# Power Line Parameters

Compute RLC parameters of overhead transmission line from its conductor characteristics and tower geometry

## Description

The Power Line Parameters app provides a tool to compute the RLC line parameters of the Distributed Parameters Line and PI Section Line blocks and the frequency-dependent parameters of a Distributed Parameters Line (Frequency-Dependent) block. The tool uses the `power_lineparam` function to compute the line parameters based on the geometry of the line and the type of conductors.

## Open the Power Line Parameters App

• powergui Block Parameters dialog box: On the Tools tab, click Power Line Parameters.

• MATLAB® command prompt: Enter `powerLineParameters`

## Parameters

Use this text box to type comments that you want to save with the line parameters, for example, voltage level, conductor types and characteristics, etc.

Opens a browser window where you can select examples of line configurations provided with Simscape™ Electrical™ Specialized Power Systems software. Select the desired `.mat` file.

Selecting Load typical parameters allows you to load one of the following line configurations:

 Line_25kV_4wires.mat 25-kV, three-phase distribution feeder with accessible neutral conductor. Line_315kV_2circ.mat 315-kV, three-phase, double-circuit line using bundles of two conductors. Phase numbering is set to obtain the RLC parameters of the two individual circuits (six-phase line). Line_450kV.mat Bipolar +/−450-kV DC line using bundles of four conductors. Line_500kV_2circ.mat 500-kV, three-phase, double-circuit line using bundles of three conductors. Phase numbering is set to obtain the RLC parameters of the three-phase line circuit equivalent to the two circuits connected in parallel. Line_735kV.mat 735-kV, three-phase line using bundles of four conductors.

Opens a browser window where you can select your own line data. Select the desired `.mat` file.

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

Creates a file containing the line input parameters and the computed RLC parameters. The MATLAB Editor opens to display the contents of the file.

General Parameters

Select `metric` to specify conductor diameter, GMR, and bundle diameter in centimeters and conductor positions in meters. Select `english` to specify conductor diameter, GMR, and bundle diameter in inches and conductor positions in feet.

Specify the ground resistivity, in ohm-meters. A zero value (perfectly conducting ground) is allowed.

Specify the frequency, in hertz, to evaluate RLC parameters.

Line Geometry

Specify the number of phase conductors (single conductors or bundles of subconductors).

Specify the number of ground wires (single conductors or bundles of subconductors). Ground wires are not usually bundled.

Lists the conductor or bundle identifiers. Phase conductors are identified as p1, p2,..., pn. Ground wires are identified as g1,g2,..., gn.

Specify the phase number to which the conductor belongs. Several conductors may have the same phase number. All conductors that have the same phase number are lumped together and are considered as a single equivalent conductor in the R, L, and C matrices. For example, if you want to compute the line parameters of a three-phase line equivalent to a double-circuit line such as the one represented in the figure Configuration of a Three-Phase Double-Circuit Line, you specify phase numbers 1, 2, 3 for conductors p1, p2, p3 (circuit 1) and phase numbers 3, 2, 1 for conductors p4, p5, p6 (circuit 2), respectively. If you prefer to simulate this line as two individual circuits and have access to the six phase conductors, you specify phase numbers 1, 2, 3, 6, 5, 4 respectively for conductors p1, p2, p3, p4, p5 and p6.

In three-phase systems, the three phases are usually labeled A, B, and C. The correspondence with the phase number is:

1, 2, 3, 4, 5, 6, 7, 8, 9,.... = A, B, C, A, B, C, A, B, C,...

You can also use the phase number to lump conductors of an asymmetrical bundle.

For ground wires, the phase number is forced to zero. All ground wires are lumped with the ground and they do not contribute to the R, L, and C matrix dimensions. If you need to access the ground wire connections in your model, you must specify these ground wires as normal phase conductors and manually connect them to the ground.

Specify the horizontal position of the conductor, in meters or feet. The location of the zero reference position is arbitrary. For a symmetrical line, you typically choose X = 0 at the center of the line.

Specify the vertical position of the conductor (at the tower) with respect to ground, in meters or feet.

Specify the vertical position of the conductor with respect to ground at mid-span, in meters or feet.

The average height of the conductor (see the figure Configuration of a Three-Phase Double-Circuit Line) is produced by this equation:

`${Y}_{average}={Y}_{\mathrm{min}}+\frac{sag}{3}=\frac{2{Y}_{\mathrm{min}}+{Y}_{tower}}{3}$`

 Ytower = height of conductor at tower Ymin = height of conductor at mid span sag = Ytower−Ymin

Instead of specifying two different values for Ytower and Ymin, you may specify the same Yaverage value.

Specify one of the conductor or bundle type numbers listed in the first column of the table of conductor characteristics.

Conductors

Specify the number of conductor types (single conductor or bundle of subconductors). This parameter determines the number of rows in the table of conductors. The phase conductors and ground conductors can be either single conductors or bundles of subconductors. For voltage levels of 230 kV and higher, phase conductors are usually bundled to reduce losses and electromagnetic interferences due to corona effect. Ground wires are usually not bundled.

For a simple AC three-phase line, single- or double-circuit, there are usually two types of conductors: one type for the phase conductors and one type for the ground wires. You need more than two types for several lines in the same corridor, DC bipolar lines or distribution feeders, where neutral and sheaths of TV and telephone cables are represented.

Select one of the following three parameters to specify how the conductor internal inductance is computed: `T/D ratio`, ```Geometric Mean Radius (GMR)```, or ```Reactance Xa at 1-foot spacing``` (or `Reactance Xa at 1-meter spacing` if the Units parameter is set to `metric`).

If you select `T/D ratio`, the internal inductance is computed from the T/D value specified in the table of conductors, assuming a hollow or solid conductor. D is the conductor diameter and T is the thickness of the conducting material (see the figure Configuration of a Three-Phase Double-Circuit Line). The conductor self-inductance and resistance are computed from the conductor diameter, T/D ratio, DC resistance, and relative permeability of conducting material and specified frequency.

If you select `Geometric Mean Radius (GMR)`, the conductor GMR evaluates the internal inductance. When the conductor inductance is evaluated from the GMR, the specified frequency does not affect the conductor inductance. You must provide the manufacturer's GMR for the desired frequency (usually 50 Hz or 60 Hz). When you are using the `T/D ratio` option, the corresponding conductor GMR at the specified frequency is displayed in the Conductors table.

Selecting `Reactance Xa at 1-foot spacing` (or `Reactance Xa at 1-meter spacing`) uses the positive-sequence reactance at the specified frequency of a three-phase line having 1-foot (or 1-meter) spacing between the three phases to compute the conductor internal inductance.

Select this check box to include the impact of frequency on conductor AC resistance and inductance (skin effect). If this parameter is cleared, the resistance is kept constant at the value specified by the Conductor DC resistance parameter and the inductance is kept constant at the value computed in DC, using the D out (conductor outside diameter) and the T/D ratio parameters of the Conductors table. When skin effect is included, the conductor AC resistance and inductance are evaluated considering a hollow conductor with T/D ratio (or solid conductor if T/D = 0.5). The T/D ratio evaluates the AC resistance even if the conductor inductance is evaluated from the GMR or from the reactance at 1-foot spacing or 1-meter spacing. The ground skin effect is always considered and it depends on the ground resistivity.

Specify the conductor outside diameter, in centimeters or inches.

Specify the T/D ratio of the hollow conductor. T is the thickness of the conducting material, and D is the outside diameter. This parameter can vary between `0` and `0.5`. A T/D value of `0.5` indicates a solid conductor. For Aluminum Cable Steel Reinforced (ACSR) conductors, you can ignore the steel core and consider a hollow aluminum conductor (typical T/D ratios are between `0.3` and `0.4`). The T/D ratio is used to compute the conductor AC resistance when the Include conductor skin effect parameter is selected. It is also used to compute the conductor self-inductance when the parameter Internal conductor inductance evaluated from is set to `T/D ratio`.

This parameter is accessible only when the parameter Internal conductor inductance evaluated from is set to ```Geometric Mean Radius (GMR)```. Specify the GMR in centimeters or inches. The GMR at 60 Hz or 50 Hz is usually provided by conductor manufacturers. When the parameter Internal conductor inductance evaluated from is set to `T/D ratio`, the value of the corresponding GMR giving the same conductor inductance is displayed. When the parameter Internal conductor inductance evaluated from is set to `Reactance Xa at 1-foot spacing` or ```Reactance Xa at 1-meter spacing```, the title of the column changes to Xa.

This parameter is accessible only when Internal conductor inductance evaluated from is set to ```Reactance Xa at 1-meter spacing``` or `Reactance Xa at 1-foot spacing`. Specify the Xa value in ohms/km or ohms/mile at the specified frequency. The Xa value at 60 Hz or 50 Hz is usually provided by conductor manufacturers.

Specify the DC resistance of conductor in ohms/km or ohms/mile.

Specify the relative permeability µr of the conducting material. µr = 1.0 for nonmagnetic conductors (such as aluminum or copper). This parameter is not accessible when the Include conductor skin effect parameter is cleared.

Specify the number of subconductors in the bundle or 1 for single conductors.

Specify the bundle diameter, in centimeters or inches. This parameter is not accessible when the Nb_cond is set to 1. When you specify bundled conductors, the subconductors are assumed to be evenly spaced on a circle. If this is not the case, you must enter individual subconductor positions in the Line Geometry table and lump these subconductors by giving them the same Phase Number parameter.

Specify an angle, in degrees, that determines the position of the first conductor in the bundle with respect to a horizontal line parallel to ground. This angle determines the bundle orientation. This parameter is not accessible when the Nb_cond is set to `1`.

Frequency-Dependent Line Parameters

Specify a frequency range for the parameter computation. Enter a vector of three elements,` [X1,X2,N]`. This parameter defines a frequency vector of `N` logarithmically equally spaced points between decades `10^X1` and `10^X2`.

Specify the length of the line, in km.

Compute

Computes the RLC parameters. After completion of the parameters computation, results are displayed in the Computed Parameters section.

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 are vectors of five values containing the following RLC sequence parameters: the positive-sequence and zero-sequence of circuit 1, the mutual zero-sequence between circuit 1 and circuit 2, and the positive-sequence and zero-sequence of circuit 2.

Computes the frequency dependent parameters. After completion of the parameters computation, results are displayed in the Computed Parameters section.

Computed Parameters

Select a Distributed Parameters Line block (either to set the matrices or sequence RLC parameters), a Pi Section Line block, or a Three-Phase PI Section Line block in your model, then click the button to confirm the block selection. The name of the selected block appears in the left window.

Downloads RLC matrices into the selected block. This button is not visible when the selected block is a Distributed Parameters Line (Frequency-Dependent) block.

Downloads RLC sequence parameters into the selected block. This button is not visible when the selected block is a Distributed Parameters Line (Frequency-Dependent) block.

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.

Downloads the frequency-dependent parameters into the selected block. This button is not visible when the block is not a Distributed Parameters Line (Frequency-Dependent) block.

## Version History

Introduced in R2020b