Nonlinear Transformer

Transformer with nonideal core

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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.

• Open Model

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