Three-Winding Nonlinear Transformer
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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.
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.
Ports
Conserving
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
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. This is the default option.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)
Value of inductance used when the magnetization inductance Lm is operating 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)
Value of inductance used when the magnetization inductance Lm is operating 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)
Value of 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 used 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 used 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)
Magnetic field strength data used to populate the magnetic flux density versus magnetic field strength lookup table.
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)
Magnetic flux density data used to populate the magnetic flux density versus magnetic field strength lookup table.
Dependencies
To enable this parameter, set the Magnetization
inductance parameterized by parameter to
Magnetic flux density versus field strength
characteristic
.
Effective length — Effective length
0.2
m
(default)
Effective core length, also defined as the average distance of the magnetic path around the transformer core.
Dependencies
To enable this parameter, set the Magnetization
inductance parameterized by parameter to
Magnetic flux density versus field strength
characteristic
.
Effective cross-sectional area — Effective cross-sectional area
2e-4
m^2
(default)
Effective core cross-sectional area, also defined as the average area of the magnetic path around the transformer core.
Dependencies
To enable this parameter, set the Magnetization
inductance parameterized by parameter to
Magnetic flux density versus field strength
characteristic
.
Anhysteretic B-H gradient when H is zero — Anhysteretic B-H gradient around zero field strength
0.005
m*T/A
(default)
Gradient of the anhysteretic B-H curve around zero field strength. Set this parameter to the average gradient of the positive-going and negative-going 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)
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.
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 — Corresponding field strength
1000
A/m
(default)
Corresponding field strength for the point defined by the Flux density point on anhysteretic B-H curve parameter.
Dependencies
To enable this parameter, set the Magnetization
inductance parameterized by parameter to
Magnetic flux density versus field strength
characteristic with hysteresis
.
Coefficient for reversible magnetization, c — Coefficient for reversible magnetization
0.1
(default)
Proportion of the magnetization that is reversible. The value should be greater than zero and less than one.
Dependencies
To enable this parameter, set the Magnetization
inductance parameterized by parameter to
Magnetic flux density versus field strength
characteristic with hysteresis
.
Bulk coupling coefficient, K — Bulk coupling coefficient
200
A/m
(default)
Jiles-Atherton parameter that primarily controls the field strength magnitude at which the B-H curve crosses the zero flux density line.
Dependencies
To enable this parameter, set the Magnetization
inductance parameterized by parameter to
Magnetic flux density versus field strength
characteristic with hysteresis
.
Inter-domain coupling factor, alpha — Inter-domain coupling factor
1e-4
(default)
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.
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
— 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)
Value of the 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)
Value of the 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)
Value of the 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.
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 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.
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)
Value of the 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)
Value of 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)
Value of magnetic field strength 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
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. A small parallel conductance may be required for the simulation of some circuit topologies.
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. A small parallel conductance may be required for the simulation of some circuit topologies.
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. A small parallel conductance may be required for the simulation of some circuit topologies.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2019b
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