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

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.

powergui Block Parameters dialog box: On the

**Tools**tab, click**Power Line Parameters**.MATLAB

^{®}command prompt: Enter`powerLineParameters`

`Comments`

— Custom commentsno default

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.

`Load > Typical parameters`

— Load typical parametersno default

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. |

`Load > User parameters`

— Load user parametersno default

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

file.

`Save`

— Save line datano default

Saves your line data by generating a `.mat`

file that contains the
GUI information and the line data.

`Report`

— Create reportno default

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

`Units`

— Conductor diameter, GMR, and bundle diameter units`english`

(default) | `metric`

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.

`Ground Resistivity`

— 100 (default) | positive scalar

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

`Nominal Frequency`

— Frequency to evaluate RLC parameters60 (default) | positive scalar

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

`Phase conductors (bundles)`

— Number of phase conductors (bundles)3 (default) | positive scalar

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

`Ground conductors (bundles)`

— Number of ground wires (bundles)2 (default) | nonnegative scalar

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

`Label`

— Conductor or bundle identifiersno default

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

`Phase, Phase Number`

— Phase numberno default

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.

`X`

— Horizontal position of conductorpositive scalar

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.

`Y tower`

— Vertical position of conductor at towerpositive scalar

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

`Y min`

— Vertical position of the conductor at mid-spanpositive scalar

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:

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

Y_{tower} = height of conductor at tower |

Y_{min} = height of conductor at mid span |

sag = Y_{tower}−Y_{min} |

Instead of specifying two different values for Y_{tower} and
Y_{min}, you may specify the same Y_{average}
value.

`Conductor type`

— Conductor or bundle type numberspositive integer

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

`Conductor types`

— Number of conductor types positive integer

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.

`Internal conductor inductance evaluated from`

— Computation method for conductor internal inductance`T/D ratio`

(default) | `Geometric Mean Radius (GMR)`

| `Reactance Xa at 1-foot spacing`

| `Reactance Xa at 1-meter spacing`

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.

`Include conductor skin effect`

— Include impact of frequency on conductor AC resistance and inductanceon (default) | off

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.

`D out`

— Conductor outside diameterpositive scalar

Specify the conductor outside diameter, in centimeters or inches.

`T/D ratio`

— Conductor T/D ratioscalar between

`0`

and `0.5`

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`

.

`GMR`

— Geometric mean radiuspositive scalar

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**.

`Xa`

— Reactance Xa at 1-meter spacing or 1-foot spacingpositive scalar

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
X_{a} value at 60 Hz or 50 Hz is usually provided by conductor
manufacturers.

`DC res`

— Conductor DC resistancepositive scalar

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

`mu_r`

— Conductor relative permeabilitypositive scalar

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

`Nb_cond`

— Number of conductors per bundlepositive integer

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

`Db`

— Bundle diameterpositive scalar

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.

`Angle`

— Angle of conductor 1positive scalar

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 range logspace `

— Frequency range for parameter computation[-2,5,141] (default) | three-element vector

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`

.

`Line Length `

— Length of line100 (default) | positive scalar

Specify the length of the line, in km.

`RLC Line Parameters`

— Compute RLC line parametersno default

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.

`Frequency Dependent Model Parameters`

— Compute frequency dependent parametersno default

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

`Block`

— Selected blockno default

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.

`Send RLC matrices to block`

— Download RLC matrices to blockno default

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

`Send Sequences to block`

— Download RLC sequence parameters to blockno default

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.

`Send to workspace`

— Send matrices and component parameters to MATLAB workspaceno default

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 Frequency-Dependent Parameters to block`

— Download frequency-dependent parameters to blockbutton

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.

- Distributed Parameters Line | Distributed Parameters Line (Frequency-Dependent) | PI Section Line | Three-Phase PI Section Line