Multiphase Coupled Lines

R2026b

Magnetically coupled multiphase lines

Since R2026b

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Multiphase Coupled Lines block

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Libraries:
Simscape / Electrical / Passive / Lines

Description

The Multiphase Coupled Lines block models magnetically coupled multiphase lines. Each line has a self inductance, a series resistance, and an optional parallel conductance. In addition, there is a mutual inductance, a mutual resistance, and an optional mutual capacitance between each pair of lines.

To model magnetic coupling of a single pair of lines, use the Coupled Lines (Pair) block. To model magnetic coupling of three lines, use the Coupled Lines (Three-Phase) block.

The Multiphase Coupled Lines block allows you to model the lines with either balanced or unbalanced impedance. To choose whether to model balanced or unbalanced impedance, set the Parameterization parameter to Balanced impedance or General impedance, respectively.

Equations

When you set the Parameterization parameter to Balanced impedance, the coupled lines are balanced and the resistance, inductance, and capacitance matrices are

$$\begin{array}{l}R=\left[\begin{array}{cccc}{R}_s& R_m& \cdots & R_m\\ R_m& R_s& \cdots & R_m\\ ⋮& ⋮& \ddots & ⋮\\ R_m& R_m& \cdots & R_s\end{array}\right]\\ L=\left[\begin{array}{cccc}{L}_s& L_m& \cdots & L_m\\ L_m& L_s& \cdots & L_m\\ ⋮& ⋮& \ddots & ⋮\\ L_m& L_m& \cdots & L_s\end{array}\right]\\ C=\left[\begin{array}{cccc}{C}_s& C_m& \cdots & C_m\\ C_m& C_s& \cdots & C_m\\ ⋮& ⋮& \ddots & ⋮\\ C_m& C_m& \cdots & C_s\end{array}\right]\end{array}$$

where:

• R_s is the self resistance of the transmission line per phase.

• R_m is the line-line mutual resistance.

• L_s is the self inductance of the transmission line per phase.

• L_m is the line-line mutual inductance.

• C_s is the self capacitance of the transmission line per phase.

• C_m is the line-line mutual capacitance.

When you set the Parameterization parameter to General impedance, the coupled lines are general or unbalanced, and you must directly specify the resistance, inductance, and capacitance matrices by using the Line inductance matrix, Line resistance matrix, and Capacitance matrix parameters.

If you set the Model capacitance parameter to Exclude capacitance, then the block uses these defining equations for the coupled lines:

$$\begin{array}{l}{V}_1-V_2=R\cdot I_L+L\frac{d{I}_L}{dt}\\ I_1=I_L\\ I_2=-I_L\end{array}$$

where:

• V₁ is the voltage vector at port 1.

• V₂ is the voltage vector at port 2.

• I₁ is the current vector flowing into port 1.

• I₂ is the current vector flowing into port 2.

• I_L is the current vector flowing through the inductors.

• R is the resistance matrix.

• L is the inductance matrix.

If you set the Model capacitance parameter to Include capacitance at one port, then the block uses these defining equations for the coupled lines:

$$\begin{array}{l}{V}_1-V_2=R\cdot I_L+L\frac{d{I}_L}{dt}\\ I_1+I_2=C\frac{d{V}_1}{dt}\\ I_2=-I_L\end{array}$$

where C is the capacitance matrix.

If you set the Model capacitance parameter to Include capacitance at both ports, then the block uses these defining equations for the coupled lines:

$$\begin{array}{l}{V}_1-V_2=R\cdot I_L+L\frac{d{I}_L}{dt}\\ I_1-I_L=\frac{C}{2}\frac{d{V}_1}{dt}\\ I_2+I_L=\frac{C}{2}\frac{d{V}_2}{dt}\end{array}$$

Assumptions and Limitations

• The 1 and 2 ports of this block represent multiple nodes as single ports. The number of nodes inside each port depends on the value of the Number of phases parameter. To access each connection port on both sides of the block, use the Array Connection block.

  

Ports

Conserving

1 — End 1 of coupled lines

electrical

Electrical conserving port associated with one end of the coupled lines.

2 — End 2 of coupled lines

electrical

Electrical conserving port associated with the other end of the coupled lines.

Parameters

Parameterization — Option to specify line impedance parameterization

Balanced impedance (default) | General impedance

Option to specify the line impedance parameterization, specified as one of these values:

• Balanced impedance — Model the coupled lines with balanced impedance. If you select this option, then you must specify the same values of resistance, inductance, and capacitance for all lines.

• General impedance — Model the coupled lines with general impedance. If you select this option, then you must specify the resistance, inductance, and capacitance separately for each line by using matrices.

Number of phases — Number of phases

3 (default) | positive scalar greater than 1

Number of phases in the coupled lines.

Line self inductance — Self inductance of line

0.5 H (default) | positive scalar

Self inductance of the line. This parameter represents the value of each of the diagonal elements, L_s, of the inductance matrix.

The value of this parameter must be greater than the value of the Mutual inductance parameter.

Dependencies

To enable this parameter, set Parameterization to Balanced impedance.

Mutual inductance — Line-line mutual inductance

0.1 H (default) | nonnegative scalar

Mutual inductance between each pair of lines. This parameter represents the value of each of the off-diagonal elements, L_m, of the inductance matrix.

The value of this parameter must be less than the value of the Line self inductance parameter and greater than the negative value of the Line self inductance parameter.

Dependencies

To enable this parameter, set Parameterization to Balanced impedance.

Line self resistance — Series resistance of line

0.02 Ohm (default) | nonnegative scalar

Series resistance of the line. This parameter represents the value of each of the diagonal elements, R_s, of the resistance matrix.

The value of this parameter must be greater than the value of the Mutual resistance parameter.

Dependencies

To enable this parameter, set Parameterization to Balanced impedance.

Mutual resistance — Line-line mutual resistance

0.01 Ohm (default) | nonnegative scalar

Mutual resistance between each pair of lines. This parameter represents the value of each of the off-diagonal elements, R_m, of the resistance matrix.

The value of this parameter must be less than the value of the Line self resistance parameter.

Dependencies

To enable this parameter, set Parameterization to Balanced impedance.

Line inductance matrix — Inductance matrix of line

[.5, .1, .1; .1, .5, .1; .1, .1, .5] H (default) | matrix

Np-by-Np inductance matrix of the line, where Np is the value of the Number of phases parameter.

The diagonal elements of this matrix must be nonnegative.

Dependencies

To enable this parameter, set Parameterization to General impedance.

Line resistance matrix — Resistance matrix of line

[.02, .01, .01; .01, .02, .01; .01, .01, .02] Ohm (default) | matrix of positive elements

Np-by-Np resistance matrix of the line, where Np is the value of the Number of phases parameter.

Dependencies

To enable this parameter, set Parameterization to General impedance.

Model capacitance — Option to model capacitance at block ports

Exclude capacitance (default) | Include capacitance at one port | Include capacitance at both ports

Option to model the capacitance at neither, one, or both ports of the block.

Self capacitance — Self capacitance of lines

0.4 uF (default) | nonnegative scalar

Self capacitance of the lines. This parameter represents the value of each of the diagonal elements, C_s, of the capacitance matrix.

Dependencies

To enable this parameter, set Parameterization to Balanced impedance and Model capacitance to Include capacitance at one port or Include capacitance at both ports.

Mutual capacitance — Line-line mutual capacitance

-0.2 uF (default) | nonpositive scalar

Mutual capacitance between each pair of lines. This parameter represents the value of each of the off-diagonal elements, C_m, of the capacitance matrix.

Dependencies

To enable this parameter, set Parameterization to Balanced impedance and Model capacitance to Include capacitance at one port or Include capacitance at both ports.

Capacitance matrix — Capacitance matrix of line

[.4, -.2, -.2; -.2, .4, -.2; -.2, -.2, .4] uF (default) | matrix

Np-by-Np capacitance matrix of the line, where Np is the value of the Number of phases parameter.

Dependencies

To enable this parameter, set Parameterization to General impedance and Model capacitance to Include capacitance at one port or Include capacitance at both ports.

Extended Capabilities

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

Version History

Introduced in R2026b