Nonlinear Transformer

Transformer with a non-ideal core.

Nonlinear Transformer

nonlinear transformer

Three-Winding Nonlinear Transformer

three winding nonlinear transformer

Multi-Winding Nonlinear Transformer

multi winding nonlinear transformer

Description

Unit Nonlinear Transformer is a transformer with a non-ideal core. The core can be non-ideal due to its magnetic properties and dimensions.

The equivalent circuit of a two-winding transformer depends on which of the two options is used for parameters Winding parameterized by:

Combined primary and secondary values.

nonlinear transformer 1 s

Separate primary and secondary values.

nonlinear transformer 2 s

where

Req is the total active resistance of the winding;
Leq - total scattering inductance;
R1 - active resistance of the primary winding;
L1 - scattering inductance of the primary winding;
R2 - active resistance of the secondary winding;
L2 - scattering inductance of the secondary winding;
Rm - active magnetising resistance;
Lm - magnetising inductance.

The figure below shows the equivalent circuit of a three-winding transformer:

three winding nonlinear transformer 1 s

where

R1 - active resistance of the primary winding;
L1 - scattering inductance of the primary winding;
R2 - active resistance of the first secondary winding;
L2 - scattering inductance of the first secondary winding;
R2 - active resistance of the second secondary winding;
L2 - scattering inductance of the second secondary winding;
Rm - active magnetising resistance;
Lm - magnetising inductance.

The block provides the following options for parameterization of nonlinear magnetising inductance:

Single inductance (linear)
One saturation point
Characterisation of the dependence of magnetic flux on current
Characterisation of the dependence of magnetic induction on magnetic field strength
Characterisation of the dependence of magnetic induction on magnetic field strength with hysteresis
Volt-ampere characteristic (VAC)

Single inductance (linear)

The relationships between voltage, current and magnetic flux are defined by the following equations:

where

- terminal voltage;
- current through the terminals;
- current through the transformer magnetising inductance;
- parasitic parallel conductivity;
- number of turns of the first winding;
- magnetic flux;
- unsaturated inductance.

One saturation point

The relationships between voltage, current and magnetic flux are defined by the following equations:

(up to the saturation point),

(after the saturation point),

where

- terminal voltage;
- current through the terminals;
- current through the transformer magnetising inductance;
- parasitic parallel conductivity;
- number of turns of the first winding;
- magnetic flux;
- magnetic flux saturation bias;
- unsaturated inductance;
- saturated inductance.

Characterisation of the dependence of magnetic flux on current

The relationships between voltage, current and flux are defined by the following equations:

where

- terminal voltage;
- current through the terminals;
- current through the magnetising inductance of the transformer;
- parasitic parallel conductivity;
- number of turns of the first winding;
- magnetic flux.

The magnetic flux is determined using a one-dimensional table consisting of a vector of current values and a vector of corresponding magnetic flux values. Both negative and positive values can be used to specify these vectors, or only positive values can be used. If only positive data are used, the vector must start at 0, while negative data will be automatically calculated by symmetrical mapping with respect to the point (0,0).

Characterisation of the dependence of magnetic induction on magnetic field strength

The relationships between voltage, current and flux are defined by the following equations:

where

- terminal voltage;
- current through the terminals;
- current through the transformer magnetising inductance;
- parasitic parallel conductivity;
- number of turns of the first winding;
- magnetic flux;
- magnetic induction;
- magnetic field strength;
- effective core length;
- effective cross-sectional area of the core.

Magnetic induction is determined using a one-dimensional table consisting of a vector of magnetic field strength values and a vector of corresponding magnetic induction values. Both negative and positive values can be used to specify these vectors, or only positive values can be used. If only positive data are used, the vector must start from 0, while negative data will be automatically calculated by symmetric mapping with respect to the point (0,0).

Characterisation of the dependence of magnetic induction on magnetic field strength with hysteresis

The relationships between voltage, current and flux are defined by the following equations:

where

- terminal voltage;
- current through the terminals;
- current through the transformer magnetising inductance;
- parasitic parallel conductivity;
- number of turns of the first winding;
- magnetic flux;
- magnetic induction;
- magnetic constant;
- magnetic field strength;
- core magnetisation;
- effective core length;
- effective cross-sectional area of the core.

Magnetisation leads to an increase in magnetic induction, and its magnitude depends on both the current value of the field strength , and its previous variation over time. The equations of the Giles-Atherton model are used to determine at any point in time.

The starting point for the Giles-Atherton equation is to separate the magnetisation effect into two parts, one of which is purely a function of the effective field strength ( ) and the other is an irreversible part that depends on past history:

The member is called the anhysteresis magnetisation because it has no hysteresis. It is described by the following function on the current value of the effective field strength :

This function defines a saturation curve with limit values and a saturation point determined by the value of , the shape factor of the anhysteresis curve. Roughly, it can be considered to describe the average of the two hysteresis curves. In the block Nonlinear Transformer values are set at and points on the angysteresis curve B-H, which are used to determine the values of and .

The parameters is the reversible magnetisation coefficient and determines which part of the behaviour is determined by , and which part is determined by the irreversible term . In the Giles-Atherton model, the irreversible term is determined by the partial derivative of the field strength:

Comparison of this equation with the standard first order differential equation shows that as the field strength H increases, the irreversible term follows the reversible term , but with a variable gain .

The tracking error serves to create hysteresis at points where changes sign. The main parameter that forms the irreversible characteristic is , which is called the bulk coupling coefficient. The parameter is called the interdomain coupling coefficient and is also used to determine the effective field strength used to construct the angysteresis curve:

The value of affects the shape of the hysteresis curve: the larger it is, the higher the curve intersects the B-axis. However, it should be noted that the term , which must be positive at and negative at , is necessary for stability. Therefore, not all values of α are acceptable; a typical maximum value is of the order of 1e-3.

Procedure for finding approximate values of the coefficients of the Giles-Atherton equation

The following procedure can be used to determine suitable parameters for the coefficients of the equation:

Specify the value of the parameters Anhysteretic B-H gradient when H is zero ( at ) plus the data point on the B-H anti-hysteresis curve. From these values, the values and are determined during block initialisation.
Set the value for the parameters Coefficient for reversible magnetization, c, so that the correct initial B-H derivative is obtained when the simulation is run from the point . The value of is approximately equal to the ratio of this initial derivative to the Anhysteretic B-H gradient when H is zero. The value of must be greater than 0 and less than 1.
Set the value for the Bulk coupling coefficient, K, A/m parameters to approximate the value of , when is on a positive hysteresis curve.
Start with a very small value of and gradually increase it to adjust the value of when it crosses the line . A typical value is in the range of 1e-4 to 1e-3. Values that are too large cause the derivative of the B-H curve to tend to infinity, which is unphysical and results in a run-time assertion error.

It may be necessary to perform these steps several times to get a good match with the predefined B-H curve.

Volt-ampere characteristic (VAC)

Based on the specified VAC, the magnetic induction vectors and current vectors are calculated for usage of the magnetic flux-current characteristic:

where

- vectors defining the transformer’s VAC, parameters values Voltage vector in RMS, v и Current vector in RMS, i respectively;
- number of turns of the first winding, value of parameters Primary number of turns;
- network frequency, parameter value System frequency.

Ports

Conserving

# 1+ — positive terminal of the first winding
electricity

Details

Electrical port, represents the terminal of the first winding with positive polarity.

Program usage name

p1

# 1- — negative terminal of the first winding
electricity

Details

Electrical port, represents the terminal of the first winding with negative polarity.

Program usage name

n1

# 2+ — positive terminal of the second winding
electricity

Details

Electricity port, represents the terminal of the second winding with positive polarity.

Program usage name

p2

# 2- — negative terminal of the second winding
electricity

Details

Electricity port, represents the terminal of the second winding with negative polarity.

Program usage name

n2

# 3+ — positive terminal of the third winding
electricity

Details

Electricity port, represents the terminal of the third winding with positive polarity.

Dependencies

To use this port, set the parameters to Number of windings value Three, Four, Five or Six.

Program usage name

p3

# 3- — negative terminal of the third winding
electricity

Details

Electricity port, represents the terminal of the third winding with negative polarity.

Dependencies

To use this port, set the parameters to Number of windings value Three, Four, Five or Six.

Program usage name

n3

# 4+ — positive terminal of the fourth winding
electricity

Details

Electricity port, represents the terminal of the fourth winding with positive polarity.

Dependencies

To use this port, set the parameters to Number of windings value Four, Five or Six.

Program usage name

p4

# 4- — negative terminal of the fourth winding
electricity

Details

Electricity port, represents the terminal of the fourth winding with negative polarity.

Dependencies

To use this port, set the parameters to Number of windings value Four, Five or Six.

Program usage name

n4

# 5+ — positive terminal of the fifth winding
electricity

Details

Electricity port, represents the terminal of the fifth winding with positive polarity.

Dependencies

To use this port, set the parameters to Number of windings value Five or Six.

Program usage name

p5

# 5- — negative terminal of the fifth winding
electricity

Details

Electricity port, represents the terminal of the fifth winding with negative polarity.

Dependencies

To use this port, set the parameters to Number of windings value Five or Six.

Program usage name

n5

# 6+ — positive terminal of the sixth winding
electricity

Details

Electricity port, represents the terminal of the sixth winding with positive polarity.

Dependencies

To use this port, set the parameters to Number of windings value Six.

Program usage name

p6

# 6- — negative terminal of the sixth winding
electricity

Details

Electricity port, represents the terminal of the sixth winding with negative polarity.

Dependencies

To use this port, set the parameters to Number of windings value Six.

Program usage name

n6

Parameters

Main

# Number of windings — switching between two-, three-, four-, five- and six-winding transformers
Two | Three | Four | Five | Six

Details

Switching between two-, three-, four-, five-, and six-winding transformer. Defined as:

Two - unit modelling a two-winding transformer.
Three - The block simulates a three-winding transformer.
Four - The block simulates a four-winding transformer.
Five - The block simulates a five-winding transformer.
Six - The block simulates a six-winding transformer.

Values	`Two` \| `Three` \| `Four` \| `Five` \| `Six`
Default value	`—`
Program usage name	`N_windings`
Evaluatable	No

# Primary number of turns — number of turns of the first winding

Details

Number of turns of the first winding wire of the transformer.

Default value	`100`
Program usage name	`N_1`
Evaluatable	Yes

# Secondary number of turns — number of turns of the second winding

Details

Number of turns of the second winding wire of the transformer.

Default value	`200`
Program usage name	`N_2`
Evaluatable	Yes

# Tertiary number of turns — number of turns of the third winding

Details

Number of turns of the third winding wire of the transformer.

Dependencies

To use this parameter, set parameter Number of windings value Three, Four, Five or Six.

Default value	`200`
Program usage name	`N_3`
Evaluatable	Yes

# Quartary number of turns — number of turns of the fourth winding

Details

Number of turns of the fourth winding wire of the transformer.

Dependencies

To use this parameter, set parameter Number of windings value Four, Five or Six.

Default value	`200`
Program usage name	`N_4`
Evaluatable	Yes

# Quintary number of turns — number of turns of the fifth winding

Details

Number of turns of the fifth winding wire of the transformer.

Dependencies

To use this parameter, set parameter Number of windings value Five or Six.

Default value	`200`
Program usage name	`N_5`
Evaluatable	Yes

# Senary number of turns — number of turns of the sixth winding

Details

Number of turns of the sixth winding wire of the transformer.

Dependencies

To use this parameter, set parameter Number of windings value Six.

Default value	`200`
Program usage name	`N_6`
Evaluatable	Yes

# Winding parameterized by — type of winding distribution representation
Combined primary and secondary values | Separate primary and secondary values

Details

The method of dissipation in the winding. Defined as:

Combined primary and secondary values - use the concentrated values of active resistance and inductance representing the combined leakage in the first and second windings.
Separate primary and secondary values - use separate active resistance and inductance values to represent the leakage in the first and second windings.

Dependencies

To use this parameter, set parameter Number of windings value Two.

Values	`Combined primary and secondary values` \| `Separate primary and secondary values`
Default value	`Combined primary and secondary values`
Program usage name	`winding_parameterization`
Evaluatable	No

# Combined winding resistance — total active resistance of windings
Ohm | GOhm | MOhm | kOhm | mOhm

Details

The concentrated equivalent active resistance Req, which represents the combined power losses of the first and second windings.

Dependencies

To use this parameter, set the parameters to Winding parameterized by value Combined primary and secondary values.

Units	`Ohm` \| `GOhm` \| `MOhm` \| `kOhm` \| `mOhm`
Default value	`0.01 Ohm`
Program usage name	`R_eq`
Evaluatable	Yes

# Combined leakage inductance — total scattering inductance
H | mH | nH | uH

Details

The cumulative equivalent inductance Leq, which is the combined magnetic flux losses of the first and second windings.

Dependencies

To use this parameter, set parameter Winding parameterized by value Combined primary and secondary values.

Units	`H` \| `mH` \| `nH` \| `uH`
Default value	`0.0001 H`
Program usage name	`L_eq`
Evaluatable	Yes

# Primary winding resistance — active resistance of the first winding
Ohm | GOhm | MOhm | kOhm | mOhm

Details

The active resistance R1, which represents the power loss of the first winding.

Dependencies

To use this parameter, set the parameters to Winding parameterized by value Separate primary and secondary values or set the parameters to Number of windings value Three, Four, Five or Six.

Units	`Ohm` \| `GOhm` \| `MOhm` \| `kOhm` \| `mOhm`
Default value	`0.01 Ohm`
Program usage name	`R_1`
Evaluatable	Yes

# Primary leakage inductance — dissipation inductance of the first winding
H | mH | nH | uH

Details

The inductance L1, which represents the magnetic flux losses of the first winding.

Dependencies

Units	`H` \| `mH` \| `nH` \| `uH`
Default value	`0.0001 H`
Program usage name	`L_1`
Evaluatable	Yes

# Secondary winding resistance — active resistance of the second winding
Ohm | GOhm | MOhm | kOhm | mOhm

Details

The active resistance R2, which represents the power loss of the second winding.

Dependencies

Units	`Ohm` \| `GOhm` \| `MOhm` \| `kOhm` \| `mOhm`
Default value	`0.01 Ohm`
Program usage name	`R_2`
Evaluatable	Yes

# Secondary leakage inductance — dissipation inductance of the second winding
H | mH | nH | uH

Details

The inductance L2, which represents the magnetic flux losses of the second winding.

Dependencies

Units	`H` \| `mH` \| `nH` \| `uH`
Default value	`0.0001 H`
Program usage name	`L_2`
Evaluatable	Yes

# Tertiary winding resistance — active resistance of the third winding
Ohm | GOhm | MOhm | kOhm | mOhm

Details

The active resistance R3, which represents the power loss of the third winding.

Dependencies

To use this parameter, set the parameters to Number of windings value Three, Four, Five or Six.

Units	`Ohm` \| `GOhm` \| `MOhm` \| `kOhm` \| `mOhm`
Default value	`0.01 Ohm`
Program usage name	`R_3`
Evaluatable	Yes

# Tertiary leakage inductance — dissipation inductance of the third winding
H | mH | nH | uH

Details

The L3 inductance, which represents the magnetic flux losses of the third winding.

Dependencies

To use this parameter, set the parameters to Number of windings value Three, Four, Five or Six.

Units	`H` \| `mH` \| `nH` \| `uH`
Default value	`0.0001 H`
Program usage name	`L_3`
Evaluatable	Yes

# Quartary winding resistance — active resistance of the fourth winding
Ohm | GOhm | MOhm | kOhm | mOhm

Details

The active resistance R4, which represents the power loss of the fourth winding.

Dependencies

To use this parameter, set the parameters to Number of windings value Four, Five or Six.

Units	`Ohm` \| `GOhm` \| `MOhm` \| `kOhm` \| `mOhm`
Default value	`0.01 Ohm`
Program usage name	`R_4`
Evaluatable	Yes

# Quartary leakage inductance — dissipation inductance of the fourth winding
H | mH | nH | uH

Details

The L4 inductance, which represents the magnetic flux losses of the fourth winding.

Dependencies

To use this parameter, set the parameters to Number of windings value Four, Five or Six.

Units	`H` \| `mH` \| `nH` \| `uH`
Default value	`0.0001 H`
Program usage name	`L_4`
Evaluatable	Yes

# Quintary winding resistance — active resistance of the fifth winding
Ohm | GOhm | MOhm | kOhm | mOhm

Details

The active resistance R5, which represents the power loss of the fifth winding.

Dependencies

To use this parameter, set the parameters to Number of windings value Five or Six.

Units	`Ohm` \| `GOhm` \| `MOhm` \| `kOhm` \| `mOhm`
Default value	`0.01 Ohm`
Program usage name	`R_5`
Evaluatable	Yes

# Quintary leakage inductance — dissipation inductance of the fifth winding
H | mH | nH | uH

Details

The L5 inductance, which represents the magnetic flux losses of the fifth winding.

Dependencies

To use this parameter, set parameters Number of windings value Five or Six.

Units	`H` \| `mH` \| `nH` \| `uH`
Default value	`0.0001 H`
Program usage name	`L_5`
Evaluatable	Yes

# Senary winding resistance — active resistance of the sixth winding
Ohm | GOhm | MOhm | kOhm | mOhm

Details

The active resistance R6, which represents the power loss of the sixth winding.

Dependencies

To use this parameter, set the parameters to Number of windings value Six.

Units	`Ohm` \| `GOhm` \| `MOhm` \| `kOhm` \| `mOhm`
Default value	`0.01 Ohm`
Program usage name	`R_6`
Evaluatable	Yes

# Senary leakage inductance — dissipation inductance of the sixth winding
H | mH | nH | uH

Details

The L6 inductance, which represents the magnetic flux losses of the sixth winding.

Dependencies

To use this parameter, set parameters Number of windings value Six.

Units	`H` \| `mH` \| `nH` \| `uH`
Default value	`0.0001 H`
Program usage name	`L_6`
Evaluatable	Yes

Magnetization

# Magnetization resistance — active magnetisation resistance
Ohm | GOhm | MOhm | kOhm | mOhm

Details

The active resistance Rm representing the magnetic losses in the transformer core.

Units	`Ohm` \| `GOhm` \| `MOhm` \| `kOhm` \| `mOhm`
Default value	`100 Ohm`
Program usage name	`R_m`
Evaluatable	Yes

# Magnetization inductance parameterized by — block parameterization
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 | Voltage versus current characteristic

Details

A method for parameterising a block. Defined as:

Single saturation point - values of the number of turns, unsaturated inductance and parasitic parallel conductance are specified.
Single inductance (linear) - Specifies the values of the number of turns, unsaturated and saturated inductances, saturation magnetic flux and parasitic parallel conductivity. This option is used by default.
Magnetic flux versus current characteristic - In addition to the number of turns and the parasitic parallel conductance value, the current vector and the magnetic flux vector are specified to complete the magnetic flux-current table.
Magnetic flux density versus magnetic field strength characteristic - In addition to the number of turns and the parasitic parallel conductance value, the effective length and cross-sectional area of the core, as well as the magnetic field strength vector and the magnetic induction vector are provided to complete the magnetic induction versus magnetic field strength table.
Magnetic flux density versus magnetic field strength characteristic with hysteresis - In addition to the number of turns, effective length and cross-sectional area of the core, the values of the initial derivative of the angysteresis B-H curve, magnetic induction and field strength at a certain point of the B-H curve, as well as the reversible magnetisation coefficient, volume coupling coefficient and interdomain coupling coefficient to determine the magnetic induction as a function of the current value and history of the magnetic field strength are given.
Voltage versus current characteristic - setting saturation through the volt-ampere characteristic (VAC).

Values	`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` \| `Voltage versus current characteristic`
Default value	`Single saturation point`
Program usage name	`saturation_parameterization`
Evaluatable	No

# Magnetic field strength vector, H — vector of magnetic field strength values
A/m

Details

Magnetic field strength values used to fill in the table of dependence of magnetic induction on magnetic field strength.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Magnetic flux versus current characteristic.

Units	`A/m`
Default value	`[0, 200, 400, 600, 800, 1000] A/m`
Program usage name	`H_vector`
Evaluatable	Yes

# Magnetic flux density vector, B — vector of magnetic induction values
G | T

Details

Magnetic induction values used to fill in the table of dependence of magnetic induction on magnetic field strength.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Magnetic flux versus current characteristic.

Units	`G` \| `T`
Default value	`[0, .81, 1.25, 1.42, 1.48, 1.49] T`
Program usage name	`B_vector`
Evaluatable	Yes

# Effective length — effective core length
m | cm | ft | in | km | mi | mm | um | yd

Details

The effective core length, i.e. the average length of the magnetic flux path.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Magnetic flux density versus magnetic field strength characteristic or Magnetic flux density versus magnetic field strength characteristic with hysteresis.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.2 m`
Program usage name	`effective_gap`
Evaluatable	Yes

# Effective cross-sectional area — effective cross-sectional area
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The effective cross-sectional area of the core, i.e. the average area of the magnetic flux path.

Dependencies

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`2e-4 m^2`
Program usage name	`A_effective`
Evaluatable	Yes

# Unsaturated inductance — unsaturated inductance
H | mH | nH | uH

Details

The inductance value used when the transformer is operating in the linear region.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Single inductance (linear) or Single saturation point.

Units	`H` \| `mH` \| `nH` \| `uH`
Default value	`4e-2 H`
Program usage name	`L_m`
Evaluatable	Yes

# Saturated inductance — saturable inductance
H | mH | nH | uH

Details

The inductance value used when the transformer is operating in the saturation zone.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Single saturation point.

Units	`H` \| `mH` \| `nH` \| `uH`
Default value	`1e-2 H`
Program usage name	`L_m_sat`
Evaluatable	Yes

# Current vector, i — current vector
A | MA | kA | mA | nA | pA | uA

Details

Current values used to populate the magnetic flux-current table.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Magnetic flux versus current characteristic.

Units	`A` \| `MA` \| `kA` \| `mA` \| `nA` \| `pA` \| `uA`
Default value	`[0, 0.4, 0.8, 1.2, 1.6, 2] A`
Program usage name	`i_vector`
Evaluatable	Yes

# Magnetic flux vector, Φ — vector of magnetic flux values
Wb | N*m/A | mN*m/A

Details

Magnetic flux values used to populate the magnetic flux-current table.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Magnetic flux versus current characteristic.

Units	`Wb` \| `Nm/A` \| `mNm/A`
Default value	`[0, 0.161, 0.25, 0.284, 0.295, 0.299] .* 1e-3 Wb`
Program usage name	`Phi_vector`
Evaluatable	Yes

# Current vector in RMS, i — vector of effective values of current VAC
A | MA | kA | mA | nA | pA | uA

Details

The vector of effective values of the SAC current.

Dependencies

To use this parameter, set the parameters to Magnetization inductance parameterized by value Voltage versus current characteristic.

Units	`A` \| `MA` \| `kA` \| `mA` \| `nA` \| `pA` \| `uA`
Default value	`[0.0, 0.1414, 0.2828, 0.4243, 0.5657, 0.7071] A`
Program usage name	`I_RMS_vector`
Evaluatable	Yes

# Voltage vector in RMS, v — vector of effective values of voltage VAC
V | MV | kV | mV

Details

The vector of effective values of the VAC voltage.

Dependencies

To use this parameter, set the parameters to Magnetization inductance parameterized by value Voltage versus current characteristic.

Units	`V` \| `MV` \| `kV` \| `mV`
Default value	`[0.0, 7.1530, 11.1072, 12.6178, 13.1065, 13.2842] V`
Program usage name	`V_RMS_vector`
Evaluatable	Yes

# System frequency — network frequency
Hz | GHz | MHz | kHz

Details

Network frequency.

Dependencies

To use this parameter, set the parameters to Magnetization inductance parameterized by value Voltage versus current characteristic.

Units	`Hz` \| `GHz` \| `MHz` \| `kHz`
Default value	`50.0 Hz`
Program usage name	`f`
Evaluatable	Yes

# Saturation magnetic flux — saturated magnetic flux
Wb | N*m/A | mN*m/A

Details

The value of the magnetic flux at which the transformer becomes saturated.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Single saturation point.

Units	`Wb` \| `Nm/A` \| `mNm/A`
Default value	`0.00016 Wb`
Program usage name	`Phi_sat`
Evaluatable	Yes

# Anhysteretic B-H gradient when H is zero — derivative of the B-H anhysteresis curve near zero field strength
H/m | mH/m | nH/m | uH/m | H/km | mH/km | T*m/A

Details

The derivative of the anhysteresis (no hysteresis) B-H curve near zero field strength. Set as the average of the derivative of the positive and negative hysteresis curves.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Magnetic flux density versus magnetic field strength characteristic with hysteresis.

Units	`H/m` \| `mH/m` \| `nH/m` \| `uH/m` \| `H/km` \| `mH/km` \| `T*m/A`
Default value	`0.005 T*m/A`
Program usage name	`dB_dH_0`
Evaluatable	Yes

# Flux density point on anhysteretic B-H curve — value of magnetic induction at the point on the angysteresis curve B-H
G | T

Details

Specify the value of magnetic induction at a point on the anhysteresis curve. The most accurate option is to select the point at high field strength when the positive and negative hysteresis curves coincide.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Magnetic flux density versus magnetic field strength characteristic with hysteresis.

Units	`G` \| `T`
Default value	`1.49 T`
Program usage name	`B_anhysteretic`
Evaluatable	Yes

# Corresponding field strength — corresponding field strength
A/m

Details

Corresponding field strength for the point given by the parameters Flux density point on anhysteretic B-H curve.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Magnetic flux density versus magnetic field strength characteristic with hysteresis.

Units	`A/m`
Default value	`1000 A/m`
Program usage name	`H_anhysteretic`
Evaluatable	Yes

# Coefficient for reversible magnetization, c — reversible magnetisation coefficient

Details

The fraction of magnetisation that is reversible. The value must be greater than zero and less than one.

Dependencies

To use this parameter, set the parameter Magnetization inductance parameterized by value Magnetic flux density versus magnetic field strength characteristic with hysteresis.

Default value	`0.1`
Program usage name	`c`
Evaluatable	Yes

# Bulk coupling coefficient, K — volume coupling coefficient
A/m

Details

A parameter of the Giles-Atherton model that primarily determines the value of field strength at which the B-H curve crosses the line of zero magnetic induction.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Magnetic flux density versus magnetic field strength characteristic with hysteresis.

Units	`A/m`
Default value	`200.0 A/m`
Program usage name	`K`
Evaluatable	Yes

# Inter-domain coupling factor, α — interdomain coefficient

Details

A Giles-Atherton parameter affecting primarily the points of intersection of the B-H curves with the zero field strength line. Typical values range from 1e-4 to 1e-3.

Dependencies

To use this parameter, set parameter Magnetization inductance parameterized by value Magnetic flux density versus magnetic field strength characteristic with hysteresis.

Default value	`1e-4`
Program usage name	`alpha`
Evaluatable	Yes

# Interpolation option — interpolation option
Linear | Smooth

Details

The interpolation option of the lookup table. Defined as:

Linear - select this option to get the best performance.
Smooth - select this option to obtain a continuous curve with continuous first order derivatives.

Values	`Linear` \| `Smooth`
Default value	`Linear`
Program usage name	`interpolation_option`
Evaluatable	No

Initial Conditions

# Combined leakage current — initial current of the total dissipation inductance
A | MA | kA | mA | nA | pA | uA

Details

Initial value of the total dissipation inductance current.

Dependencies

To use this parameter, set parameter Winding parameterized by value Combined primary and secondary values.

Units	`A` \| `MA` \| `kA` \| `mA` \| `nA` \| `pA` \| `uA`
Default value	`0 A`
Program usage name	`i_Leq_start`
Evaluatable	Yes

# Primary leakage inductance current — initial current of the first winding dissipation inductance
A | MA | kA | mA | nA | pA | uA

Details

Initial value of the dissipation inductance current of the first winding of the transformer.

Dependencies

To use this parameter, set parameters Winding parameterized by value Separate primary and secondary values or set the parameters to Number of windings value Three, Four, Five or Six..

Units	`A` \| `MA` \| `kA` \| `mA` \| `nA` \| `pA` \| `uA`
Default value	`0 A`
Program usage name	`i_L1_start`
Evaluatable	Yes

# Secondary leakage inductance current — initial current of the second winding dissipation inductance
A | MA | kA | mA | nA | pA | uA

Details

Initial value of the dissipation inductance current of the second winding of the transformer.

Dependencies

To use this parameter, set parameter Winding parameterized by value Separate primary and secondary values or set the parameters to Number of windings value Three, Four, Five or Six..

Units	`A` \| `MA` \| `kA` \| `mA` \| `nA` \| `pA` \| `uA`
Default value	`0 A`
Program usage name	`i_L2_start`
Evaluatable	Yes

# Tertiary leakage inductance current — initial current of the third winding dissipation inductance
A | MA | kA | mA | nA | pA | uA

Details

Initial value of the dissipation inductance current of the third winding of the transformer.

Dependencies

To use this parameter, set parameter Number of windings value Three, Four, Five or Six.

Units	`A` \| `MA` \| `kA` \| `mA` \| `nA` \| `pA` \| `uA`
Default value	`0 A`
Program usage name	`i_L3_start`
Evaluatable	Yes

# Quartary leakage inductance current — initial current of the fourth winding dissipation inductance
A | MA | kA | mA | nA | pA | uA

Details

Initial value of the dissipation inductance current of the fourth winding of the transformer.

Dependencies

To use this parameter, set parameter Number of windings value Four, Five or Six.

Units	`A` \| `MA` \| `kA` \| `mA` \| `nA` \| `pA` \| `uA`
Default value	`0 A`
Program usage name	`i_L4_start`
Evaluatable	Yes

# Quintary leakage inductance current — initial current of the fifth winding dissipation inductance
A | MA | kA | mA | nA | pA | uA

Details

Initial value of the dissipation inductance current of the fifth winding of the transformer.

Dependencies

To use this parameter, set parameter Number of windings value Five or Six.

Units	`A` \| `MA` \| `kA` \| `mA` \| `nA` \| `pA` \| `uA`
Default value	`0 A`
Program usage name	`i_L5_start`
Evaluatable	Yes

# Senary leakage inductance current — initial current of the sixth winding dissipation inductance
A | MA | kA | mA | nA | pA | uA

Details

Initial value of the dissipation inductance current of the sixth winding of the transformer.

Dependencies

To use this parameter, set parameter Number of windings value Six.

Units	`A` \| `MA` \| `kA` \| `mA` \| `nA` \| `pA` \| `uA`
Default value	`0 A`
Program usage name	`i_L6_start`
Evaluatable	Yes

# Specify magnetization inductance state by — option for setting the initial state
Current | Magnetic flux

Details

Initial state option. Defined as:

Current - setting the initial state of the transformer by the initial current through the transformer. This option is used by default.
Magnetic flux - setting the initial state of the transformer by magnetic flux.

Dependencies

To use this parameter, set the parameters to Magnetization inductance parameterized by value Magnetic flux density versus magnetic field strength characteristic with hysteresis.

Values	`Current` \| `Magnetic flux`
Default value	`Current`
Program usage name	`saturation_start_option`
Evaluatable	No

# Magnetization inductance current — initial magnetising inductance current
A | MA | kA | mA | nA | pA | uA

Details

The initial current value used to calculate the magnetic flux value at zero time. This is the current flowing through the magnetising inductance of the transformer. The total magnetising current consists of the current through the active magnetising resistance and the current through the magnetising inductance.

Dependencies

This parameter is only used when a value of Current for the parameters Specify magnetization inductance state by.

Units	`A` \| `MA` \| `kA` \| `mA` \| `nA` \| `pA` \| `uA`
Default value	`0 A`
Program usage name	`i_Lm_start`
Evaluatable	Yes

# Magnetization inductance magnetic flux — initial magnetic flux of the magnetising inductance
Wb | N*m/A | mN*m/A

Details

The value of the magnetic flux at zero time.

Dependencies

This parameter is only used when selecting a value of Magnetic flux for the parameters Specify magnetization inductance state by.

Units	`Wb` \| `Nm/A` \| `mNm/A`
Default value	`0 Wb`
Program usage name	`Phi_start`
Evaluatable	Yes

# Magnetization inductance magnetic flux density — initial magnetic induction of the magnetising inductance
G | T

Details

The value of magnetic induction at zero time.

Dependencies

This parameter is used when the parameter is set to Magnetization inductance parameterized by value is selected Magnetic flux density versus magnetic field strength characteristic with hysteresis.

Units	`G` \| `T`
Default value	`0 T`
Program usage name	`B_start`
Evaluatable	Yes

# Magnetization inductance field strength — initial field strength of magnetising inductance
A/m

Details

The value of the magnetic field strength at zero time.

Dependencies

This parameter is used if the parameter Magnetization inductance parameterized by value is selected Magnetic flux density versus magnetic field strength characteristic with hysteresis.

Units	`A/m`
Default value	`0 A/m`
Program usage name	`H_start`
Evaluatable	Yes

Parasitic

# Combined leakage inductance parasitic parallel conductance — parasitic parallel conductance of the total scattering inductance
S | mS | nS | uS | 1/Ohm

Details

This parameters is used to represent small parasitic effects in parallel to the aggregate scattering inductance. The small parallel conductance may be required for modelling some circuit topologies.

Dependencies

To use this parameter, set parameter Winding parameterized by value Combined primary and secondary values.

Units	`S` \| `mS` \| `nS` \| `uS` \| `1/Ohm`
Default value	`1e-9 1/Ohm`
Program usage name	`g_Leq`
Evaluatable	Yes

# Primary leakage inductance parasitic parallel conductance — parasitic parallel conductance of the first winding scattering inductance
S | mS | nS | uS | 1/Ohm

Details

This parameter is used to represent small parasitic effects in parallel with the scattering inductance on the first winding. The small parallel conductance may be required for modelling some circuit topologies.

Dependencies

Units	`S` \| `mS` \| `nS` \| `uS` \| `1/Ohm`
Default value	`1e-9 1/Ohm`
Program usage name	`g_L1`
Evaluatable	Yes

# Secondary leakage inductance parasitic parallel conductance — parasitic parallel conductance of the second winding scattering inductance
S | mS | nS | uS | 1/Ohm

Details

This parameter is used to represent small parasitic effects parallel to the scattering inductance on the second winding.

Dependencies

Units	`S` \| `mS` \| `nS` \| `uS` \| `1/Ohm`
Default value	`1e-9 1/Ohm`
Program usage name	`g_L2`
Evaluatable	Yes

# Tertiary leakage inductance parasitic parallel conductance — parasitic parallel conductance of the third winding scattering inductance
S | mS | nS | uS | 1/Ohm

Details

This parameter is used to represent small parasitic effects in parallel to the scattering inductance on the third winding. The small parallel conductance may be required for modelling some circuit topologies.

Dependencies

To use this parameter, set parameter Number of windings value Three, Four, Five or Six.

Units	`S` \| `mS` \| `nS` \| `uS` \| `1/Ohm`
Default value	`1e-9 1/Ohm`
Program usage name	`g_L3`
Evaluatable	Yes

# Quartary leakage inductance parasitic parallel conductance — parasitic parallel conductance of the fourth winding scattering inductance
S | mS | nS | uS | 1/Ohm

Details

This parameter is used to represent small parasitic effects in parallel to the scattering inductance on the fourth winding. The small parallel conductance may be required for modelling some circuit topologies.

Dependencies

To use this parameter, set parameter Number of windings value Four, Five or Six.

Units	`S` \| `mS` \| `nS` \| `uS` \| `1/Ohm`
Default value	`1e-9 1/Ohm`
Program usage name	`g_L4`
Evaluatable	Yes

# Quintary leakage inductance parasitic parallel conductance — parasitic parallel conductance of the fifth winding scattering inductance
S | mS | nS | uS | 1/Ohm

Details

This parameter is used to represent small parasitic effects in parallel to the scattering inductance on the fifth winding. The small parallel conductance may be required for modelling some circuit topologies.

Dependencies

To use this parameter, set parameter Number of windings value Five or Six.

Units	`S` \| `mS` \| `nS` \| `uS` \| `1/Ohm`
Default value	`1e-9 1/Ohm`
Program usage name	`g_L5`
Evaluatable	Yes

# Senary leakage inductance parasitic parallel conductance — parasitic parallel conductance of the sixth winding scattering inductance
S | mS | nS | uS | 1/Ohm

Details

This parameter is used to represent small parasitic effects parallel to the scattering inductance on the sixth winding. The small parallel conductance may be required for modelling some circuit topologies.

Dependencies

To use this parameter, set the parameter Number of windings value Six.

Units	`S` \| `mS` \| `nS` \| `uS` \| `1/Ohm`
Default value	`1e-9 1/Ohm`
Program usage name	`g_L6`
Evaluatable	Yes