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

expand all

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

expand all

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

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

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

Three-Winding Nonlinear Transformer

Description

Ports

Conserving

1+ — Line 1 positive terminal electrical

1- — Line 1 negative terminal electrical

2+ — Line 2 positive terminal electrical

2- — Line 2 negative terminal electrical

3+ — Line 3 positive terminal electrical

3- — Line 3 negative terminal electrical

Parameters

Main

Primary number of turns — Winding 1 primary turns number 100 (default) | positive scalar integer

First secondary number of turns — Winding 2 turns number 200 (default) | positive scalar integer

Second secondary number of turns — Winding 3 turns number 200 (default) | positive scalar integer

Primary winding resistance — Winding 1 resistance 0.01 Ohm (default) | nonnegative scalar

Primary leakage inductance — Winding 1 leakage inductance 0.0001 H (default) | nonnegative scalar

First secondary winding resistance — Winding 2 resistance 0.01 Ohm (default) | nonnegative scalar

First secondary leakage inductance — Winding 2 leakage inductance 0.0001 H (default) | nonnegative scalar

Second secondary winding resistance — Winding 3 resistance 0.01 Ohm (default) | nonnegative scalar

Second secondary leakage inductance — Winding 3 leakage inductance 0.0001 H (default) | nonnegative scalar

Magnetization

Magnetization resistance — Magnetization resistance 100 Ohm (default)

Unsaturated inductance — Unsaturated inductance 4e-2 H (default)

Dependencies

Saturated inductance — Saturated inductance 1e-2 H (default)

Dependencies

Saturation magnetic flux — Saturation magnetic flux 1.6e-04 Wb (default)

Dependencies

Current vector, i — Current data [0, .4, .8, 1.2, 1.6, 2] A (default)

Dependencies

Magnetic flux vector, phi — Magnetic flux vector [0, .161, .25, .284, .295, .299] .* 1e-3 Wb (default)

Dependencies

Magnetic field strength vector, H — Magnetic field strength vector [0, 200, 400, 600, 800, 1000] A/m (default) | vector

Dependencies

Magnetic flux density vector, B — Magnetic flux density vector [0, .81, 1.25, 1.42, 1.48, 1.49] T (default) | vector

Dependencies

Effective length — Effective core length 0.2 m (default) | positive finite scalar

Dependencies

Effective cross-sectional area — Effective core cross-sectional area 2e-4 m^2 (default) | positive finite scalar

Dependencies

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

Dependencies

Flux density point on anhysteretic B-H curve — Flux density point on anhysteretic B-H curve 1.49 T (default) | scalar

Dependencies

Corresponding field strength — Field strength at measurement point 1000 A/m (default) | scalar

Dependencies

Coefficient for reversible magnetization, c — Coefficient for reversible magnetization 0.1 (default) | scalar in the range [0,1]

Dependencies

Bulk coupling coefficient, K — Bulk coupling coefficient 200 A/m (default) | finite positive scalar

Dependencies

Inter-domain coupling factor, alpha — Inter-domain coupling factor 1e-4 (default) | scalar

Dependencies

Interpolation option — Interpolation option Linear (default) | Smooth

Dependencies

Initial Conditions

Primary leakage inductance initial current — Primary leakage inductance initial current 0 A (default)

First secondary leakage inductance initial current — First secondary leakage inductance initial current 0 A (default)

Second secondary leakage inductance initial current — Second secondary leakage inductance initial current 0 A (default)

Specify magnetization inductance initial state by — Initial state specification option Current (default) | Magnetic flux

Dependencies

Magnetization inductance initial current — Magnetization inductance initial current 0 A (default)

Dependencies

Magnetization inductance initial magnetic flux — Magnetization inductance initial magnetic flux 0 Wb (default)

Dependencies

Magnetization inductance initial magnetic flux density — Magnetization inductance initial magnetic flux density 0 T (default)

Dependencies

Magnetization inductance initial field strength — Magnetization inductance initial field strength 0 A/m (default)

Dependencies

Parasitics

Primary leakage inductance parasitic parallel conductance — Winding 1 leakage inductance parasitic parallel conductance 1e-9 1/Ohm (default) | nonneagative scalar

First secondary leakage inductance parasitic parallel conductance — Winding 2 leakage inductance parasitic parallel conductance 1e-9 1/Ohm (default) | nonneagative scalar

Second secondary leakage inductance parasitic parallel conductance — Winding 3 leakage inductance parasitic parallel conductance 1e-9 1/Ohm (default) | nonneagative scalar

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

1+ — Line 1 positive terminal
electrical

1- — Line 1 negative terminal
electrical

2+ — Line 2 positive terminal
electrical

2- — Line 2 negative terminal
electrical

3+ — Line 3 positive terminal
electrical

3- — Line 3 negative terminal
electrical

Primary number of turns — Winding 1 primary turns number
`100` (default) | positive scalar integer

First secondary number of turns — Winding 2 turns number
`200` (default) | positive scalar integer

Second secondary number of turns — Winding 3 turns number
`200` (default) | positive scalar integer

Primary winding resistance — Winding 1 resistance
`0.01` `Ohm` (default) | nonnegative scalar

Primary leakage inductance — Winding 1 leakage inductance
`0.0001` `H` (default) | nonnegative scalar

First secondary winding resistance — Winding 2 resistance
`0.01` `Ohm` (default) | nonnegative scalar

First secondary leakage inductance — Winding 2 leakage inductance
`0.0001` `H` (default) | nonnegative scalar

Second secondary winding resistance — Winding 3 resistance
`0.01` `Ohm` (default) | nonnegative scalar

Second secondary leakage inductance — Winding 3 leakage inductance
`0.0001` `H` (default) | nonnegative scalar

Magnetization resistance — Magnetization resistance
`100` `Ohm` (default)

Unsaturated inductance — Unsaturated inductance
`4e-2` `H` (default)

Saturated inductance — Saturated inductance
`1e-2` `H` (default)

Saturation magnetic flux — Saturation magnetic flux
`1.6e-04` `Wb` (default)

Current vector, i — Current data
`[0, .4, .8, 1.2, 1.6, 2]` `A` (default)

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

Magnetic field strength vector, H — Magnetic field strength vector
`[0, 200, 400, 600, 800, 1000]` `A/m` (default) | vector

Magnetic flux density vector, B — Magnetic flux density vector
`[0, .81, 1.25, 1.42, 1.48, 1.49]` `T` (default) | vector

Effective length — Effective core length
`0.2` `m` (default) | positive finite scalar

Effective cross-sectional area — Effective core cross-sectional area
`2e-4` `m^2` (default) | positive finite scalar

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

Flux density point on anhysteretic B-H curve — Flux density point on anhysteretic B-H curve
`1.49` `T` (default) | scalar

Corresponding field strength — Field strength at measurement point
`1000` `A/m` (default) | scalar

Coefficient for reversible magnetization, c — Coefficient for reversible magnetization
`0.1` (default) | scalar in the range [0,1]

Bulk coupling coefficient, K — Bulk coupling coefficient
`200` `A/m` (default) | finite positive scalar

Inter-domain coupling factor, alpha — Inter-domain coupling factor
`1e-4` (default) | scalar

Interpolation option — Interpolation option
`Linear` (default) | `Smooth`

Primary leakage inductance initial current — Primary leakage inductance initial current
`0` `A` (default)

First secondary leakage inductance initial current — First secondary leakage inductance initial current
`0` `A` (default)

Second secondary leakage inductance initial current — Second secondary leakage inductance initial current
`0` `A` (default)

Specify magnetization inductance initial state by — Initial state specification option
`Current` (default) | `Magnetic flux`

Magnetization inductance initial current — Magnetization inductance initial current
`0` `A` (default)

Magnetization inductance initial magnetic flux — Magnetization inductance initial magnetic flux
`0` `Wb` (default)

Magnetization inductance initial magnetic flux density — Magnetization inductance initial magnetic flux density
`0` `T` (default)

Magnetization inductance initial field strength — Magnetization inductance initial field strength
`0` `A/m` (default)

Primary leakage inductance parasitic parallel conductance — Winding 1 leakage inductance parasitic parallel conductance
`1e-9` `1/Ohm` (default) | nonneagative scalar

First secondary leakage inductance parasitic parallel conductance — Winding 2 leakage inductance parasitic parallel conductance
`1e-9` `1/Ohm` (default) | nonneagative scalar

Second secondary leakage inductance parasitic parallel conductance — Winding 3 leakage inductance parasitic parallel conductance
`1e-9` `1/Ohm` (default) | nonneagative scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.