2c:null 2d:["$","title",null,{"children":"Cascading line failures caused by renewable fluctiations | Fons van der Plas (old) | Observable"}] 32:T44f,loader = html`

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`33:T415,{ let svgWidth = Math.min(width, 400) let svg = d3.select(DOM.svg(svgWidth,40)) let n = 300 let rampwidth = Math.min(width, 300) let rampoffset = (svgWidth - rampwidth)/2 let rampheight = 20 svg.append("g") .attr("class", "ramp") svg.append("g") .attr("class", "labels") svg.select("g.ramp") .selectAll('line') .data([...Array(n).keys()]) .enter() .append('rect') .attr('x', (d) => rampoffset + d*(rampwidth/n)) .attr('y', (d) => 40-rampheight) .attr('width', (d) => 1.5*rampwidth/n) .attr('height', (d) => rampheight) .attr('fill', (d) => colorscale(1.0-d/n)) let numLabels = 5 svg.select("g.labels") .selectAll('line') .data([...Array(numLabels).keys()]) .enter() .append('text') .text((d) => (Math.round(100*d/(numLabels-1))) + "%") .attr('x', (d) => rampoffset + d*(rampwidth/(numLabels-1))) .attr('y', (d) => 40-rampheight-10) .attr("font-family", "monospace") .style("text-anchor", "middle") return svg.node() }34:T5ed,svgB = { let svg = d3.select(DOM.svg(width,height)); let path = d3.geoPath(projection) svg.append('rect') .attr('fill', '#f0f5ff') .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(coords) .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(linedata) .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 * zoomratio) .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 }35:T603,drawB = { svgB.select("g.buses") .selectAll('circle') .data(currentInjectionNormalised) .transition() .duration(500) .attr('r',(d) => Math.sqrt(Math.abs(d / 10)) * zoomratio) .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 = true || phase >= 2 let linesPossibleTransitioned = phase === 0 || cascadeTime === 1 ? lines : lines.transition().duration(200) linesPossibleTransitioned .attr("stroke-dasharray", (d) => ((d < -0.1 ) && showFailures) ? [1,3] : 0) .transition() .duration(800) .attr('stroke', (d) => colorscale(1.0-.8*d)) svgB.select("g.extra") .select("circle") .attr("cx", projection(linePosition)[0]) .attr("cy", projection(linePosition)[1]) .attr("r", phase === 0 ? 0 : 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() return "👍" }36:[] 30:{"id":"64919305ed256c86","slug":"cascading-line-failures-caused-by-renewable-fluctiations","title":"Cascading line failures caused by renewable fluctiations","thumbnail":"6ce749432eb5a98736c8ac399fc1f2f959c7702e35207c90f3b6b034acb2cee4","access_level":"public","create_time":"$D2019-06-30T15:27:57.054Z","update_time":"$D2022-05-25T22:41:28.912Z","view_time":null,"first_public_time":"$D2019-06-30T16:59:33.844Z","fork":{"id":"f64f45b9a8c737c6","slug":"cascading-line-failures-by-renewables","title":"Line failures caused by renewable fluctuations","owner":{"id":"b69f7fc06db3bdd0","login":"olivier_plas","name":"Fons van der Plas (old)"}},"stars":4,"starred":false,"owner":{"type":"team","id":"b69f7fc06db3bdd0","login":"olivier_plas","name":"Fons van der Plas (old)","avatar_url":"https://avatars-next.observableusercontent.com/fc10801f5fbe921128a3cc392873b717ae3d0139b87114acc4230f7303ff142e","tier":"starter_2024"},"version":1796,"publish_version":1796,"role":null,"authored":false,"authors":[{"type":"individual","id":"6aca374b28a4bb6d","login":"olivier_plas_123456","name":"","avatar_url":null,"tier":null}],"members":[{"type":"individual","id":"b6cde2fab5c6f5fa","login":"fonsp","name":"Fons van der Plas","avatar_url":"https://avatars-next.observableusercontent.com/edacdd0fa6b6c876851449177905d972d41fe02bd327094b210ded28d855f3c8","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Cascading line failures caused by renewable fluctiations","cells":[{"id":0,"value":"md`# Cascading line failures caused by renewable fluctiations\n_Interactive Figure_ for my [Bachelor thesis](https://github.com/fons-/grid-analysis), based on [Nesti et al. (2018)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.258301).`\n/*\n### Click anywhere on the map to simulate a 3 GW power injection.\n\nA matching 3 GW load is connected to the previously selected bus. Line current is simulated using the Linear Power Flow (LPF) algorithm, and shown as percentage of line capacity.\n\nLine thickness repesents line capacity; line color represents line saturation.`*/","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":475,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1687,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":656,"value":"{\n thesis.x;\n return md`First, choose the propagation phase:\n\nIn the **_'Nominal'_** phase, the average injection at 1 Jan 2011, 11:00 is shown, before the assumed failure.\n\nIn the **_'Most likely injection'_** phase, we select a line, and assume that it overloaded because of a grid-wide *fluctuation in renewable generation*. The most likely fluctuation that caused this overload is shown, and line currents are updated.\n\nIn the **_'Cascade'_** phase, overloaded lines are removed from the network, causing a _redistributed flow_. Some new lines might now become overloaded, and the process is repeated until the network is stable.`\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":649,"value":"{\n thesis.x;\n return md`Next, choose a line number. _The selected line will be indicated with a black circle._` \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":399,"value":"viewof phaseStr = {\n thesis;\n let r = radio({\n title: 'Phase',\n description: \"\",\n options: [\n { label: 'Nominal', value: 0 },\n { label: 'Most likely injection', value: 1 },\n { label: 'Cascade', value: 2 },\n ],\n value: 0\n })\n return r\n /*return number({\n min: 0 * thesis.x.length, \n max: 2, \n value: 0, \n title: \"Phase\", \n description: \"\"\n })*/\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1656,"value":"lineForm={\n if(phase >= 0){\n return html`

Line

\n\n${viewof firstFailure.bind(html``)} ${viewof firstFailure.bind(html` `)}`\n } else {\n return html``\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1382,"value":"cascadeForm={\n if(phase < 2){\n let disp = html``\n disp.value = -1\n return disp\n } else {\n if(cascade){\n // return html``\n return html`

Cascade phase

\n\n${viewof cascadeTime.bind(html``)} ${viewof cascadeTime.bind(html` `)}`\n } else {\n let disp = html`Cascades could not be computed 😢`\n disp.value = -1\n return disp\n }\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1634,"value":"{\n const form = html``;\n let cascadeInputs = cascadeForm.getElementsByTagName(\"input\")\n form.dec.addEventListener(\"click\", () => {\n cascadeInputs[0].stepDown();\n cascadeInputs[1].stepDown();\n cascadeInputs[0].dispatchEvent(new CustomEvent(\"input\"));\n })\n form.inc.addEventListener(\"click\", () => {\n cascadeInputs[0].stepUp();\n cascadeInputs[1].stepUp();\n cascadeInputs[0].dispatchEvent(new CustomEvent(\"input\"));\n })\n if(phase === 2){\n return form;\n } else {\n return html``\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":411,"value":"svgB.node()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":667,"value":"md`Remaining lines: **${thesis.bus0.length - failedLines.length}/${thesis.bus0.length}**`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":717,"value":"md`Overload probability: ${manyzeroes(thesis.Poverload[firstFailure]*100)}%`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1704,"value":"mostProbableFailures = [...Array(thesis.threshold.length).keys()].sort((i,j) => thesis.Poverload[j] - thesis.Poverload[i])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1766,"value":"md`Line saturation:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1733,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":686,"value":"md`---\n_Plotting:_`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":194,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":413,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":9,"value":"projection = d3.geoAlbers()\n .center([0.6, 51.0])\n .parallels([50.0, 15.0])\n .translate([width / 2, height / 2])\n .rotate([-10.0, 0.0])\n .scale(3400 * zoomratio)\n .precision(.1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":14,"value":"colorscale = d3.interpolateInferno","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":10,"value":"//width = 400","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1593,"value":"zoomratio = Math.min(1.2, width/400)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":12,"value":"height = 500 * zoomratio","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":503,"value":"linePosition = [(thesis.x[thesis.bus0[firstFailure]] + thesis.x[thesis.bus1[firstFailure]]) / 2, \n (thesis.y[thesis.bus0[firstFailure]] + thesis.y[thesis.bus1[firstFailure]]) / 2]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":566,"value":"lineEndpointsOnScreen = ({\n p0: projection([thesis.x[thesis.bus0[firstFailure]], thesis.y[thesis.bus0[firstFailure]]]),\n p1: projection([thesis.x[thesis.bus1[firstFailure]], thesis.y[thesis.bus1[firstFailure]]])\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":508,"value":"lineLengthOnScreen = {\n let dx = lineEndpointsOnScreen.p0[0] - lineEndpointsOnScreen.p1[0]\n let dy = lineEndpointsOnScreen.p0[1] - lineEndpointsOnScreen.p1[1]\n \n return Math.sqrt(dx*dx + dy*dy)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":724,"value":"manyzeroes = function(x){\n if(x == 0.0){\n return \"0.0\"\n }\n if(x >= 1.0)\n {\n return x.toPrecision(3)\n }\n let exponent = Math.floor(Math.log10(x))+1\n let withoutzeroes = (x/Math.pow(10, exponent)).toPrecision(3)\n return withoutzeroes.slice(0,2) + \"0\".repeat(-exponent) + withoutzeroes.slice(2)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1581,"value":"md`---\n_Advancing cascade:_`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":272,"value":"viewof firstFailure = new View(251)/*slider({\n min: 0, \n max: thesis.x.length, \n value: 251, \n step: 1,\n title: \"Line\", \n description: \"\"\n})*/","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1495,"value":"viewof cascadeTime = {\n firstFailure;\n return new View(1)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":629,"value":"phase = Number(phaseStr)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":332,"value":"currentInjection = mathjs.squeeze((phase === 0) ? muP : mostLikelyInjectionGivenFailure(firstFailure))._data","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1787,"value":"currentInjectionNormalised = {\n let avg = currentInjection.reduce((x,y) => x+y) / currentInjection.length\n return currentInjection.map(x => x-avg)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":422,"value":"currentSaturation = {\n if((phase < 2) || !Boolean(cascade)){\n if(phase === 1){\n return flowcustom(currentInjection).map(el => Math.abs(el))\n }\n return muFnormabs\n } else {\n return Array.prototype.map.call(cascade[cascadeTime-1], c => (c.charCodeAt() - 48)/64)\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":851,"value":"failedLines = {\n if((phase === 0) || !Boolean(cascade)){\n return []\n }\n var str = cascade[cascadeTime-1]\n var indices = []\n for(var i=0; i= 0.0 ? 1.0 : -1.0\n }\n \n let diff = mathjs.dotMultiply((signMod(thesis.mu_f_norm[l]) - thesis.mu_f_norm[l]) / thesis.sigma_f_norm[l][l], mathjs.multiply(sigmaP, mathjs.dotDivide(thesis.F[l], thesis.threshold[l])))\n return mathjs.add(muP, diff)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1726,"value":"md`_Cascade phases are precomputed for each line. This requires solving a linear least squares problem, which is (computationally) difficult in JS._`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1373,"value":"cascade = thesisCascades[firstFailure]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1669,"value":"flowcustom = function(power_injection){\n /*return thesis.F.map((row, i) => \n Math.abs(row.map((el,j) => el*power_injection[j]).reduce((a,b) => a+b)) / thesis.threshold[i])*/\n return matrixvectormult(thesis.F, power_injection).map((el, i) => el / thesis.threshold[i])\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1672,"value":"matrixvectormult = function(mat, vec){\n return mat.map((row, i) => \n row.map((el,j) => el*vec[j]).reduce((a,b) => a+b))\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":16,"value":"md`----------\n_Loading dataset:_`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":210,"value":"thesis = d3.json(\"https://fonsp.com/flowandcorrelations_approx.json\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1354,"value":"thesisCascades = d3.json(\"https://fonsp.com/simulated_cascades_corrected_interactive.json\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":30,"value":"md`---------\n_Pre-processing:_`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":262,"value":"coords = thesis.x.map((xel, i) => {\n let yel = thesis.y[i]\n let pxy = projection([xel, yel])\n return {x: pxy[0], y: pxy[1]}\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":268,"value":"linedata = thesis.threshold.map((t, i) => {\n return {\n 'x1': coords[thesis.bus0[i]].x, \n 'y1': coords[thesis.bus0[i]].y, \n 'x2': coords[thesis.bus1[i]].x, \n 'y2': coords[thesis.bus1[i]].y, \n 'threshold': thesis.threshold[i]/1000\n }})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":290,"value":"sigmaP = mathjs.matrix(thesis.sigma_p)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":293,"value":"muP = mathjs.matrix(thesis.mu_p)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1393,"value":"muFnormabs = thesis.mu_f_norm.map(sat => Math.abs(sat))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":46,"value":"md`---------\n_Topography:_`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":48,"value":"land = topojson.feature(world, world.objects.land)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":50,"value":"countries = topojson.mesh(world, world.objects.countries, (a, b) => a !== b)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":52,"value":"md`----------\n_Imports:_`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":54,"value":"mathjs = require(\"https://cdnjs.cloudflare.com/ajax/libs/mathjs/5.9.0/math.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":56,"value":"d3 = require('d3@5')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":58,"value":"d3proj = require(\"d3-geo@1\", \"d3-geo-polygon@1\", \"d3-geo-projection@2\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":60,"value":"world = fetch(\"https://unpkg.com/world-atlas@1/world/50m.json\").then(response => response.json())","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":62,"value":"topojson = require(\"topojson-client@3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":401,"value":"import {radio, slider, select, number, button} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1723,"value":"import {allowedSlider} from \"@olivier_plas/prime-numbers-slider\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1497,"value":"import {View} from \"@mbostock/synchronized-views\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1735,"value":"import {ramp} from \"@d3/working-with-color\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W36","stdlib":"1","titling":"auto"}} 31:"$30:body"