Lightning protection of underground cables

This example models a single-phase underground cable fed by an overhead line. Scout arresters, placed on poles on either side of the riser pole, are optional. These have the same discharge voltage as the riser-pole arrester.

The plot shows the cable voltages at the riser pole, 75% down the cable, and at the cable open point.

         #: name=inputtemplate
* adapted from openetran/Test/scout.dat
time 2 0.01e-6 14.0e-6

* overhead line geometry
span 1
conductor 1 10.0  0.0 0.00715 -11097.0
conductor 2  8.0  0.0 0.00715      0.0

* single-phase underground attached to upper phase
span 2
cable 1 30.0 1.5e8 -11097.0
end
end

* overhead line spans
line 1 2 1 SPAN 1 0
line 2 3 1 SPAN 0 0
line 3 4 1 SPAN 0 0
line 4 5 1 SPAN 0 1
* underground spans
line 3 6 2 CABLELEN1 0 0
line 6 7 2 CABLELEN2 0 0
end

labelphase 0 G
labelphase 1 A
labelphase 2 B
labelphase 3 C
labelphase 4 N

labelpole 3 riser
labelpole 6 xfmr
labelpole 7 opntie

* riser pole and scout arresters
arrester 0.0e3 RISERVOLTAGE 0.28 0.4e-6 LEADLEN
pairs 1 0
poles RISERLOCATIONS

* open-tie arresters
arrbez 0.0e3 ELBOWVOLTAGE 0.0 0.0 0.0 0
pairs 1 0
poles 7

surge -10.0e3 1.0e-6 50.0e-6 0.0e-6
pairs 1 0
poles SURGEPOLE

meter
pairs 1 0
poles 3 6 7

```yaml #: jquery=dform class : form html: - name: LEADLEN type: number step: 1.0 bs3caption : "Lead length at the riser pole, ft" value: 3.0 css: width: 13em - name: arresteratopen type: checkbox bs3caption: Use an open-point arrester - name: scouts type: checkbox bs3caption: Use scout arresters - name: RISERVOLTAGE type: number step: 5.0 bs3caption : "Riser-pole arrester discharge voltage, kV" value: 40.0 css: width: 13em - name: ELBOWVOLTAGE type: number step: 5.0 bs3caption : "Open-point arrester discharge voltage" value: 50.0 css: width: 13em - name: CABLELEN type: number step: 50.0 bs3caption : "Cable length, ft" value: 800.0 css: width: 13em - name: SPAN type: number step: 50.0 bs3caption : "Distance between poles, ft" value: 200.0 css: width: 13em ```

```js if (!arresteratopen) ELBOWVOLTAGE = 10000.0 if (scouts) {RISERLOCATIONS = "2 3 4"} else {RISERLOCATIONS = "3"} inputdata = inputtemplate.replace("RISERVOLTAGE", 1000.0 * RISERVOLTAGE) SURGEPOLE = 1 inputdata = inputdata.replace("SURGEPOLE", SURGEPOLE) inputdata = inputdata.replace("LEADLEN", LEADLEN) inputdata = inputdata.replace("ELBOWVOLTAGE", 1000.0 * ELBOWVOLTAGE) inputdata = inputdata.replace("CABLELEN1", 0.75 * 1/3.28 * CABLELEN) inputdata = inputdata.replace("CABLELEN2", 0.25 * 1/3.28 * CABLELEN) inputdata = inputdata.replace(/SPAN/g, 1/3.28 * SPAN) inputdata = inputdata.replace("RISERLOCATIONS", RISERLOCATIONS) inputdata = inputdata.replace("SURGEPOLE", SURGEPOLE) Module.FS_createDataFile("/", "file.dat", inputdata, true, true) Module["arguments"] = ["-plot", "csv", "file"] Module['calledRun'] = false; shouldRunNow = true; Module.run(); out = intArrayToString(FS.findObject("/file.out").contents); csv = intArrayToString(FS.findObject("/file.csv").contents); FS.unlink("/file.dat"); // delete the input file FS.unlink("/file.out"); // delete the output files FS.unlink("/file.csv"); ```

Results

```js x = $.csv.toArrays(csv, {onParseValue: $.csv.hooks.castToScalar}) // `header` has the column names. The first is the time, and the rest // of the columns are the variables. header = x.slice(0,1)[0] // Select graph variables with a select box based on the header values if (typeof(graphvar) == "undefined") graphvar = header[1]; ``` Cable voltages, kV ```js yidx = header.indexOf(graphvar); xidx = 0; // pick out the column to plot series = [{label: "Riser", data: x.slice(1).map(function(x) {return [x[0]*1e6, x[1]/1e3];})}, {label: "75% to end", data: x.slice(1).map(function(x) {return [x[0]*1e6, x[2]/1e3];})}, {label: "End", data: x.slice(1).map(function(x) {return [x[0]*1e6, x[3]/1e3];})}]; plot(series, {legend: {noColumns: 3, container: $("#legend")}}); ```

Time, μsec

Discussions

This app uses EPRI OpenETran to simulate the transients on the underground cable system.

Note that this app simplifies some aspects, particularly:

Ground-potential effects are not included.
Attenuation on the cables is not included.
Effects of flashovers on the overhead line are not included.
The ac voltage effect is included, but it is hard-coded into the model.
The lightning current injection is hard coded at -10 kA with a 1-usec risetime.
The arresters use a simplified, piecewise-linear model.

Also, this app does not consider cable BIL nor does it calculate protective margins.

Background

Emscripten was used to compile OpenETran’s code to JavaScript. The user interface was created in mdpad. See here for the code with the user interface and OpenETran model input. OpenETran and the GNU GSL library (an OpenETran dependency) are distributed under the GNU GPL version 3.0 license. The source codes are available as follows: OpenETran and GNU GSL.

Electric Power Distribution Handbook, T. A. Short