# Cable Parameters Tool

Compute RLC parameters of radial copper cables with single screen

## Description

The Cable Parameters Tool app computes the RLC parameters of radial cooper cables that have a single screen. The app computes the parameters based on conductor and insulator characteristics.

For a set of N cables, the Cable Parameters Tool computes the self- and mutual impedances, the phase-to-screen, and screen to ground capacitances of radial cables with screen.

The Cable Parameters Tool assumes that a cable consists of an inner copper phase conductor with an outer screen conductor, using cross-linked polyethylene (XLPE) insulator material.

### The Cable and Insulator Parameters

The following figure shows a typical high-voltage cable. The variables used in the equations are:

N: The number of cables

n: the number of strands contained in the phase conductor.

d: the diameter of one strand (m)

f: the nominal frequency of the cable application

r: the radius of the phase conductor

µr: the relative permeability of phase conductor

rint, rext: the internal and external radius of the screen conductor

GMD: Geometric mean distance between the phase conductors.

ρ: Resistivity of the screen conductor

ɛrax: Relative permittivity of the phase-screen insulator

ɛrxe: Relative permittivity of the outer screen insulator

dax,Dax: the internal and external diameter of phase-screen insulator

dxe,Dxe: the internal and external diameter of the outer screen insulator

### Self-Impedance of Phase Conductor(s)

The self-impedance of the copper phase conductor is calculated as:

`$\begin{array}{cc}{Z}_{aa}={R}_{\varphi }+{R}_{e}+j{k}_{1}\mathrm{log}\left(\frac{{D}_{e}}{GM{R}_{\varphi }}\right)& \Omega /\text{km}\end{array}$`

The DC resistance of phase conductor is given by:

`$\begin{array}{cc}{R}_{\varphi }={\rho }_{Cu}\frac{1000}{{S}_{Cu}}=\left(17.8e-9\right)\frac{1000}{n\pi {\left(d/2\right)}^{2}}& \Omega /\text{km}\end{array}$`

The resistance of earth return is given by:

`$\begin{array}{cc}{R}_{e}={\pi }^{2}\cdot {10}^{-4}\cdot f& \Omega /\text{km}\end{array}$`

The frequency factor is given by:

The distance to equivalent earth return path is given by:

`$\begin{array}{cc}{D}_{e}=1650\sqrt{{\rho }_{e}/\left(2\pi f\right)}& m\\ {\rho }_{Cu}=17.8e-9& \Omega /m\end{array}$`

The geometric mean radius of phase conductor is given by:

`$GM{R}_{\varphi }=r\cdot \mathrm{exp}\left(-\frac{{\mu }_{r}}{4}\right)$`

### Self Impedance of Screen Conductor(s)

The self-impedance of the screen conductor is calculated as:

`$\begin{array}{cc}{Z}_{xx}={R}_{N}+{R}_{e}+j{k}_{1}\mathrm{log}\left(\frac{{D}_{e}}{GM{R}_{N}}\right)& \Omega /\text{km}\end{array}$`

The DC resistance of the screen conductor is given by:

`$\begin{array}{cc}{R}_{N}=\rho \frac{1000}{S}& \Omega /\text{km}\end{array}$`

The geometric mean radius of the screen conductor is given by:

`$GM{R}_{N}={r}_{\mathrm{int}}+\frac{\left({r}_{ext}-{r}_{\mathrm{int}}\right)}{2}$`

### Mutual Impedance Between the Phase and Screen Conductors

The mutual impedance between the phase conductor and its corresponding screen conductor is calculated as:

`$\begin{array}{cc}{Z}_{ax}={R}_{e}+j{k}_{1}\mathrm{log}\left(\frac{{D}_{e}}{{D}_{n}}\right)& \Omega /\text{km}\end{array}$`

Dn corresponds to the distance between the phase conductor and the mean radius of the screen conductor.

### Mutual Impedance Between the Phase Conductors

If more than one cable is modeled (N>1), the mutual impedance between the N phase conductors is calculated as:

`$\begin{array}{cc}{Z}_{ab}={R}_{e}+j{k}_{1}\mathrm{log}\left(\frac{{D}_{e}}{GMD}\right)& \Omega /\text{km}\end{array}$`

In general, the geometric mean distance (GMD) between the phase conductors of a given set of cables can be calculated as

`$GMD=\sqrt[n]{\prod _{1}^{n}{d}_{xy}}$`

where n is the total number of distances between the conductors. However, the GMD value is not calculated by the app and needs to be specified directly as an input parameter.

### Capacitance Between the Phase and Screen Conductors

The capacitance between the phase conductor and its corresponding screen conductor is calculated as:

The cross-linked polyethylene (XLPE) insulator material is assumed in this equation.

### Capacitance Between the Screen Conductor and the Ground

The same equation is used to calculate the capacitance between the screen conductor and the ground:

### Capacitance Between the Phase Conductors

The capacitive effect between the phase conductors is negligible and therefore not computed by the `power_cableparam` function.

## Open the Cable Parameters Tool App

• MATLAB® command prompt: Enter `powerCableParameters`

## Parameters

Configuration

Ground resistivity, in Ohm-meters.

Frequency, in hertz, that is used to evaluate RLC parameters.

Number of cables. A cable consists of an inner phase conductor, an outer screen conductor, and insulator. This parameter determines the dimension of the R, L, and C matrices as 2N-by-2N, where N is the number of cables.

Geometric mean distance between the cables.

#### Dependencies

To enable this parameter, set Number of cables to `2` or higher.

Phase Conductor

Number of strands contained in the phase conductor.

Diameter of one strand, in mm, cm, or m.

DC resistivity of conductor, in ohm*m.

Relative permeability of the conductor material.

Phase conductor outside diameter, in mm, cm, or m.

Screen Conductor

DC resistivity of conductor, in ohm*m.

Total section of screen conductor, in mm^2, cm^2, or m^2.

The screen total section value is sometimes provided in datasheets. If you do not know this value, you can compute it as follows:

Total section = pi*r_out^2 – pi*r_in^2 where:

• r_out is the external radius of screen conductor

• r_in is the internal radius of screen conductor

Phase conductor outside diameter, in mm, cm, or m.

Phase conductor outside diameter, in mm, cm, or m.

Phase-Screen insulator

Relative permittivity of the phase-screen material.

Phase conductor outside diameter, in mm, cm, or m.

Phase conductor outside diameter, in mm, cm, or m.

Outer Screen insulator

Relative permittivity of the outer screen material.

Phase conductor outside diameter, in mm, cm, or m.

Phase conductor outside diameter, in mm, cm, or m.

Buttons

Computes the RLC matrices for a given cable. After computing the parameters, the app displays the results in the Computed Parameters section. The obtained results are of the form of 2N-by-2N RLC matrices that can be directly used in the block you selected to model your cable. For an example, see the ```4 Cables with screen (PI model)``` block in the `power_cable` example.

Confirms the block selection. The name of the selected block appears in the field to the right of the button.

Sends the RLC parameters to the Distributed Parameter Line or Pi Section Line blocks specified in the parameter.

Sends the R, L, and C matrices to the MATLAB workspace. The app creates the variables R_matrix, L_matrix, and C_matrix in your workspace.

Load the default cable parameters provided with Simscape™ Electrical™ Specialized Power Systems software. This command opens a browser window where you can select the `DefaultCableParameters.mat` file, which represents the four-cable configuration used in the `power_cable` example..

Opens a browser window where you can select your own cable data. Select the desired MAT-file.

Saves your cable data by generating a MAT-file that contains the GUI information and cable data.

Open the documentation page of the app.

## Version History

Introduced in R2021b