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Transformer with nonideal core

**Library:**Simscape / Electrical / Passive / Transformers

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 which of the two winding leakage parameterization options you select:

`Combined primary and secondary values`

`Separate primary and secondary values`

where:

*Req*is the combined winding resistance.*Leq*is the combined leakage inductance.*R1*is the primary winding resistance.*L1*is the primary winding inductance.*R2*is the secondary winding resistance.*L2*is the secondary winding inductance.*Rm*is the magnetization resistance.*Lm*is the magnetization inductance.

The block provides the following parameterization options for the nonlinear magnetization inductance:

`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.

`1+`

— Primary winding positive polarityelectrical

Electrical conserving port associated with the primary winding positive polarity.

`1-`

— Primary winding negative polarityelectrical

Electrical conserving port associated with the primary winding negative polarity.

Electrical conserving port associated with the primary winding negative polarity.

`2+`

— Secondary winding positive polarityelectrical

Electrical conserving port associated with the secondary winding positive polarity.

`2-`

— Secondary winding negative polarityelectrical

Electrical conserving port associated with the secondary winding negative polarity.

`Primary number of turns`

— Primary number of turns`100`

(default)The number of turns of wire on the primary winding of the transformer.

`Secondary number of turns`

— Secondary number of turns`200`

(default)The 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`

Select one of the following methods for the winding leakage parameterization:

`Combined primary and secondary values`

— Use the lumped resistance and inductance values representing the combined leakage in the primary and secondary windings. This is the default option.`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)The lumped equivalent resistance *Req*, which represents the
combined power loss of the primary and secondary windings.

This parameter is visible only when you select ```
Combined primary and
secondary values
```

for the **Winding parameterized
by** parameter.

`Combined leakage inductance`

— Combined leakage inductance`0.0001`

`H`

(default)The lumped equivalent inductance *Leq*, which represents the
combined magnetic flux loss of the primary and secondary windings.

This parameter is visible only when you select ```
Combined primary and
secondary values
```

for the **Winding parameterized
by** parameter.

`Primary winding resistance`

— Primary winding resistance`0.01`

`Ohm`

(default)The resistance *R1*, which represents the power loss of the
primary winding.

This parameter is visible only when you select ```
Separate primary and
secondary values
```

for the **Winding parameterized
by** parameter.

`Primary leakage inductance`

— Primary leakage inductance`0.0001`

`H`

(default)The inductance *L1*, which represents the magnetic flux loss of
the primary winding.

This parameter is visible only when you select ```
Separate primary and
secondary values
```

for the **Winding parameterized
by** parameter.

`Secondary winding resistance`

— Secondary winding resistance`0.01`

`Ohm`

(default)The resistance *R2*, which represents the power loss of the
secondary winding.

This parameter is visible only when you select ```
Separate primary and
secondary values
```

for the **Winding parameterized
by** parameter.

`Secondary leakage inductance`

— Secondary leakage inductance`0.0001`

`H`

(default)The inductance *L2*, which represents the magnetic flux loss of
the secondary winding.

```
Separate primary and
secondary values
```

for the **Winding parameterized
by** parameter.

`Averaging period for power logging`

— Averaging period for power logging`0`

`s`

(default)Averaging period for power logging

`Magnetization resistance`

— Magnetization resistance`100`

`Ohm`

(default)The 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. This is the default option.`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)The value of inductance used when the magnetization inductance
*Lm* is operating in its linear region.

This parameter is visible only when you select ```
Single inductance
(linear)
```

or `Single saturation point`

for
the **Magnetization inductance parameterized by** parameter.

`Saturated inductance`

— Saturated inductance`1e-2`

`H`

(default)The value of inductance used when the magnetization inductance
*Lm* is operating beyond its saturation point.

This parameter is visible only when you select ```
Single saturation
point
```

for the **Magnetization inductance parameterized
by** parameter.

`Saturation magnetic flux`

— Saturation magnetic flux`1.6e-04`

`Wb`

(default)The value of magnetic flux at which the magnetization inductance
*Lm* saturates.

This parameter is visible only when you select ```
Single saturation
point
```

for the **Magnetization inductance parameterized
by** parameter.

`Current vector, i`

— Current data`[0, .4, .8, 1.2, 1.6, 2]`

`A`

(default)The current data used to populate the magnetic flux versus current lookup table.

This parameter is visible only when you select ```
Magnetic flux versus
current characteristic
```

for the **Magnetization inductance
parameterized by** parameter.

`Magnetic flux vector, phi`

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

`Wb`

(default)The magnetic flux data used to populate the magnetic flux versus current lookup table.

This parameter is visible only when you select ```
Magnetic flux versus
current characteristic
```

for the **Magnetization inductance
parameterized by** parameter.

`Magnetic field strength vector, H`

— Magnetic field strength vector`[0, 200, 400, 600, 800, 1000]`

`A/m`

(default)The magnetic field strength data used to populate the magnetic flux density versus magnetic field strength lookup table.

This parameter is visible only when you select ```
Magnetic flux
density versus field strength characteristic
```

for the
**Magnetization inductance parameterized by** parameter.

`Magnetic flux density vector, B`

— Magnetic flux density vector`[0, .81, 1.25, 1.42, 1.48, 1.49]`

`T`

(default)The magnetic flux density data used to populate the magnetic flux density versus magnetic field strength lookup table.

This parameter is visible only when you select ```
Magnetic flux
density versus field strength characteristic
```

for the
**Magnetization inductance parameterized by** parameter.

`Effective length`

— Effective length`0.2`

`m`

(default)The effective core length, that is, the average distance of the magnetic path around the transformer core.

This parameter is visible only when you select ```
Magnetic flux
density versus field strength characteristic
```

for the
**Magnetization inductance parameterized by** parameter.

`Effective cross-sectional area`

— Effective cross-sectional area`2e-4`

`m^2`

(default)The effective core cross-sectional area, that is, the average area of the magnetic path around the transformer core.

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

for the
**Magnetization inductance parameterized by** parameter.

`Anhysteretic B-H gradient when H is zero`

— Anhysteretic B-H gradient around zero field strength`0.005`

`m*T/A`

(default)The gradient of the anhysteretic (no hysteresis) B-H curve around zero field strength. Set it to the average gradient of the positive-going and negative-going hysteresis curves.

This parameter is visible only when you select ```
Magnetic flux
density versus field strength characteristic with hysteresis
```

for the
**Magnetization inductance parameterized by** parameter.

`Flux density point on anhysteretic B-H curve`

— Flux density point on anhysteretic B-H curve`1.49`

`T`

(default)Specify a point on the anhysteretic curve by providing its flux density value. Picking a point at high field strength where the positive-going and negative-going hysteresis curves align is the most accurate option.

This parameter is visible only when you select ```
Magnetic flux
density versus field strength characteristic with hysteresis
```

for the
**Magnetization inductance parameterized by** parameter.

`Corresponding field strength`

— Corresponding field strength`1000`

`A/m`

(default)The corresponding field strength for the point that you define by the
**Flux density point on anhysteretic B-H curve** parameter.

This parameter is visible only when you select ```
Magnetic flux
density versus field strength characteristic with hysteresis
```

for the
**Magnetization inductance parameterized by** parameter.

`Coefficient for reversible magnetization, c`

— Coefficient for reversible magnetization`0.1`

(default)The proportion of the magnetization that is reversible. The value should be greater than zero and less than one.

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

for the
**Magnetization inductance parameterized by** parameter.

`Bulk coupling coefficient, K`

— Bulk coupling coefficient`200`

`A/m`

(default)The Jiles-Atherton parameter that primarily controls the field strength magnitude at which the B-H curve crosses the zero flux density line.

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

for the
**Magnetization inductance parameterized by** parameter.

`Inter-domain coupling factor, alpha`

— Inter-domain coupling factor`1e-4`

(default)The Jiles-Atherton parameter that 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.

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

for the
**Magnetization inductance parameterized by** parameter.

`Interpolation option`

— Interpolation option`Linear`

(default) | `Smooth`

The 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.

This parameter is visible only when you select ```
Magnetic flux versus
current characteristic
```

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

for the **Magnetization
inductance parameterized by** parameter.

`Combined leakage inductance initial current`

— Combined leakage inductance initial current`0`

`A`

(default)The value of current through the combined leakage inductance
*Leq* at time zero.

This parameter is visible only when you select ```
Combined primary and
secondary values
```

for the **Winding parameterized
by** parameter on the **Main** tab.

`Primary leakage inductance initial current`

— Primary leakage inductance initial current`0`

`A`

(default)The value of current through the primary leakage inductance *L1*
at time zero.

This parameter is visible only when you select ```
Separate primary and
secondary values
```

for the **Winding parameterized
by** parameter on the **Main** tab.

`Secondary leakage inductance initial current`

— Secondary leakage inductance initial current`0`

`A`

(default)The value of current through the secondary leakage inductance
*L2* at time zero.

This parameter is visible only when you select ```
Separate primary and
secondary values
```

for the **Winding parameterized
by** parameter on the **Main** tab.

`Specify magnetization inductance initial state by`

— Initial state specification option`Current`

(default) | `Magnetic flux`

Select the appropriate initial state specification option:

`Current`

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

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

This parameter is not visible only when you select ```
Magnetic flux
density versus magnetic field strength characteristic with
hysteresis
```

for the **Magnetization inductance parameterized
by** parameter on the **Magnetization** tab.

`Magnetization inductance initial current`

— Magnetization inductance initial current`0`

`A`

(default)The initial current value used to calculate the value of magnetic flux within the
magnetization inductance *Lm* at time zero. This 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*.

This parameter is visible only when you select
`Current`

for the **Specify magnetization
inductance initial state by** parameter.

`Magnetization inductance initial magnetic flux`

— Magnetization inductance initial magnetic flux`0`

`Wb`

(default)The value of the magnetic flux in the magnetization inductance
*Lm* at time zero.

This parameter is visible only when you select ```
Magnetic
flux
```

for the **Specify magnetization inductance initial
state by** parameter.

`Magnetization inductance initial magnetic flux density`

— Magnetization inductance initial magnetic flux density`0`

`T`

(default)The value of magnetic flux density at time zero. This parameter is visible only
when you select ```
Magnetic flux density versus magnetic field strength
characteristic with hysteresis
```

for the **Magnetization
inductance parameterized by** parameter on the
**Magnetization** tab.

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

for the
**Magnetization inductance parameterized by** parameter.

`Magnetization inductance initial field strength`

— Magnetization inductance initial field strength`0`

`A/m`

(default)The value of magnetic field strength at time zero.

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

for the
**Magnetization inductance parameterized by** parameter.

`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*. A small parallel conductance may
be required for the simulation of some circuit topologies.

This parameter is visible only when you select ```
Combined primary and
secondary values
```

for the **Winding parameterized
by** parameter on the **Main** tab.

`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*. A small parallel conductance may be required
for the simulation of some circuit topologies.

This parameter is visible only when you select ```
Separate primary and
secondary values
```

for the **Winding parameterized
by** parameter on the **Main** tab.

`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*. A small parallel conductance may
be required for the simulation of some circuit topologies.

```
Separate primary and
secondary values
```

for the **Winding parameterized
by** parameter on the **Main** tab.

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

Earthing Transformer | Ideal Transformer | Tap-Changing Transformer | Three-Winding Transformer (Three-Phase) | Two-Winding Transformer (Three-Phase) | Zigzag-Delta-Wye Transformer

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