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Nonlinear Transformer

Model transformer with nonideal core

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Passive Devices

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 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 leakage resistance.

  • Leq is the combined leakage inductance.

  • R1 is the primary leakage resistance.

  • L1 is the primary leakage inductance.

  • R2 is the secondary leakage resistance.

  • L2 is the secondary leakage 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

For more information, see the Nonlinear Inductor block reference page.

Dialog Box and Parameters

Main Tab

Primary number of turns

The number of turns of wire on the primary winding of the transformer. The default value is 100.

Secondary number of turns

The number of turns of wire on the secondary winding of the transformer. The default value is 200.

Winding parameterized by

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 leakage resistance

The lumped equivalent resistance Req, which represents the combined power loss of the primary and secondary windings. This parameter is only visible when you select Combined primary and secondary values for the Winding parameterized by parameter. The default value is 0.01 Ω.

Combined leakage inductance

The lumped equivalent inductance Leq, which represents the combined magnetic flux loss of the primary and secondary windings. This parameter is only visible when you select Combined primary and secondary values for the Winding parameterized by parameter. The default value is 1e-4 H.

Primary leakage resistance

The resistance R1, which represents the power loss of the primary winding. This parameter is only visible when you select Separate primary and secondary values for the Winding parameterized by parameter. The default value is 0.01 Ω.

Primary leakage inductance

The inductance L1, which represents the magnetic flux loss of the primary winding. This parameter is only visible when you select Separate primary and secondary values for the Winding parameterized by parameter. The default value is 1e-4 H.

Secondary leakage resistance

The resistance R2, which represents the power loss of the secondary winding. This parameter is only visible when you select Separate primary and secondary values for the Winding parameterized by parameter. The default value is 0.01 Ω.

Secondary leakage inductance

The inductance L2, which represents the magnetic flux loss of the secondary winding. This parameter is only visible when you select Separate primary and secondary values for the Winding parameterized by parameter. The default value is 1e-4 H.

Magnetization Tab

Magnetization resistance

The resistance Rm, which represents the magnetic losses in the transformer core. The default value is 100 Ω.

Magnetization inductance parameterized by

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 magnetic 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.

Unsaturated inductance

The value of inductance used when the magnetization inductance Lm is operating in its linear region. This parameter is only visible when you select Single inductance (linear) or Single saturation point for the Magnetization inductance parameterized by parameter. The default value is 0.04 H.

Saturated inductance

The value of inductance used when the magnetization inductance Lm is operating beyond its saturation point. This parameter is only visible when you select Single saturation point for the Magnetization inductance parameterized by parameter. The default value is 0.01 H.

Saturation magnetic flux

The value of magnetic flux at which the magnetization inductance Lm saturates. This parameter is only visible when you select Single saturation point for the Magnetization inductance parameterized by parameter. The default value is 1.6e-4 Wb.

Current, i

The current data used to populate the magnetic flux versus current lookup table. This parameter is only visible when you select Magnetic flux versus current characteristic for the Magnetization inductance parameterized by parameter. The default value is [ 0 0.4 0.8 1.2 1.6 2.0 ] A.

Magnetic flux vector, phi

The magnetic flux data used to populate the magnetic flux versus current lookup table. This parameter is only visible when you select Magnetic flux versus current characteristic for the Magnetization inductance parameterized by parameter. The default value is [0 0 0.161 0.25 0.284 0.295 0.299 ].*1e-3 Wb.

Magnetic field strength vector, H

The magnetic field strength data used to populate the magnetic flux density versus magnetic field strength lookup table. This parameter is only visible when you select Magnetic flux density versus magnetic field strength characteristic for the Magnetization inductance parameterized by parameter. The default value is [ 0 200 400 600 800 1000 ] A/m.

Magnetic flux density vector, B

The magnetic flux density data used to populate the magnetic flux density versus magnetic field strength lookup table. This parameter is only visible when you select Magnetic flux density versus magnetic field strength characteristic for the Magnetization inductance parameterized by parameter. The default value is [ 0 0.81 1.25 1.42 1.48 1.49 ] T.

Effective length

The effective core length, that is, the average distance of the magnetic path around the transformer core. This parameter is only visible when you select Magnetic flux density versus magnetic field strength characteristic for the Magnetization inductance parameterized by parameter. The default value is 0.2 m.

Effective cross-sectional area

The effective core cross-sectional area, that is, the average area of the magnetic path around the transformer core. This parameter is only visible when you select Magnetic flux density versus magnetic field strength characteristic for the Magnetization inductance parameterized by parameter. The default value is 2e-4 m^2.

Interpolation option

The lookup table interpolation option. This parameter is only visible when you select Magnetic flux versus current characteristic or Magnetic flux density versus magnetic field strength characteristic for the Magnetization inductance parameterized by parameter. Select one of the following interpolation methods:

  • Linear — Uses a linear interpolation function.

  • Cubic — Uses the Piecewise Cubic Hermite Interpolation Polinomial (PCHIP).

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

Initial Conditions Tab

Combined leakage inductance initial current

The value of current through the combined leakage inductance Leq at time zero. This parameter is only visible when you select Combined primary and secondary values for the Winding parameterized by parameter on the Main tab. The default value is 0 A.

Primary leakage inductance initial current

The value of current through the primary leakage inductance L1 at time zero. This parameter is only visible when you select Separate primary and secondary values for the Winding parameterized by parameter on the Main tab. The default value is 0 A.

Secondary leakage inductance initial current

The value of current through the secondary leakage inductance L2 at time zero. This parameter is only visible when you select Separate primary and secondary values for the Winding parameterized by parameter on the Main tab. The default value is 0 A.

Specify magnetization inductance initial state by

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.

Magnetization inductance initial current

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 only visible when you select Current for the Specify magnetization inductance initial state by parameter. The default value is 0 A.

Magnetization inductance initial magnetic flux

The value of the magnetic flux in the magnetization inductance Lm at time zero. This parameter is only visible when you select Magnetic flux for the Specify magnetization inductance initial state by parameter. The default is 0 Wb.

Parasitics Tab

Combined leakage inductance parasitic parallel conductance

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 only visible when you select Combined primary and secondary values for the Winding parameterized by parameter on the Main tab. The default value is 1e-9 1/Ω.

Primary leakage inductance parasitic parallel conductance

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 only visible when you select Separate primary and secondary values for the Winding parameterized by parameter on the Main tab. The default value is 1e-9 1/Ω.

Secondary leakage inductance parasitic parallel conductance

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. This parameter is only visible when you select Separate primary and secondary values for the Winding parameterized by parameter on the Main tab. The default value is 1e-9 1/Ω.

Examples

For comparison of nonlinear transformer behavior with different parameterization options, see the Nonlinear Transformer Characteristics example.

Ports

The block has four electrical conserving ports. Polarity is indicated by the + and - signs.

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