31:Td05,chart = { const cx = width / 2; const cy = height / 2; const tooltip = d3.select("body").append("div").call(createTooltip) const tipContent = d => { return `Azimuth: ${d.plane[0]}
Angle: ${d.plane[1]}
Radiation: ${d.rad}`; } const svg = d3.create("svg") .attr("viewBox", [0, 0, width, height]) .attr("font-family", "sans-serif") .attr("font-size", 10) .attr("text-anchor", "middle") .attr("fill", "currentColor") .style("margin", "0 -14px") .style("display", "block"); const defs = svg.append("g").append("defs") defs.append("clipPath") .attr("id", "horizonClip") .append("path") .attr("d", path(outline)); const insolation = svg.append("g"); svg.append("path") .attr("d", path(graticule)) .attr("fill", "none") .attr("stroke", "currentColor") .attr("stroke-opacity", 0.2) .attr("clip-path", "url(#horizonClip)"); svg.append("path") .attr("d", path(outline)) .attr("fill", "none") .attr("stroke", "currentColor"); svg.append("g") .call(xAxis); svg.append("g") .call(yAxis); function update(radmap) { insolation.selectAll("path") .data(radmap, d => d) .join( enter => enter.append("path") .attr("fill", d => color(d.rad)) .attr("d", d => path(d3.geoGraticule().extent(d.extent).outline())) .on("mouseover", function(d) { tooltip.style("display", null); d3.select(this) .attr("fill", "#333333"); tooltip.html(tipContent(d)) .style("left", (d3.event.pageX) + "px") .style("top", (d3.event.pageY - 28) + "px"); }) .on("mousemove", function(d) { tooltip .style("left", (d3.event.pageX) + "px") .style("top", (d3.event.pageY - 28) + "px"); }) .on("mouseout", function(d) { d3.select(this) .attr("fill", color(d.rad)); tooltip.style("display", "none"); }), update => update .attr("fill", d => color(d.rad)) .attr("d", d => path(d3.geoGraticule().extent(d.extent).outline())) .on("mouseover", function(d) { tooltip.style("display", null); d3.select(this) .attr("fill", "#333333"); tooltip.html(tipContent(d)) .style("left", (d3.event.pageX) + "px") .style("top", (d3.event.pageY - 28) + "px"); }) .on("mousemove", function(d) { tooltip .style("left", (d3.event.pageX) + "px") .style("top", (d3.event.pageY - 28) + "px"); }) .on("mouseout", function(d) { d3.select(this) .attr("fill", color(d.rad)); tooltip.style("display", "none"); }), exit => exit .remove()); } return Object.assign(svg.node(), {update}); }32:Td80,poa = function(solar, plane, dat) { //all angle inputs are in degrees az: solar azimuth, al: solar altitude, t: plane tilt, paz: plane azimuth. //all azimuth angles measures as degress from north (N = 0, E = 90, etc.) //dat: hourly weather file information const [az, al] = solar.position(dat.date); const [paz, t] = plane; const z = 90 - al > 90 ? 90 : 90 - al; const x = Math.cos(z * Math.PI / 180) * Math.cos(t * Math.PI / 180); const y = Math.sin(z * Math.PI / 180) * Math.sin(t * Math.PI / 180) * Math.cos((az - paz) * Math.PI / 180); const AOI = Math.acos(x + y); //calculate direct beam irradiance const beam = Math.cos(AOI) <= 0 ? 0 : dat.direct_normal_radiation * Math.cos(AOI); //modified perez 1990 coefficients const coeff = d => { let c = {f11: 0.677747, f12: -0.3272588, f13: -0.2504286, f21: 0.1561313, f22: -1.3765031, f23: 0.2506212}; if (d <= 1.065) { c = {f11: -0.0083117, f12: 0.5877285, f13: -0.0620636, f21: -0.0596012, f22: 0.0721249, f23: -0.0220216}; } else if (d > 1.065 && d <= 1.23) { c = {f11: 0.1299457, f12: 0.6825954, f13: -0.1513752, f21: -0.0189325, f22: 0.065965, f23: -0.0288748}; } else if (d > 1.23 && d <= 1.5) { c = {f11: 0.3296958, f12: 0.4868735, f13: -0.2210958, f21: 0.055414, f22: -0.0639588, f23: -0.0260542}; } else if (d > 1.5 && d <= 1.95) { c = {f11: 0.5682053, f12: 0.1874525, f13: -0.295129, f21: 0.1088631, f22: -0.1519229, f23: -0.0139754}; } else if (d > 1.95 && d <= 2.8) { c = {f11: 0.873028, f12: -0.3920403, f13: -0.3616149, f21: 0.2255647, f22: -0.4620442, f23: 0.0012448}; } else if (d > 2.8 && d <= 4.5) { c = {f11: 1.1326077, f12: -1.2367284, f13: -0.4118494, f21: 0.2877813, f22: -0.8230357, f23: 0.0558651}; } else if (d > 4.5 && d <= 6.2) { c = {f11: 1.0601591, f12: -1.5999137, f13: -0.3589221, f21: 0.2642124, f22: -1.127234, f23: 0.1310694}; } return c; } //calculate pereze diffuse: https://pvpmc.sandia.gov/modeling-steps/1-weather-design-inputs/plane-of-array-poa- irradiance/calculating-poa-irradiance/poa-sky-diffuse/perez-sky-diffuse-model/ const a = Math.max(0, Math.cos(AOI)); const b = Math.max(Math.cos(85 * Math.PI / 180), Math.cos(z * Math.PI / 180)); const DHI = dat.diffuse_horizontal_radiation; const AM = 1 / Math.cos(z * Math.PI / 180); //calculate extraterrestrial radiation const et = (doy) => { let g = 2 * Math.PI * (doy / 365); return 1367 * (1.00011 + 0.034221 * Math.cos(g) + 0.00128 * Math.sin(g) + 0.000719 * Math.cos(2 * g) + 0.000077 * Math.sin(2 * g)); } const delta = (DHI * AM) / et(dat.doy); const ep = ((DHI + dat.direct_normal_radiation) / DHI + (0.000005535 * Math.pow(z, 3))) / (1 + (0.000005535 * Math.pow(z, 3))); const f2 = coeff(ep).f21 + coeff(ep).f22 * delta + (z * Math.PI / 180) * coeff(ep).f13; const f1 = Math.max(0, (coeff(ep).f11 + coeff(ep).f12 * delta + (z * Math.PI / 180) * coeff(ep).f13)); const ed = DHI * ((1 - f1) * ((1 + Math.cos(t * Math.PI / 180)) / 2) + f1 * (a / b) + f2 * Math.sin(t * Math.PI / 180)); //calculate ground diffuse irradiance const ground = dat.albedo * (dat.direct_normal_radiation * Math.cos(z) + dat.diffuse_horizontal_radiation) * ((1 - Math.cos(t * Math.PI / 180)) / 2); // return al > 0 ? ed + beam + ground: 0; return al > 0 ? beam: 0; } 33:[{"id":"f4cfd2717165d8abe3bfac2dcaa1f155a2bf690c46543dba4d33144f94b8adc5a77267a1002f7c626ccdc8ac2d197940ea9a3088953296ab773d38ae7df0b5e2","href":"https://static.observableusercontent.com/files/f4cfd2717165d8abe3bfac2dcaa1f155a2bf690c46543dba4d33144f94b8adc5a77267a1002f7c626ccdc8ac2d197940ea9a3088953296ab773d38ae7df0b5e2","name":"sample_az_180_t_30.json","type":"application/json","lastModified":1575583825463.511,"size":294409}] 2f:{"title":"Clear Sky Calculations","cells":[{"id":0,"value":"md`# Clear Sky Calculations\nBased on calculations from [NREL PVWatts](https://www.nrel.gov/docs/fy14osti/62641.pdf) and [Sandia Labs](https://energy.sandia.gov/energy/renewable-energy/solar-energy/)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":53,"value":"viewof epw","pinned":false,"hidden":false,"mode":"ojs"},{"id":366,"value":"md`Calculate the angle of incidence between the sun's rays and the reference plane. The general formula is below where ${tex`\\theta_A`} and ${tex`\\theta_Z`} are the solar azimuth and zenith angles respectively. ${tex`\\theta_T`} and ${tex`\\theta_{A, plane}`} are the tilt and azimuth angles of the reference plane, respectively. Then calculate the direct beam irradiance ${tex`I_b`} in ${tex`W/m^2`} by adjusting the direct normal irradiance ${tex`DNI`} from the station weather file by the angle of incidence.\n\n${tex`AOI = \\cos^{-1}[\\cos(\\theta_Z)\\cos(\\theta_T) + \\sin(\\theta_Z)\\sin(\\theta_T)\\cos(\\theta_A - \\theta_{A, plane})]`}

\n${tex`I_b = DNI \\times \\cos(AOI)`}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":461,"value":"md`The Perez model describes the diffuse irradiance properties based on a set of empirical coefficients for each term. The basic formula to calculate diffuse irradiance ${tex`E_d`} is below, with ${tex`F_1`} and ${tex`F_2`} defining circumsolar and horizon brightness respectively.\n\n${tex`E_d = DHI \\times [(1 - F_1) \\times (\\frac{1 + \\cos(\\theta_T)}{2}) + F_1(\\frac{a}{b}) + F_2\\sin(\\theta_T)]`}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":530,"value":"$31","pinned":true,"hidden":false,"mode":"ojs"},{"id":570,"value":"radmap = {\n \n const step = 10;\n const azimuths = _.range(0, 361 - step, step);\n const altitudes = _.range(0, 91 - step, step);\n \n const coordinates = azimuths.map(az => altitudes.map(al => [az, al])).flat();\n let values = [];\n \n for (let [az, al] of coordinates) {\n const extent = [[az, al], [az + step, al + step]];\n const plane = [az + step / 2, al + step / 2];\n const rad = _.sum(epw.data.map(d => poa(solar, plane, d))) / 1000;\n \n values.push({extent: extent, plane: plane, rad: rad});\n yield values\n \n }\n\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":543,"value":"update = chart.update(radmap)","pinned":false,"hidden":false,"mode":"ojs"},{"id":522,"value":"height = width","pinned":false,"hidden":false,"mode":"ojs"},{"id":663,"value":"color = d3.scaleSequential([50, 1200], d3.interpolateRdPu)","pinned":true,"hidden":false,"mode":"ojs"},{"id":524,"value":"scale = (width - 120) * 0.5","pinned":true,"hidden":false,"mode":"ojs"},{"id":520,"value":"projection = d3.geoProjection((x, y) => d3.geoStereographicRaw(x, -y))\n .scale(scale)\n .clipExtent([[0, 0], [width, height]])\n .rotate([0, -90])\n .translate([width / 2, height / 2])\n .precision(0.1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":526,"value":"outline = d3.geoCircle().radius(90).center([0, 90])()","pinned":true,"hidden":false,"mode":"ojs"},{"id":532,"value":"graticule = d3.geoGraticule().stepMinor([15, 10])()","pinned":true,"hidden":false,"mode":"ojs"},{"id":535,"value":"path = d3.geoPath(projection)","pinned":true,"hidden":false,"mode":"ojs"},{"id":528,"value":"yAxis = g => g\n .call(g => g.append(\"g\")\n .selectAll(\"text\")\n .data(d3.range(10, 91, 10)) // every 10°\n .join(\"text\")\n .attr(\"dy\", \"0.35em\")\n .text(d => `${d}°`)\n .datum(d => projection([0, d]))\n .attr(\"x\", ([x]) => x)\n .attr(\"y\", ([, y]) => y))","pinned":true,"hidden":false,"mode":"ojs"},{"id":518,"value":"xAxis = g => g\n .call(g => g.append(\"g\")\n .attr(\"stroke\", \"currentColor\")\n .selectAll(\"line\")\n .data(d3.range(360))\n .join(\"line\")\n .datum(d => [\n projection([d, 0]),\n projection([d, d % 10 ? -1 : -2])\n ])\n .attr(\"x1\", ([[x1]]) => x1)\n .attr(\"x2\", ([, [x2]]) => x2)\n .attr(\"y1\", ([[, y1]]) => y1)\n .attr(\"y2\", ([, [, y2]]) => y2))\n .call(g => g.append(\"g\")\n .selectAll(\"text\")\n .data(d3.range(0, 360, 10))\n .join(\"text\")\n .attr(\"dy\", \"0.35em\")\n .text(d => d === 0 ? \"N\" : d === 90 ? \"E\" : d === 180 ? \"S\" : d === 270 ? \"W\" : `${d}°`)\n .attr(\"font-size\", d => d % 90 ? null : 14)\n .attr(\"font-weight\", d => d % 90 ? null : \"bold\")\n .datum(d => projection([d, -4]))\n .attr(\"x\", ([x]) => x)\n .attr(\"y\", ([, y]) => y))","pinned":true,"hidden":false,"mode":"ojs"},{"id":226,"value":"viewof hour = slider({\n min: 0, \n max: 8760, \n step: 1, \n value: 10, \n title: \"Hour\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":9,"value":"location = [epw.longitude, epw.latitude]","pinned":false,"hidden":false,"mode":"ojs"},{"id":8,"value":"solar = (await require(\"solar-calculator@0.2\"))(location)","pinned":false,"hidden":false,"mode":"ojs"},{"id":18,"value":"position = solar.position(sample.date)","pinned":false,"hidden":false,"mode":"ojs"},{"id":282,"value":"validation.outputs.poa[hour]","pinned":false,"hidden":false,"mode":"ojs"},{"id":478,"value":"poa(solar, [0, 10], sample);","pinned":false,"hidden":false,"mode":"ojs"},{"id":81,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":68,"value":"sample = epw.data[hour]","pinned":false,"hidden":false,"mode":"ojs"},{"id":48,"value":"import {viewof epw} from \"@jwperakis/epw-reader\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":223,"value":"import {slider} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":279,"value":"validation = FileAttachment(\"sample_az_180_t_30.json\").json()","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"d3 = require(\"d3@v5\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":674,"value":"import {createTooltip} from \"@jwperakis/tooltips\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":707,"value":"_=require('lodash')","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W33","stdlib":"1","titling":"auto"}