2e:null 2f:["$","title",null,{"children":"Line failures caused by renewable fluctiations | Fons van der Plas (old) | Observable"}] 34:T44f,loader = html`

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`35:T5e0,svgB = { let svg = d3.select(DOM.svg(width,height)); let path = d3.geoPath(projection) svg.append('rect') .attr('fill', '#eee') .attr('width', width) .attr('height', height) svg.append("path") .attr("d", path(land)) .attr("stroke", "black") .attr("stroke-width", 1) .attr("fill", "#fff") svg.append("path") .attr("d", path(countries)) .attr("stroke", "black") .attr("stroke-width", .5) .attr("fill", "none") svg.append("g") .attr("class", "buses") svg.append("g") .attr("class", "lines") svg.append("g") .attr("class", "extra") svg.select("g.buses") .selectAll('circle') .data(coordsB) .enter() .append('circle') .attr('cx',(d) => d.x) .attr('cy',(d) => d.y) .attr('r',(d) => 0) .attr('fill',(d) => d.c) /*.on("click", (d, i) => { d3.select(this).attr('cy',50); d3.event.stopPropagation(); })*/ svg.select("g.lines") .selectAll('line') .data(linedataB) .enter() .append('line') .attr('x1', (d) => d.x1) .attr('y1', (d) => d.y1) .attr('x2', (d) => d.x2) .attr('y2', (d) => d.y2) .attr('stroke-width', (d) => d.threshold) .attr('stroke', (d) => "white") svg.select("g.extra") .append("circle") .attr("stroke", "black") .attr("stroke-width", 3) .attr("fill", "none") svg.select("g.extra") .append("line") .attr("stroke", "pink") .attr("stroke-width", 20) return svg }36:T53b,drawB = { svgB.select("g.buses") .selectAll('circle') .data(currentInjection) .transition() .duration(500) .attr('r',(d) => Math.sqrt(Math.abs(d / 10))) .attr('fill',(d) => d > 0 ? "#6fd08c" : "#7b9ea8") let lines = svgB.select("g.lines").selectAll('line') .data(currentSaturation) /*let pulse = function(d, i){ d3.select(this) .transition() .duration(500) .attr("stroke-width", thesis.threshold[i]/1000) .transition() .duration(500) .attr("stroke-width", 100*thesis.threshold[i]/1000) }*/ /*if(phase === 0){ lines .filter((d,i) => i === firstFailure) .attr('stroke-width', (d) => 1000) }*/ let showFailures = phase % 2 === 0 lines .transition() .duration(500) .attr('stroke', (d) => colorscale(1.0-d)) .attr("stroke-dasharray", (d) => (d >= 1.0 && showFailures) ? [1,3] : 0) svgB.select("g.extra") .select("circle") .attr("cx", projection(linePosition)[0]) .attr("cy", projection(linePosition)[1]) .attr("r", lineLengthOnScreen/2) /*svgB.select("g.extra") .select("line") .attr('x1', lineEndpointsOnScreen.p0[0]) .attr('y1', lineEndpointsOnScreen.p0[1]) .attr('x2', lineEndpointsOnScreen.p1[0]) .attr('y2', lineEndpointsOnScreen.p1[1])*/ loader.remove() }37:T8c0,"old plot, uncomment to view" /*display = { let svg = d3.select(DOM.svg(width,height)); let from = 0; let to = 2; svg.on("click", function (d,i) { let m = d3.mouse(this) let mousex = m[0] let mousey = m[1] let s = n => n*n; let dist = (coord, mx, my) => s(coord.x-mx)+s(coord.y-my); let best = coordsA.map((e,i) => [dist(e,mousex,mousey),i]).reduce((a,b) => a[0] <= b[0] ? a : b)[1]; update(best) }) let path = d3.geoPath(projection) svg.append('rect') .attr('fill', '#eee') .attr('width', width) .attr('height', height) svg.append("path") .attr("d", path(land)) .attr("stroke", "black") .attr("stroke-width", 1) .attr("fill", "#fff") svg.append("path") .attr("d", path(countries)) .attr("stroke", "black") .attr("stroke-width", .5) .attr("fill", "none") svg.selectAll('circle') .data(coordsA) .enter() .append('circle') .attr('cx',(d) => d.x) .attr('cy',(d) => d.y) svg.selectAll('line') .data(linedataA) .enter() .append('line') .attr('x1', (d) => d.x1) .attr('y1', (d) => d.y1) .attr('x2', (d) => d.x2) .attr('y2', (d) => d.y2) .attr('stroke-width', (d) => d.cap) .attr('stroke', (d) => "white") let update = (next) => { coordsA[from].r = 0 coordsA[from].c = "#44dd44" coordsA[to].r = 10 coordsA[to].c = "#dddd33" coordsA[next].r = 10 coordsA[next].c = "#44dd44" from = to to = next let p_inj = mathjs.zeros(thesis.x.length,1) p_inj.subset(mathjs.index(from,0), 3000.0) p_inj.subset(mathjs.index(to,0), -3000.0) let line_flow = flowcustom(mathjs.squeeze(p_inj)._data) //let line_flow = flow(p_inj) linedataA.forEach((line, i) => { line.current = line_flow[i] }) let circles = svg.selectAll('circle') .data(coordsA) .transition() .duration(500) .attr('r',(d) => d.r) .attr('fill',(d) => d.c) svg.selectAll('line') .data(linedataA) .transition() .duration(500) .attr('stroke', (d) => colorscale(1.0-d.current)) }; coordsA.forEach(c => {c.r = 0}) update(0) return svg.node(); }*/38:[] 32:{"id":"f64f45b9a8c737c6","slug":"cascading-line-failures-by-renewables","title":"Line failures caused by renewable fluctiations","thumbnail":"9ee851e802f2f982ba51c7a981089fae93beef3e2b4f1f43d9e5e0037a572166","access_level":"public","create_time":"$D2019-06-25T18:04:14.848Z","update_time":"$D2019-06-30T20:53:34.762Z","view_time":null,"first_public_time":"$D2019-06-25T23:17:54.663Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"b69f7fc06db3bdd0","login":"olivier_plas","name":"Fons van der Plas (old)","avatar_url":"https://avatars-next.observableusercontent.com/fc10801f5fbe921128a3cc392873b717ae3d0139b87114acc4230f7303ff142e","tier":"starter_2024"},"version":761,"publish_version":761,"role":null,"authored":false,"authors":[{"type":"individual","id":"6aca374b28a4bb6d","login":"olivier_plas_123456","name":"","avatar_url":null,"tier":null}],"members":[{"type":"individual","id":"b6cde2fab5c6f5fa","login":"fonsp","name":"Fons van der Plas","avatar_url":"https://avatars-next.observableusercontent.com/edacdd0fa6b6c876851449177905d972d41fe02bd327094b210ded28d855f3c8","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Line failures caused by renewable fluctiations","cells":[{"id":0,"value":"md`# Line failures caused by renewable fluctiations\n_Interactive Figure_ for my [Bachelor thesis](https://github.com/fons-/grid-analysis), based on [Nesti et al. (2018)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.258301).`\n/*\n### Click anywhere on the map to simulate a 3 GW power injection.\n\nA matching 3 GW load is connected to the previously selected bus. Line current is simulated using the Linear Power Flow (LPF) algorithm, and shown as percentage of line capacity.\n\nLine thickness repesents line capacity; line color represents line saturation.`*/","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":475,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":649,"value":"{\n thesis.x;\n return md`---\nFirst, choose a line number. _The selected line will be indicated with a black circle._` \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":656,"value":"{\n thesis.x;\n return md`Next, choose the propagation phase:\n\nIn the **_'Nominal'_** phase, the average injection at 1 Jan 2011, 11:00 is shown, before the assumed failure.\n\nIn the **_'Most likely injection'_** phase, we will assume that the selected line overloaded because of a grid-wide **fluctuation in renewable generation**. The most likely fluctuation that caused this overload is shown, and line currents are updated.\n\nIn the **_'Joint failures'_** phase, we remove all lines that are overloaded in the most likely injection scenario. In general, failure of the chosen line is likely to occur jointly with many more lines.\n\n---`\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":272,"value":"viewof firstFailure = slider({\n min: 0, \n max: thesis.x.length, \n value: 251, \n step: 1,\n title: \"Line\", \n description: \"\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":399,"value":"viewof phaseStr = {\n thesis;\n let r = radio({\n title: 'Phase',\n description: \"\",\n options: [\n { label: 'Nominal', value: 0 },\n { label: 'Most likely injection', value: 1 },\n { label: 'Joint failures', value: 2 },\n ],\n value: 0\n })\n return r\n /*return number({\n min: 0 * thesis.x.length, \n max: 2, \n value: 0, \n title: \"Phase\", \n description: \"\"\n })*/\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":704,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":411,"value":"svgB.node()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":667,"value":"md`Remaining lines: **${currentSaturation.filter(s => s < 1.0).length}/${thesis.bus0.length}**`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":717,"value":"md`Overload probability: ${manyzeroes(thesis.Poverload[firstFailure]*100)}%`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":712,"value":"md`note: _Cascading failures have not yet been implemented!_`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":686,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":194,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":413,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"projection = d3.geoAlbers()\n .center([0.6, 51.0])\n .parallels([50.0, 15.0])\n .translate([width / 2, height / 2])\n .rotate([-10.0, 0.0])\n .scale(3400)\n .precision(.1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"colorscale = d3.interpolateInferno","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"width = 400","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"height = 500","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":503,"value":"linePosition = [(thesis.x[thesis.bus0[firstFailure]] + thesis.x[thesis.bus1[firstFailure]]) / 2, \n (thesis.y[thesis.bus0[firstFailure]] + thesis.y[thesis.bus1[firstFailure]]) / 2]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":566,"value":"lineEndpointsOnScreen = ({\n p0: projection([thesis.x[thesis.bus0[firstFailure]], thesis.y[thesis.bus0[firstFailure]]]),\n p1: projection([thesis.x[thesis.bus1[firstFailure]], thesis.y[thesis.bus1[firstFailure]]])\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":508,"value":"lineLengthOnScreen = {\n let dx = lineEndpointsOnScreen.p0[0] - lineEndpointsOnScreen.p1[0]\n let dy = lineEndpointsOnScreen.p0[1] - lineEndpointsOnScreen.p1[1]\n \n return Math.sqrt(dx*dx + dy*dy)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":694,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":629,"value":"phase = Number(phaseStr)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":332,"value":"currentInjection = mathjs.squeeze((phase === 0) ? muP : mostLikelyInjectionGivenFailure(firstFailure))._data","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":422,"value":"currentSaturation = flowcustom(currentInjection)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"md`----------\n_SciGRID dataset:_`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":210,"value":"thesis = d3.json(\"https://fonsp.com/flowandcorrelations_approx.json\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"md`---------\n_Pre-processing:_`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":262,"value":"coordsB = thesis.x.map((xel, i) => {\n let yel = thesis.y[i]\n let pxy = projection([xel, yel])\n return {x: pxy[0], y: pxy[1]}\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":268,"value":"linedataB = thesis.threshold.map((t, i) => {\n return {\n 'x1': coordsB[thesis.bus0[i]].x, \n 'y1': coordsB[thesis.bus0[i]].y, \n 'x2': coordsB[thesis.bus1[i]].x, \n 'y2': coordsB[thesis.bus1[i]].y, \n 'threshold': thesis.threshold[i]/1000\n }})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":36,"value":"Fmatrix = mathjs.matrix(thesis.F)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":290,"value":"sigmaP = mathjs.matrix(thesis.sigma_p)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":293,"value":"muP = mathjs.matrix(thesis.mu_p)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":38,"value":"md`----------\n_LPF:_`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":40,"value":"flow = function(power_injection) {\n let unnormalised = mathjs.squeeze(mathjs.multiply(Fmatrix, mathjs.squeeze(power_injection)))\n return mathjs.abs(mathjs.dotDivide(unnormalised, thesis.threshold))._data\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":42,"value":"md`This is faster than \\`Mathjs.multiply\\`:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"flowcustom = function(power_injection){\n return thesis.F.map((row, i) => \n Math.abs(row.map((el,j) => el*power_injection[j]).reduce((a,b) => a+b)) / thesis.threshold[i])\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":359,"value":"mostLikelyInjectionGivenFailure = function(l){\n let signMod = function(x){\n return x >= 0.0 ? 1.0 : -1.0\n }\n \n let diff = mathjs.dotMultiply((signMod(thesis.mu_f_norm[l]) - thesis.mu_f_norm[l]) / thesis.sigma_f_norm[l][l], mathjs.multiply(sigmaP, mathjs.dotDivide(thesis.F[l], thesis.threshold[l])))\n return mathjs.add(muP, diff)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":46,"value":"md`---------\n_Topography:_`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"land = topojson.feature(world, world.objects.land)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":50,"value":"countries = topojson.mesh(world, world.objects.countries, (a, b) => a !== b)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":52,"value":"md`----------\n_Imports:_`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"mathjs = require(\"https://cdnjs.cloudflare.com/ajax/libs/mathjs/5.9.0/math.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":56,"value":"d3 = require('d3@5')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":58,"value":"d3proj = require(\"d3-geo@1\", \"d3-geo-polygon@1\", \"d3-geo-projection@2\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"world = fetch(\"https://unpkg.com/world-atlas/world/50m.json\").then(response => response.json())","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":62,"value":"topojson = require(\"topojson-client@3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":401,"value":"import {radio, slider, select, number} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":724,"value":"manyzeroes = function(x){\n if(x == 0.0){\n return \"0.0\"\n }\n if(x >= 1.0)\n {\n return x.toPrecision(3)\n }\n let exponent = Math.floor(Math.log10(x))+1\n let withoutzeroes = (x/Math.pow(10, exponent)).toPrecision(3)\n return withoutzeroes.slice(0,2) + \"0\".repeat(-exponent) + withoutzeroes.slice(2)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"\"old...\"\n/*coordsA = thesis.x.map((xel, i) => {\n let yel = thesis.y[i]\n let pxy = projection([xel, yel])\n return {x: pxy[0], y: pxy[1], r: 0, c: \"#ffff44\"}\n})*/","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":34,"value":"\"old...\"\n/*linedataA = thesis.threshold.map((t, i) => {\n return {\n 'x1': coordsA[thesis.bus0[i]].x, \n 'y1': coordsA[thesis.bus0[i]].y, \n 'x2': coordsA[thesis.bus1[i]].x, \n 'y2': coordsA[thesis.bus1[i]].y, \n 'cap': thesis.threshold[i]/1000, \n 'current': 0\n }})*/","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W38","stdlib":"1","titling":"auto"}} 33:"$32:body"