary values`

.

**Secondary leakage inductance** — Secondary leakage inductance

`0.0001`

`H`

(default)

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

#### Dependencies

To enable this parameter, set **Winding parameterized by** to
`Separate primary and secondary values`

.

**Averaging period for power logging** — Averaging period for power logging

`0`

`s`

(default)

Averaging period for power logging.

### Magnetization

**Magnetization resistance** — Magnetization resistance

`100`

`Ohm`

(default)

Resistance *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
```

Select one of the following methods for 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, to populate the magnetic flux versus current lookup table.`Magnetic flux density versus field strength characteristic`

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

— In addition to the number of turns and the effective core length and cross-sectional area, provide the values for the initial anhysteretic*B*-*H*curve gradient, the magnetic flux density and field strength at a certain point on the*B*-*H*curve, as well as the coefficient for the reversible magnetization, bulk coupling coefficient, and inter-domain coupling factor, to define magnetic flux density as a function of both the current value and the history of the field strength.

**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 **Magnetization inductance parameterized
by** 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 **Magnetization inductance parameterized
by** 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 **Magnetization inductance parameterized
by** 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 **Magnetization inductance parameterized
by** 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 **Magnetization inductance parameterized
by** to ```
Magnetic flux versus current
characteristic
```

.

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

`[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 **Magnetization inductance parameterized
by** to ```
Magnetic flux density versus field strength
characteristic
```

.

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

`[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 **Magnetization inductance parameterized
by** 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 the following interpolation methods:

`Linear`

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

— Select this option to 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 **Magnetization inductance parameterized
by** to ```
Magnetic flux versus current
characteristic
```

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

.

### Initial Conditions

**Combined leakage inductance initial current** — Combined leakage inductance initial current

`0`

`A`

(default)

Current through the combined leakage inductance *Leq* at time
zero.

#### Dependencies

To enable this parameter, in the **Main** settings, set the
**Winding parameterized by** parameter to ```
Combined
primary and secondary values
```

.

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

`0`

`A`

(default)

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

#### Dependencies

To enable this parameter, in the **Main** settings, set the
**Winding parameterized by** parameter to ```
Separate
primary and secondary values
```

.

**Secondary leakage inductance initial current** — Secondary leakage inductance initial current

`0`

`A`

(default)

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

#### Dependencies

To enable this parameter, in the **Main** settings, set the
**Winding parameterized by** parameter to ```
Separate
primary and secondary values
```

.

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

`Current`

(default) | `Magnetic flux`

Initial state specification method. 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, in the **Magnetization** settings,
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`

**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 **Specify magnetization inductance initial
state by** 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 **Specify magnetization inductance initial
state by** 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, in the **Magnetization** settings,
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, in the **Magnetization** settings,
set the **Magnetization inductance parameterized by** parameter to
```
Magnetic flux density versus field strength characteristic with
hysteresis
```

.

### Parasitics

**Combined leakage inductance parasitic parallel conductance** — Combined leakage inductance parasitic parallel conductance

`1e-9`

`1/Ohm`

(default)

Use this parameter to represent small parasitic effects in parallel to the
combined leakage inductance *Leq*. To simulate some circuit
topologies, you need a small parallel conductance.

#### Dependencies

To enable this parameter, in the **Main** settings, set
**Winding parameterized by** to ```
Combined primary and
secondary values
```

.

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

`1e-9`

`1/Ohm`

(default)

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

#### Dependencies

To enable this parameter, in the **Main** settings, set
**Winding parameterized by** to ```
Separate primary and
secondary values
```

.

**Secondary leakage inductance parasitic parallel conductance** — Secondary leakage inductance parasitic parallel conductance

`1e-9`

(default)

Use this parameter to represent small parasitic effects in parallel to the
secondary leakage inductance *L2*. To simulate some circuit
topologies, you need a small parallel conductance.

#### Dependencies

To enable this parameter, in the **Main** settings, set
**Winding parameterized by** to ```
Separate primary and
secondary values
```

.

## Extended Capabilities

### C/C++ Code Generation

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

## Version History

**Introduced in R2012b**

## Comando de MATLAB

Ha hecho clic en un enlace que corresponde a este comando de MATLAB:

Ejecute el comando introduciéndolo en la ventana de comandos de MATLAB. Los navegadores web no admiten comandos de MATLAB.

Select a Web Site

Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .

You can also select a web site from the following list:

## How to Get Best Site Performance

Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.

### Americas

- América Latina (Español)
- Canada (English)
- United States (English)

### Europe

- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)

- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)