Documentation

# power_cableparam

Compute RLC parameters of radial copper cables with single screen, based on conductor and insulator characteristics

## Syntax

```power_cableparam ```

## Description

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

The `power_cableparam` function 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 follow

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

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 follow

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

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 follow

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

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 follow

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

In general, the Geometric Mean Distance (GMD) between the phase conductors of a given set of cables can be calculated as follow

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

where n is the total number of distances between the conductors. However the GMD value is not calculated by the function 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 follow

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.

## Input Arguments

`[r,l,c,z] = power_cableparam(CableData)` computes the impedances and capacitances of a given set of cables with screen conductor. The conductor and insulator characteristics are given in the `CableParam` structure with the following fields

Field

Description

`N`

the number of cables

f

the frequency in hertz to be used to evaluate RLC parameters

rh0_e

the ground resistivity (in ohm.meters)

n_ba

the number of strands contained in one phase conductor

d_ba

diameter of one strand (in m)

rho_ba

DC resistivity of conductor in ohms*m.

mu_r_ba

relative permeability of the conductor material.

D_a

phase conductor outside diameter (in m)

rho_x

DC resistivity of the screen conductor in ohms*m.

S_x

Total section of screen conductor (in m^2)

d_x

screen conductor internal diameter (in m)

D_x

screen conductor external diameter (in m)

GMD_phi

Geometric Mean Distance between the cables.

d_iax

phase-screen insulator internal diameter (in m)

D_iax

phase-screen insulator external diameter (in m)

epsilon_iax

relative permittivity of the phase-screen insulator material.

d_ixe

outer screen insulator internal diameter (in m)

D_ixe

outer screen insulator external diameter (in m)

epsilon_ixe

relative permittivity of the outer screen insulator material.

## Output Arguments

The output arguments are of the form of structure variables with the following fields

Variable, Field

Description

`r.aa`

Self resistance of phase conductor, in Ohm/Km

r.xx

Self resistance of screen conductor, in Ohm/Km

r.ab

Mutual resistance between the phase conductors, in Ohm/Km

r.ax

Mutual resistance between phase and screen conductors, in Ohm/Km

l.aa

Self inductance of phase conductor, in Henries/Km

l.xx

Self inductance of screen conductor, in Henries/Km

l.ab

Mutual inductance between the phase conductors, in Henries/Km

l.ax

Mutual inductance between phase and screen conductor, in Henries/Km

c.ax

Capacitance between the phase conductor and its screen conductor, in Farad/Km

c.xe

Capacitance between the screen conductor and the ground, in Farad/Km

z.aa

Self impedance of phase conductor, in Ohm/Km

z.xx

Self impedance of screen conductor, in Ohm/Km

z.ab

Mutual impedance between phase conductors, in Ohm/Km

z.ax

Mutual impedance between phase and corresponding screen conductors, in Ohm/Km

### Building the RLC Matrices

These computed resistances, impedances, and capacitances need to be organized into 2N-by-2N matrices that can be directly used in the Cable block. See the `power_cable` example for an example on how to build a block that represents a 4-Cables with Screen block.

The RLC matrices are defined as follows (the example is given for a 3-cable configuration):

`$\begin{array}{cc}R=\left[\begin{array}{cccccc}{r}_{aa}& {r}_{ax}& {r}_{ab}& {r}_{ab}& {r}_{ab}& {r}_{ab}\\ {r}_{ax}& {r}_{xx}& {r}_{ab}& {r}_{ab}& {r}_{ab}& {r}_{ab}\\ {r}_{ab}& {r}_{ab}& {r}_{aa}& {r}_{ax}& {r}_{ab}& {r}_{ab}\\ {r}_{ab}& {r}_{ab}& {r}_{ax}& {r}_{xx}& {r}_{ab}& {r}_{ab}\\ {r}_{ab}& {r}_{ab}& {r}_{ab}& {r}_{ab}& {r}_{aa}& {r}_{ax}\\ {r}_{ab}& {r}_{ab}& {r}_{ab}& {r}_{ab}& {r}_{ax}& {r}_{xx}\end{array}\right]& L=\left[\begin{array}{cccccc}{l}_{aa}& {l}_{ax}& {l}_{ab}& {l}_{ab}& {l}_{ab}& {l}_{ab}\\ {l}_{ax}& {l}_{xx}& {l}_{ab}& {l}_{ab}& {l}_{ab}& {l}_{ab}\\ {l}_{ab}& {l}_{ab}& {l}_{aa}& {l}_{ax}& {l}_{ab}& {l}_{ab}\\ {l}_{ab}& {l}_{ab}& {l}_{ax}& {l}_{xx}& {l}_{ab}& {l}_{ab}\\ {l}_{ab}& {l}_{ab}& {l}_{ab}& {l}_{ab}& {l}_{aa}& {l}_{ax}\\ {l}_{ab}& {l}_{ab}& {l}_{ab}& {l}_{ab}& {l}_{ax}& {l}_{xx}\end{array}\right]\end{array}$`
`$C=\left[\begin{array}{cccccc}{c}_{ax}& -{c}_{ax}& 0& 0& 0& 0\\ -{c}_{ax}& {c}_{ax}+{c}_{xe}& 0& 0& 0& 0\\ 0& 0& {c}_{ax}& -{c}_{ax}& 0& 0\\ 0& 0& -{c}_{ax}& {c}_{ax}+{c}_{xe}& 0& 0\\ 0& 0& 0& 0& {c}_{ax}& -{c}_{ax}\\ 0& 0& 0& 0& -{c}_{ax}& {c}_{ax}+{c}_{xe}\end{array}\right]$`

## Dialog Box

`power_cableparam` command opens a user interface (UI) that is used to specify the cable parameters and to compute the electrical R, L, C cable parameters. ### Configuration Parameters

Number of cables

Specify the 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 follows: 2N-by-2N, where N is the number of cables.

Frequency

Specify the frequency in hertz to be used to evaluate RLC parameters.

Ground resistivity

Specify the ground resistivity in ohm.meters.

Geometric mean distance between cables

Specify the Geometric Mean Distance (GMD) between the cables. Set this value to zero if the Number of cables parameter is set 1.

Comments

Use this window to type comments that you want to save with the line parameters, for example, voltage level, conductor types, and other information.

### Phase Conductor Parameters

Number of strands

Specify the number of strands contained in the phase conductor.

Strand diameter

Specify the diameter of one strand (in mm, cm, or m).

Resistivity

Specify the DC resistivity of conductor in ohm*m.

Relative permeability

Specify the relative permeability of the conductor material.

External diameter

Specify the phase conductor outside diameter (in mm, cm, or m).

### Screen Conductor Parameters

Resistivity

Specify the DC resistivity of conductor in ohm*m.

Total section

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
Internal diameter

Specify the phase conductor outside diameter (in mm, cm, or m).

External diameter

Specify the phase conductor outside diameter (in mm, cm, or m).

### Phase-Screen Insulator Parameters

Relative permittivity

Specify the relative permittivity of the phase-screen material.

Internal diameter

Specify the phase conductor outside diameter (in mm, cm, or m).

External diameter

Specify the phase conductor outside diameter (in mm, cm, or m).

### Outer Screen Insulator Parameters

Relative permittivity

Specify the relative permittivity of the outer-screen material.

Internal diameter

Specify the phase conductor outside diameter (in mm, cm, or m).

External diameter

Specify the phase conductor outside diameter (in mm, cm, or m).

### Buttons

Load typical data

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

Load user data

Opens a browser window letting you select your own cable data. Select the desired `.mat` file.

Save

Saves your cable data by generating a `.mat` file that contains the GUI information and the cable data.

Compute RLC matrices

Computes the RLC matrices for a given cable. After completion of the parameters computation, results are displayed in a new window, entitled Display RLC Values. See Display RLC Values GUI for more details on this window. The obtained results are of the form of 2N-by-2N RLC matrices that can be directly used in the cable block. For an example, see the 4 Cables with screen block in the `power_cable` example.

## Examples

See the `power_cable` model for an example using the `power_cableparam` function.

## See Also

#### 10 Ways to Speed Up Power Conversion Control Design with Simulink

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