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

$\begin{matrix} Z_{a a} = R_{ϕ} + R_{e} + j k_{1} \log (\frac{D_{e}}{G M R_{ϕ}}) & Ω / km \end{matrix}$

The DC resistance of phase conductor is given by

$\begin{matrix} R_{ϕ} = ρ_{C u} \frac{1000}{S_{C u}} = (17.8 e - 9) \frac{1000}{n π {(d / 2)}^{2}} & Ω / km \end{matrix}$

The resistance of earth return is given by

$\begin{matrix} R_{e} = π^{2} \cdot 10^{- 4} \cdot f & Ω / km \end{matrix}$

The frequency factor is given by

$\begin{matrix} k_{1} = 0.0529 \cdot \frac{f}{0.3048 \cdot 60} & u n i t s (Ω / km) \end{matrix}$

The distance to equivalent earth return path is given by

$\begin{matrix} D_{e} = 1650 \sqrt{ρ_{e} / (2 π f)} & m \\ ρ_{C u} = 17.8 e - 9 & Ω / m \end{matrix}$

The geometric mean radius of phase conductor is given by

$G M R_{ϕ} = r \cdot \exp (- \frac{μ_{r}}{4})$

Self Impedance of Screen Conductor(s)

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

$\begin{matrix} Z_{x x} = R_{N} + R_{e} + j k_{1} \log (\frac{D_{e}}{G M R_{N}}) & Ω / km \end{matrix}$

The DC resistance of the screen conductor is given by

$\begin{matrix} R_{N} = ρ \frac{1000}{S} & Ω / km \end{matrix}$

The geometric mean radius of the screen conductor is given by

$G M R_{N} = r_{int} + \frac{(r_{e x t} - r_{int})}{2}$

Mutual Impedance Between the Phase and Screen Conductors

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

$\begin{matrix} Z_{a x} = R_{e} + j k_{1} \log (\frac{D_{e}}{D_{n}}) & Ω / km \end{matrix}$

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

$\begin{matrix} Z_{a b} = R_{e} + j k_{1} \log (\frac{D_{e}}{G M D}) & Ω / km \end{matrix}$

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

$G M D = \sqrt[n]{\prod_{1}^{n} d_{x y}}$

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

$\begin{matrix} C_{a x} = \frac{1}{0.3048} (\frac{0.00736 ε_{r a x}}{log (D_{a x} / d_{a x})}) & μ F / km \end{matrix}$

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

$\begin{matrix} C_{x e} = \frac{1}{0.3048} (\frac{0.00736 ε_{r x e}}{log (D_{x e} / d_{x e})}) & μ F / km \end{matrix}$

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):

$\begin{matrix} R = [\begin{matrix} r_{a a} & r_{a x} & r_{a b} & r_{a b} & r_{a b} & r_{a b} \\ r_{a x} & r_{x x} & r_{a b} & r_{a b} & r_{a b} & r_{a b} \\ r_{a b} & r_{a b} & r_{a a} & r_{a x} & r_{a b} & r_{a b} \\ r_{a b} & r_{a b} & r_{a x} & r_{x x} & r_{a b} & r_{a b} \\ r_{a b} & r_{a b} & r_{a b} & r_{a b} & r_{a a} & r_{a x} \\ r_{a b} & r_{a b} & r_{a b} & r_{a b} & r_{a x} & r_{x x} \end{matrix}] & L = [\begin{matrix} l_{a a} & l_{a x} & l_{a b} & l_{a b} & l_{a b} & l_{a b} \\ l_{a x} & l_{x x} & l_{a b} & l_{a b} & l_{a b} & l_{a b} \\ l_{a b} & l_{a b} & l_{a a} & l_{a x} & l_{a b} & l_{a b} \\ l_{a b} & l_{a b} & l_{a x} & l_{x x} & l_{a b} & l_{a b} \\ l_{a b} & l_{a b} & l_{a b} & l_{a b} & l_{a a} & l_{a x} \\ l_{a b} & l_{a b} & l_{a b} & l_{a b} & l_{a x} & l_{x x} \end{matrix}] \end{matrix}$

$C = [\begin{matrix} c_{a x} & - c_{a x} & 0 & 0 & 0 & 0 \\ - c_{a x} & c_{a x} + c_{x e} & 0 & 0 & 0 & 0 \\ 0 & 0 & c_{a x} & - c_{a x} & 0 & 0 \\ 0 & 0 & - c_{a x} & c_{a x} + c_{x e} & 0 & 0 \\ 0 & 0 & 0 & 0 & c_{a x} & - c_{a x} \\ 0 & 0 & 0 & 0 & - c_{a x} & c_{a x} + c_{x e} \end{matrix}]$

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. To enable this parameter, set Number of cables to 2 or higher.
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. For more details on this window, see Display RLC Values GUI. 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.

Display RLC Values GUI

When you click the Compute RLC matrices, the Display RLC Values window opens. In this window, you can view and download parameters into your workspace and into your transmission line models.

The frequency and ground resistivity used for evaluation of the R, L, and C matrices are displayed first. Then the computed RLC parameters are displayed.

Note

The R, L, and C parameters are always displayed respectively in ohms/km, henries/km, and farads/km, even if the English units specify the input parameters.

If the number of phase conductors is 3 or 6, the symmetrical component parameters are also displayed:

For a three-phase line (one circuit), R10, L10, and C10 vectors of two values are displayed for positive-sequence and zero-sequence RLC values.
For a six-phase line (two coupled three-phase circuits), R10, L10, and C10 vectors of five values containing the following RLC sequence parameters are displayed: positive-sequence and zero-sequence of circuit 1, mutual zero-sequence between circuit 1 and circuit 2, positive-sequence and zero-sequence of circuit 2.

Send RLC parameters to workspace: Sends the R, L, and C matrices, as well as the symmetrical component parameters to the MATLAB^® workspace. The following variables are created in your workspace: R_matrix, L_matrix, C_matrix, and R10, L10, C10 for symmetrical components.
Send RLC parameters to block: Sends the RLC parameters into one of the following three blocks that you previously selected in your model: the Distributed Parameters Line block (either matrices or sequence RLC parameters), the single-phase PI Section Line block (one dimension matrix required), or the Three-Phase PI Section Line block (sequence components only).
Selected block: Confirms the block selection. The name of the selected block appears in the left window.
RLC Matrices: Downloads RLC matrices into the selected block.
Sequences: Downloads RLC sequence parameters into the selected block.
Create a report: Creates a file, XXX.rep, containing the line input parameters and the computed RLC parameters. The MATLAB editor opens to display the contents of the XXX.rep file.
Close: Closes the Display RLC Values window.

Examples

For an example using the power_cableparam function, see the power_cable model .

Documentation