Parallel three-phase transmission lines taking into account the mutual inductance between them.
Description
The Double-Circuit Transmission Line block simulates two parallel three-phase lines (including double-circuit lines) represented by a U-shaped substitution diagram with concentrated parameters, with the possibility of modelling zero-sequence coupling between them. Each line is modelled with phase active resistances, phase inductances, phase inductances, phase-to-phase mutual active resistances and inductances, phase-to-phase capacitances, phase-to-ground capacitances.
Regardless of the method of assignment, the model will generate matrices , , , which describe the three-phase lines and the connection between them:
,
,
.
The values with indices 1 and 2 are the intrinsic and mutual active resistances, inductances, capacitances of lines 1 and 2.
The values with the index are mutual active resistances, inductances, capacitances between the phases of one line and the phases of the other line. It is assumed that each phase of one line affects equally any phase of the other line.
Information on line parameters such as mutual inductance, mutual active resistance, formulas for the relationship between eigenvalues and mutual values with the values of direct and zero sequence are given in the documentation for the units Coupled Lines (Three-Phase) and Transmission Line (Three-Phase).
Ports
Non-directional
~1 - three-phase port `three-phase electricity
Three-phase electrical port, corresponds to the positive terminals of the first line.
~2 - three-phase port `three-phase electricity
Three-phase electrical port, corresponds to the negative terminals of the first line.
~3 - three-phase port `Three-phase electricity
Three-phase electrical port, corresponds to the positive terminals of the second line.
~4 - three-phase port `Three-phase electricity
Three-phase electrical port, corresponds to the negative terminals of the second line.
Parameters
Main
Parameterization - method of setting parameters of lines and zero-sequence communications Balanced impedance | General impedance | Sequence impedance | Sequence impedance (R, X, B) (by default)
The line parameters are set as follows:
Balanced impedance - set the same series active resistance, series inductance and cross capacitance for all phases.
General impedance - set different series active resistance, series inductance and cross capacitance for each phase.
Sequence impedance - set active resistance, inductance and cross capacitance (, , ) for direct and zero sequences.
Sequence impedance (R, X, B) - set the active resistance, inductive resistance and capacitive conductance (, , ) for direct and neutral sequences.
Line coupling parameters are set in zero sequence values , , if the option Sequence impedance (R, X, B) is selected, and in zero sequence values , , otherwise.
Per unit length parameters - set unit length parameters of lines on (By default) | off
If the value of this parameter is "on", then for lines and zero-sequence communication, specific parameter values are set, i.e. parameter values per unit length of the line. If the value of this parameter is off, the full values are set and the Line length parameter is hidden.
Identical lines - parameters of line 1 and line 2 are the same On (By default) | Off.
If the value of this parameter is enabled, the line 2 parameters are assumed to be equal to the line 1 parameters and the corresponding Line 2 parameter group is hidden.
Zero-sequence coupling - modelling of zero-sequence coupling On (By default) | Off
If the value of this parameter is disabled, the zero-sequence coupling between lines is not modelled and the corresponding parameter group Zero-sequence mutual coupling is hidden.
Frequency used for line parameters specification - frequency for which line parameters are specified 50.0 Hz (By default).
The frequency for which line parameters are specified.
Line length - length of the transmission line 1.0 km (by default)
Transmission line length.
Dependencies
To use this parameter, set the Per unit length parameters to `enabled'.
Line 1
Positive-sequence resistance - specific active resistance of the direct sequence `0.02 ohm/km (by default)
Specific active resistance of the direct sequence. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B) or Sequence impedance' and the Per unit length parameters to `on.
Positive-sequence reactance - specific inductive resistance of the direct sequence `0.1256637 ohm/km (by default)'.
Specific inductive resistance of the direct sequence. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B) and the Per unit length parameters to on.
Positive-sequence capacitive conductance is the specific capacitive conductance of the direct sequence 3.141593e2 µSm/km (by default).
The specific capacitive capacitive conductance of the direct sequence. This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B) and the Per unit length parameters to on.
Zero-sequence resistance - specific active resistance of zero sequence 0.02 Ohm/km (by default).
Zero-sequence specific active resistance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B) or Sequence impedance and the Per unit length parameters to enabled.
Zero-sequence specific capacitive conductance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B) and the Per unit length parameters to on.
Positive-sequence inductance is the specific inductance of the forward sequence 0.4 mGN/km (by default)
Specific direct-sequence inductance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance' and the Per unit length parameters to `on.
Positive-sequence capacitance - specific capacitance of the direct sequence `1 µF/km (By default)
Specific direct-sequence capacitance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance' and the Per unit length parameters to `on.
Zero-sequence inductance - zero-sequence specific inductance `0.7 mGN/km (By default)
Zero-sequence specific inductance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance' and the Per unit length parameters to `on.
Zero-sequence capacitance - zero-sequence specific capacitance `0.1 µF/km (by default)
Zero-sequence specific capacitance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance' and the Per unit length parameters to `on.
Resistance - specific series active resistance of the line 0.02 Ohm/km (by default)
Specific series active resistance of the line. This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to Balanced impedance' and the Per unit length parameters to `on.
Mutual resistance - specific mutual active resistance `0 ohm (by default)'.
Specific mutual active resistance of each pair of lines. This value must be greater than or equal to zero.
Use this value to account for losses in the common neutral.
Dependencies
To use this parameter, set the Parameterization parameter to Balanced impedance' and the Per unit length parameters to `on.
Inductance is the specific inductance of the line 0.5 mGN/km (by default).
Specific intrinsic inductance of the line. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Balanced impedance' and the Per unit length parameters to `on.
Mutual inductance - specific mutual inductance `0.1 mGN/km (by default)'.
Specific mutual inductance of each pair of lines. If the coupling coefficient is known , set this value to , where is the specific mutual inductance of each line. To be physically realisable, this value must satisfy the inequality:
Dependencies
To use this parameter, set parameterization to Balanced impedance.
Line-ground capacitance - specific capacitance of phases with respect to ground `0.1 µF/km (By default)
The specific capacitance of each phase with respect to ground. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Balanced impedance' and the Per unit length parameters to `on.
Line-line capacitance - specific capacitance between phases `0.3 µF/km (By default)
The specific capacitance between each pair of phases. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Balanced impedance' and the Per unit length parameters to `on.
Line a resistance - specific series active resistance of phase a 0.02 Ohm/km (by default)
Specific series active resistance of the phase . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line b resistance - specific series active resistance of phase b 0.02 Ohm/km (by default).
Specific series active resistance of the phase . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line c resistance - specific series active resistance of phase c 0.02 Ohm/km (by default).
Specific series active resistance of the phase . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line a-b mutual resistance - specific mutual active resistance between phases a and b `0 ohm/km (by default)
Specific mutual resistance between phases а and . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line b-c mutual resistance - specific mutual active resistance between phases b and c `0 ohm/km (by default)'.
Specific mutual resistance between phases and . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line c-a mutual resistance - specific mutual active resistance between phases a and c `0 ohm/km (by default)'.
Specific mutual resistance between phases and . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line a inductance - specific natural inductance of phase a 0.5 mGN/km (by default).
Specific phase eigeninductance а. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line b inductance - specific natural inductance of phase b 0.5 mGN/km (by default).
Specific phase eigeninductance . This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line c inductance - specific natural inductance of phase c 0.5 mGN/km (by default).
Specific phase eigeninductance . This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line a-b mutual inductance - specific mutual inductance between phases a and b `0.1 mGN/km (by default)
Specific mutual inductance between phases а and .
If the coupling coefficient is known , set the value of this parameter to , where and are the inductances of the phases and . To have a physically realisable mutual inductance, this value must be satisfied:
.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line b-c mutual inductance - specific mutual inductance between phases b and c `0.1 mGN/km (By default)
Specific mutual inductance between phases and .
If the coupling coefficient is known , set the value of this parameter to , where and are the inductances of the phases and . To have a physically realisable mutual inductance, this value must be satisfied:
.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line c-a mutual inductance - specific mutual inductance between phases a and c `0.1 mGN/km (By default)
Specific mutual inductance between phases and .
If the coupling coefficient is known , set the value of this parameter to , where and are the inductances of the phases and . To have a physically realisable mutual inductance, this value must be satisfied:
.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line a-ground capacitance - specific capacitance of phase a with respect to ground `0.1 µF/km (By default)
Specific capacitance of phase with respect to ground. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to enabled.
Line b-ground capacitance - specific capacitance of phase b to ground `0.1 µF/km (By default)
Specific capacitance of phase with respect to ground. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to enabled.
Line c-ground capacitance - specific capacitance of phase c to ground `0.1 µF/km (by default)
Specific capacitance of phase with respect to ground. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to enabled.
Line a-line b capacitance - specific capacitance between phases a and b `0.3 µF/km (by default)
Specific capacitance between phases and . This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line b-line c capacitance - specific capacitance between phases b and c `0.3 µF/km (By default)
Specific capacitance between phases and . This value should be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Line c-line a capacitance - specific capacitance between phases c and a `0.3 µF/km (By default)
Specific capacitance between phases and . This value should be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to on.
Total positive-sequence resistance - active resistance of direct sequence `0.02 ohms (by default)
Active positive-sequence resistance. This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B) or Sequence impedance and the Per unit length parameters to off.
The inductive resistance of the positive-sequence reactance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B) and the Per unit length parameters to off.
Total positive-sequence capacitive conductance is Total positive-sequence capacitive conductance' `3.141593e2 µSm (by default).
Direct-sequence capacitive conductance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B) and the Per unit length parameters to disabled.
Total zero-sequence resistance is the active zero-sequence resistance 0.02 ohms (by default).
Zero-sequence active resistance. This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B) or Sequence impedance and the Per unit length parameters to off.
The positive-sequence capacitance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance' and the Per unit length parameters to `off.
Total zero-sequence inductance - zero-sequence inductance `0.7 mGN (by default)'.
Zero-sequence inductance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance' and the Per unit length parameters to `off.
Total zero-sequence capacitance - zero-sequence capacitance 0.1 µF (By default).
Zero-sequence capacitance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance' and the Per unit length parameters to `off.
Total resistance is the series active resistance of the line `0.02 ohms (by default)
Series active resistance of the line. This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to Balanced impedance' and the Per unit length parameters to `off.
Total mutual resistance - mutual resistance `0 ohms (by default)'.
The mutual resistance of each pair of lines. This value must be greater than or equal to zero.
Use this value to account for losses in the common neutral.
Dependencies
To use this parameter, set the Parameterization parameter to Balanced impedance' and the Per unit length parameters to `off.
Total inductance is the line’s own inductance `0.5 mGN (by default)'.
The line’s own inductance. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Balanced impedance' and the Per unit length parameters to `off.
Total mutual inductance - mutual inductance `0.1 mGN (by default)'.
Mutual inductance of each pair of lines. If the coupling coefficient is known , set this value to , where is the intrinsic inductance of each line. To be physically realisable, this value must satisfy the inequality:
Dependencies
To use this parameter, set the Parameterization parameter to Balanced impedance' and the Per unit length parameters to `off.
Total line-ground capacitance - phase-to-ground capacitance `0.1 µF (By default)
The capacitance of each phase with respect to ground. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Balanced impedance' and the Per unit length parameters to `off.
Total line-line capacitance - phase-to-phase capacitance `0.3 µF (By default)
The capacitance between each pair of phases. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Balanced impedance' and the Per unit length parameters to `off.
Total line a resistance - series active resistance of phase a `0.02 ohm (by default)
Series active phase resistance . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line b resistance - series active resistance of phase b 0.02 ohm (by default).
Series phase active resistance . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line c resistance - series active resistance of phase c `0.02 ohm (by default)'.
Series phase active resistance . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line a-b mutual resistance - mutual active resistance between phases a and b `0 ohm (by default)'.
Mutual active resistance between phases а and . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line b-c mutual resistance - mutual active resistance between phases b and c `0 ohm (by default)'.
Mutual active resistance between phases and . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line c-a mutual resistance - mutual active resistance between phases a and c `0 ohm (by default)'.
Mutual active resistance between phases and . This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line a inductance - phase a phase a inductance `0.5 mGN (by default)'.
Own phase inductance а. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line b inductance - phase b inductance proper `0.5 mGN (by default)'.
Own phase inductance . This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line c inductance - phase c inductance of the phase `0.5 mGN (by default)'.
Eigen inductance . This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line a-b mutual inductance - mutual inductance between phases a and b `0.1 mGN (by default)'.
Mutual inductance between phases а and .
If the coupling coefficient is known , set the value of this parameter to , where and are the inductances of the phases and . To have a physically realisable mutual inductance, this value must be satisfied:
.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line b-c mutual inductance - mutual inductance between phases b and c `0.1 mGN (by default)'.
Mutual inductance between phases and .
If the coupling coefficient is known , set the value of this parameter to , where and are the inductances of the phases and . To have a physically realisable mutual inductance, this value must be satisfied:
.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line c-a mutual inductance - mutual inductance between phases a and c `0.1 mGN (by default)'.
Mutual inductance between phases and .
If the coupling coefficient is known , set the value of this parameter to , where and are the inductances of the phases and . To have a physically realisable mutual inductance, this value must be satisfied:
.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line a-ground capacitance - capacitance of phase a to ground 0.1 µF (by default).
The capacitance of phase with respect to ground. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line b-ground capacitance - capacitance of phase b to ground 0.1 µF (by default).
Capacitance of phase with respect to ground. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line c-ground capacitance - capacitance of phase c to ground 0.1 µF (by default).
The capacitance of phase with respect to ground. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line a-line b capacitance - capacitance between phases a and b 0.3 µF (by default).
Capacitance between phases and . This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line b-line c capacitance - capacitance between phases b and c 0.3 µF (by default).
Capacitance between phases and . This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Total line c-line a capacitance - capacitance between phases c and a 0.3 μF (by default)
Capacitance between phases and . This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to General impedance and the Per unit length parameters to off.
Line 2
Line 2 settings are available when Identical lines is set to `disabled'. In this case, the parameter values for the second line are assumed to be different from those for the first line. The description and names of the parameters are the same as those given in section Line 1.
Zero-sequence mutual coupling
Resistance - specific mutual zero-sequence active resistance `0.01 Ohm/km (by default)
Specific reciprocal zero sequence resistance between lines 1 and 2. This value must be greater than or equal to zero.
Dependencies
To use this parameter, set the Zero-sequence coupling and Per unit length parameters to `enabled'.
The specific reciprocal inductive zero-sequence resistance between lines 1 and 2. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B) and the Zero-sequence coupling and Per unit length parameters to on.
Zero-sequence specific mutual capacitive conductance between lines 1 and 2. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B) and the Zero-sequence coupling and Per unit length parameters to on.
Inductance - specific mutual zero-sequence inductance 0.3 mGN/km (by default).
The specific zero-sequence mutual inductance between lines 1 and 2. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance, Balanced impedance or General impedance and the Zero-sequence coupling and Per unit length parameters to enabled.
Capacitance - specific mutual zero-sequence capacitance 0.01 µF/km (by default).
Specific zero sequence mutual capacitance between lines 1 and 2. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance, Balanced impedance or General impedance and the Zero-sequence coupling and Per unit length parameters to enabled.
Total resistance - zero sequence mutual active resistance `0.01 ohm (by default)
Mutual active zero sequence resistance between lines 1 and 2. This value must be greater than or equal to zero.
Dependencies
To use this parameter, set Zero-sequence coupling to on and Per unit length parameters to off.
Total reactance - zero sequence mutual inductive resistance 0.09424778 ohms (by default).
Mutual inductive zero sequence resistance between lines 1 and 2. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B), the Zero-sequence coupling parameter to on and the Per unit length parameters to off.
Mutual zero sequence capacitive conductance between lines 1 and 2. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance (R, X, B), the Zero-sequence coupling parameter to on, and the Per unit length parameters to off.
Total inductance - zero-sequence mutual inductance `0.3 mGN (by default)'.
Mutual zero sequence inductance between lines 1 and 2. This value must be greater than zero.
Dependencies
To use this parameter, set the Parameterization parameter to Sequence impedance', `Balanced impedance' or `General impedance', the Zero-sequence coupling parameter to `on and the Per unit length parameters to off.
Total capacitance - zero-sequence mutual capacitance 0.01 µF (by default).
Mutual zero sequence capacitance between lines 1 and 2. This value must be greater than zero.
Dependencies
To use this parameter, set parameterization to Sequence impedance, Balanced impedance or General impedance, Zero-sequence coupling to on and Per unit length parameters to off.
Initial Targets
Line 1 inductor currents [i_a1 i_b1 i_c1] - initial values of currents through inductors of line 1, A zeros(3) (by default)
Initial values of currents through inductors of line 1.
Line 2 inductor currents [i_a2 i_b2 i_c2] - initial values of currents through inductors of line 2, A zeros(3) (by default)
Initial values of currents through inductors of line 2.