2e:null 2f:["$","title",null,{"children":"Swarthmore Battery Optimization | jameswperakis | Observable"}] 34:T16f0,chart = { const width = 960; const height = 500; const svg = d3.select(DOM.svg(width, height)).property("value", []);//.attr("view", []); const margin1 = {top: 20, right: 20, bottom: 110, left: 40}; const margin2 = {top: 430, right: 20, bottom: 30, left: 40}; const chart_width = width - margin1.left - margin1.right; const chart_height = height - margin1.top - margin1.bottom; const context_height = height - margin2.top - margin2.bottom; // const x = d3.scaleTime().range([0, chart_width]); // const x2 = d3.scaleTime().range([0, chart_width]); const x = d3.scaleLinear().range([0, chart_width]); const x2 = d3.scaleLinear().range([0, chart_width]); const y = d3.scaleLinear().range([chart_height, 0]); const y2 = d3.scaleLinear().range([context_height, 0]); const xAxis = d3.axisBottom(x); const xAxis2 = d3.axisBottom(x2); const yAxis = g => g .call(d3.axisLeft(y)) .call(g => g.select(".domain").remove()) .call(g => g.select(".tick:last-of-type text").clone() .attr("x", 3) .attr("text-anchor", "start") .attr("font-weight", "bold") .text("Kilowatts")); const brush = d3.brushX() .extent([[0, 0], [chart_width, context_height]]) .on("brush end", brushed); const zoom = d3.zoom() .scaleExtent([1, Infinity]) .translateExtent([[0, 0], [chart_width, chart_height]]) .extent([[0, 0], [chart_width, chart_height]]) .on("zoom", zoomed); const area1 = d3.area() // .x(d => x(d.data.date)) .curve(d3.curveMonotoneX) .x(d => x(d.data.index)) .y0(d => y(d[0])) .y1(d => y(d[1])); const area2 = d3.area() // .x(d => x2(d.date)) .curve(d3.curveMonotoneX) .x(d => x2(d.index)) .y0(d => y2(0)) .y1(d => y2(d.project_demand)); // const line = d3.line() // .defined(d => !isNaN(d.grid_to_project + d.grid_to_battery)) // .x(d => x(d.index)) // .y(d => y(d.grid_to_project + d.grid_to_battery)); svg.append("defs").append("clipPath") .attr("id", "clip") .append("rect") .attr("width", chart_width) .attr("height", chart_height); const focus = svg.append("g") .attr("class", "focus") .attr("transform", `translate(${margin1.left},${margin1.top})`); const context = svg.append("g") .attr("class", "context") .attr("transform", `translate(${margin2.left},${margin2.top})`); svg.append("rect") .attr("class", "zoom") .attr("width", chart_width) .attr("height", chart_height) .attr("cursor", "move") .attr("fill", "none") .attr("pointer-events", "all") .attr("transform", "translate(" + margin1.left + "," + margin1.top + ")") .call(zoom); function brushed() { if (d3.event.sourceEvent && d3.event.sourceEvent.type === "zoom") return; // ignore brush-by-zoom let s = d3.event.selection || x2.range(); x.domain(s.map(x2.invert), x2); focus.selectAll(".area").attr("d", area1); // focus.select(".demandLine").attr("d", line); focus.select(".axis--x").call(xAxis); svg.select(".zoom").call(zoom.transform, d3.zoomIdentity .scale(chart_width / (s[1] - s[0])) .translate(-s[0], 0)); } function zoomed() { if (d3.event.sourceEvent && d3.event.sourceEvent.type === "brush") return; // ignore zoom-by-brush let value = []; let t = d3.event.transform; x.domain(t.rescaleX(x2).domain()); value = x.domain(); svg.property("value", value).dispatch("input"); focus.selectAll(".area").attr("d", area1); // focus.select(".demandLine").attr("d", line); focus.select(".axis--x").call(xAxis); context.select(".brush").call(brush.move, x.range().map(t.invertX, t)); } const stacked = Object.assign(d3.stack().keys(keys)(peaks), { keys: keys }); console.log(stacked); const formatHour = d3.timeFormat("%I %p"); const formatMonth = d3.timeFormat("%B"); const months = _.range(12).map((d, i) => i*24); //convert indices to months xAxis2.tickValues(months).tickFormat(i => formatMonth(peaks[i].date)); xAxis.tickFormat(i => formatHour(peaks[i].date)); // x.domain(d3.extent(data, function(d) { return d.date; })); // x2.domain(d3.extent(data, function(d) { return d.date; })); x.domain(d3.extent(peaks, function(d) { return d.index; })); x2.domain(d3.extent(peaks, function(d) { return d.index; })); y.domain([0, d3.max(stacked.flat(2))]).nice(); y2.domain([0, d3.max(peaks, function(d) { return d.project_demand; })]); focus.selectAll("path") .data(stacked) .enter().append("path") .attr("class", "area") .attr("clip-path", "url(#clip)") .attr("fill", (d, i) => color(stacked.keys[i])) .attr("d", area1) // focus.append("path") // .datum(data) // .attr("fill", "none") // .attr("stroke-width", 1.5) // .attr("stroke", "#2171b5") // .attr("class", "demandLine") // .attr("clip-path", "url(#clip)") // .attr("d", line); focus.append("g") .attr("class", "axis axis--x") .attr("transform", "translate(0," + chart_height + ")") .call(xAxis); focus.append("g") .attr("class", "axis axis--y") .call(yAxis); context.append("path") .datum(peaks) .attr("class", "area") .attr("fill", "#3182bd") .attr("clip-path", "url(#clip)") .attr("d", area2); context.append("g") .attr("class", "axis axis--x") .attr("transform", "translate(0," + context_height + ")") .call(xAxis2); //this is the value of the previous svg node if (!this) { context.append("g") .attr("class", "brush") .call(brush) .call(brush.move, x.range()); } else { let range = d3.select(this).property("value").map(x); context.append("g") .attr("class", "brush") .call(brush) .call(brush.move, range); } return svg.node(); }35:Tc5b,viewof frequency = { const width = 960; const height = 420; let sorted = []; switch (data_set) { case "Show Original Distribution": sorted = results.map((d, i) => ({index: i, value: d.project_demand})) .sort((a, b) => b.value - a.value); break; case "Distribution With PV and Battery": sorted = results.map((d, i) => ({index: i, value: (d.grid_to_project + d.grid_to_battery)})) .sort((a, b) => b.value - a.value); break; } const percentile = 0.2; const n = _.round(sorted.length * percentile); const threshold = sorted[n].value; const slice = sorted.slice(0, n); const svg = d3.select(DOM.svg(width, height)).property("value", {percentile: percentile, threshold: threshold}); const margin = {top: 20, right: 20, bottom: 30, left: 40}; const x = d3.scaleLinear() .domain(d3.extent(results, (d, i) => i)) .range([0, width - -margin.left - margin.right]); const y = d3.scaleLinear() .domain([0, d3.max(results, d => d.project_demand)]).nice() .range([height - margin.bottom - margin.top, 0]); const xAxis = g => g .attr("transform", `translate(0,${height - margin.bottom - margin.top})`) //.call(d3.axisBottom(x).ticks(width / 80).tickSizeOuter(0)); .call(d3.axisBottom(x).ticks([])); const yAxis = g => g .call(d3.axisLeft(y)) .call(g => g.select(".domain").remove()) .call(g => g.select(".tick:last-of-type text").clone() .attr("x", 3) .attr("text-anchor", "start") .attr("font-weight", "bold") .text("Kilowatts")) .call(g => g.select(".tick:first-of-type text").clone() .attr("x", 3) .attr("y", 15) .attr("text-anchor", "start") .attr("font-weight", "bold") .text("Annual Hours (8760)")); const area = d3.area() .x((d, i) => x(i)) .y0(y(0)) .y1(d => y(d.value)) // const line = d3.line() // .defined(d => !isNaN(d.value)) // .x((d, i) => x(i)) // .y(d => y(d.value)); const g = svg.append("g") .attr("class", "chart") .attr("transform", `translate(${margin.left},${margin.top})`); const a = svg.append("g") .attr("class", "annotation") .attr("transform", `translate(${margin.left},${margin.top})`); g.append("path") .datum(sorted) .attr("fill", "#9ecae1") .attr("d", area); g.append("path") .datum(slice) .attr("fill", "#3182bd") .attr("d", area); // g.append("path") // .datum(sorted) // .attr("fill", "none") // .attr("stroke-width", 1.5) // .attr("stroke", "#3182bd") // .attr("d", line); g.append("g") .attr("class", "axis axis--x") .attr("transform", "translate(0," + (height - margin.top - margin.bottom) + ")") .call(xAxis); g.append("g") .attr("class", "axis axis--y") .call(yAxis); a.append("line") .attr("fill", "none") .attr("stroke", "#ffffff") .attr("stroke-width", 1) .attr("stroke-linejoin", "round") .attr("stroke-linecap", "round") .attr("x1", x(n)) .attr("x2", x(n)) .attr("y1", y.range()[0]) .attr("y2", y.range()[1]); return svg.node(); }36:T624,function peak(f, m, s) { //f = the period of evaluation (frame), m = max capacity of the battery, s = starting charge of battery const demand = f.map(d => Math.max(d.project_demand - d.pv_generation, 0)); const avg = _.sum(demand) / demand.length; const max_rate = m / 8; //find the non-applicable charging periods for peak reduction let right_index = demand.length - 1; for (var [i, e] of Array.from(demand.entries()).reverse()) { if (e >= avg) { right_index = i; break; } } const area = _.sum(demand.map((d, i, arr) => { if (d <= avg && i <= right_index) { return Math.min((avg - d), max_rate); } })); let capacity = Math.min(m, (area + s)); //generate default discharge schedule const schedule = new Array(demand.length).fill(0); const curve = demand.slice(); //iteratively reduce values by 5 (seems to run reasonable fast) while (capacity > 0) { let [index, highest] = _.maxBy(Array.from(curve.entries()), d => d[1]); curve[index] = highest - 5; capacity -= 5; } for (var [i, e] of Array.from(schedule.entries())) { if (demand[i] > avg) { if (curve[i] > avg) { schedule[i] = {discharge: 1, discharge_limit: (demand[i] - curve[i]), period_average: avg}; } else { schedule[i] = {discharge: 1, discharge_limit: (demand[i] - avg), period_average: avg}; } } else { schedule[i] = {discharge: 0, discharge_limit: 0, period_average: avg}; } } return schedule; }37:Te3c,function sim(d, p) { const pv_size = p.pv_size || 0; const battery = p.battery_size || 0; const forecast = p.forecast || 1; const controls = p.controls || peak; const max_capacity = battery * 1000 * 4; const max_rate = max_capacity / 8; d.map((d, i, arr) => { let x = {...d} x = {...x, pv_generation: pv_size * x.pv_potential / 1000}; arr[i] = x; }); const frames = _.range(0, d.length, forecast * 24).map((i) => d.slice(i, i + (forecast * 24))); let start_charge = 0; frames.map((frame, frame_index, arr) => { if (frame_index > 0) { start_charge = arr[frame_index-1].slice(-1)[0].battery_charge; } let schedule = controls(frame, max_capacity, start_charge); frame.map((d, hour, hours) => { let j = {...d}; j = {...j, ...schedule[hour]}; let diff = Math.abs(j.project_demand - j.pv_generation - j.period_average); j = {...j, date: parse_date(`${j.month.toString().padStart(2, "0")} ${j.day.toString().padStart(2, "0")} ${j.hour.toString().padStart(2, "0")}`)}; //update the battery charge, pull from last hour if (hour === 0) { if (frame_index === 0) { j = {...j, battery_charge: 0}; } else { j = {...j, battery_charge: arr[frame_index-1].slice(-1)[0].battery_charge}; } } else { j = {...j, battery_charge: hours[hour-1].battery_charge}; } //update pv to project if (j.project_demand - j.pv_generation > 0) { j = {...j, pv_to_project: j.pv_generation}; } else { j = {...j, pv_to_project: j.project_demand}; } //update battery to project if (j.discharge === 1) { if (j.battery_charge < j.discharge_limit) { j = {...j, battery_to_project: j.battery_charge}; } else { j = {...j, battery_to_project: j.discharge_limit}; } } else { j = {...j, battery_to_project: 0}; } //update the battery charge j = {...j, battery_charge: j.battery_charge - j.battery_to_project}; //update grid to project j = {...j, grid_to_project: j.project_demand - j.pv_to_project - j.battery_to_project}; //pv to battery if (j.battery_charge < max_capacity) { let spare_capacity = max_capacity - j.battery_charge; let extra_output = j.pv_generation - j.pv_to_project; if (extra_output - spare_capacity > 0) { j = {...j, pv_to_battery: Math.min(max_rate, diff)}; } else { j = {...j, pv_to_battery: Math.min(extra_output, diff, max_rate)}; } } else { j = {...j, pv_to_battery: 0}; } //update the battery charge again j = {...j, battery_charge: j.battery_charge + j.pv_to_battery}; //grid to battery if (j.project_demand - j.pv_generation < j.period_average) { let spare_capacity = max_capacity - j.battery_charge; j = {...j, grid_to_battery: Math.min(spare_capacity, diff, max_rate)}; } else { j = {...j, grid_to_battery: 0}; } //update the battery charge again j = {...j, battery_charge: j.battery_charge + j.grid_to_battery}; //find the total grid j = {...j, total_grid: j.grid_to_project + j.grid_to_battery}; hours[hour] = j; }) arr[frame_index] = frame; }) return frames.flat(); //return frames.reduce((acc, val) => acc.concat(val), []); }38:T93f,viewof savings = { const width = 960; const height = 440; const svg = d3.select(DOM.svg(width, height)); const margin = {top: 20, right: 20, bottom: 50, left: 40}; const payback = [{cost: 0, savings: 0}, {cost: max_savings * assumptions.payback, savings: max_savings}]; const x = d3.scaleLinear() .domain([0, max_costs]).nice() .range([0, width - -margin.left - margin.right]); const y = d3.scaleLinear() .domain([0, max_savings]) .range([height - margin.bottom - margin.top, 0]); const xAxis = g => g .attr("transform", `translate(0,${height - margin.bottom - margin.top})`) .call(d3.axisBottom(x).tickFormat(d3.format(".2s"))); const yAxis = g => g .call(d3.axisLeft(y).tickFormat(d3.format(".2s"))) .call(g => g.select(".domain").remove()) .call(g => g.select(".tick:last-of-type text").clone() .attr("x", 3) .attr("text-anchor", "start") .attr("font-weight", "bold") .text("$ Annual Savings")) .call(g => g.select(".tick:first-of-type text").clone() .attr("x", 3) .attr("y", 30) .attr("text-anchor", "start") .attr("font-weight", "bold") .text("Installed Costs"));; const area = d3.area() .x(d => x(d.cost)) .y1(0) .y0(d => y(d.savings)) const line = d3.line() .defined(d => !isNaN(d.savings)) .x(d => x(d.cost)) .y(d => y(d.savings)); const g = svg.append("g") .attr("class", "chart") .attr("transform", `translate(${margin.left},${margin.top})`); g.append("path") .datum(payback) .attr("fill", "#9ecae1") .attr("opacity", 0.2) .attr("d", area); g.append("path") .datum(payback) .attr("fill", "none") .attr("stroke-width", 1.5) .attr("stroke", "#3182bd") .attr("d", line); g.append("g") .attr("class", "axis axis--x") .attr("transform", "translate(0," + (height - margin.top - margin.bottom) + ")") .call(xAxis); g.append("g") .attr("class", "axis axis--y") .call(yAxis); const plot = {cost: (assumptions.battery_cost * battery_size * 4 * 1000 + assumptions.pv_cost * pv_size), savings: cost_savings}; g.append("circle") .attr("cx", x(plot.cost)) .attr("cy", y(plot.savings)) .attr("r", 5) .attr("fill", "#3182bd"); return svg.node(); }39:T611,function costs(d) { const rates = { //average for all months //customer charge $ cc: 295.41, //improvement charge $ ic: 33.80, //energy efficiency charge $ ec: 2597.52, //tax adjustment $ ta: -1.82, //distrubtion charge kWh dckwh: -0.00079, //transmission charge kWh tc: 0.05138, //distribution charge kW dckw: 4.67, //high voltage discount kW hvd: -0.15, //balanceing congestion charge $ bc: 85.90, //gross receipt reimbursement & rr: 1466.95 } const months = []; for (var i = 1; i < 13; i++) { let fixed = _.sum([rates.cc, rates.ic, rates.ec, rates.ta, rates.bc, rates.rr]); let baseline_demand = d.filter(dd => (dd.month === i)).map(dd => dd.project_demand); let kwb = _.max(baseline_demand) * (rates.hvd + rates.dckw); let kwhb = _.sum(baseline_demand) * (rates.tc + rates.dckwh); let total_grid = d.filter(dd => (dd.month === i)).map(dd => dd.total_grid); let kws = _.max(total_grid) * (rates.hvd + rates.dckw); let kwhs = _.sum(total_grid) * (rates.tc + rates.dckwh); let x = { month: i, baseline_costs: (fixed + kwb + kwhb), baseline_total: _.sum(baseline_demand), baseline_peak: _.max(baseline_demand), scenario_costs: (fixed + kws + kwhs), scenario_total: _.sum(total_grid), scenario_peak: _.max(total_grid), cost_savings: (kwb + kwhb - kws - kwhs) }; months.push(x); } return months; }3a:[] 32:{"id":"8c8562acfebafb9e","slug":"battery-optimization","title":"Swarthmore Battery Optimization","thumbnail":"c9f9c9a88883c6b67930afa7a50f496506633d79ab3e14c1d7d1557b31cbf4ab","access_level":"public","create_time":"$D2019-01-11T18:06:36.911Z","update_time":"$D2026-02-04T17:23:48.601Z","view_time":null,"first_public_time":"$D2019-01-23T22:52:45.787Z","has_unpublished_edits":null,"fork":false,"stars":4,"starred":false,"owner":{"type":"team","id":"c679d8c3e6bf5d25","login":"jameswperakis","name":"","avatar_url":"https://avatars-next.observableusercontent.com/f5bc12cb871edc5200dd29f2e3097ee77df9ef9047687f4d711480d16c9d491a","tier":"starter_2024"},"version":1637,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"a979f347f60b0766","login":"jameswperakis","name":"","avatar_url":"https://avatars-next.observableusercontent.com/f5bc12cb871edc5200dd29f2e3097ee77df9ef9047687f4d711480d16c9d491a","tier":null}],"members":[{"type":"individual","id":"a979f347f60b0766","login":"jameswperakis","name":"","avatar_url":"https://avatars-next.observableusercontent.com/f5bc12cb871edc5200dd29f2e3097ee77df9ef9047687f4d711480d16c9d491a","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":6,"collection":{"id":"11cfcb472e1f1a98","slug":"climate-analysis","title":"Archive","owner":{"id":"c679d8c3e6bf5d25","login":"jameswperakis","name":""}},"type":"notebook","body":{"title":"Swarthmore Battery Optimization","cells":[{"id":0,"value":"md`# Swarthmore Battery Optimization\n\nUse the dropdown menu to change the data set.` ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1425,"value":"viewof dataset = {\n const select = html``;\n\n return select;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1448,"value":"md`Adjust the photovoltaic and battery size to see how the two systems work together to reduce peak demand over the course of the year. The graph shows the demand profile for the peak day for each month.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":495,"value":"md`Photovoltaic Array Size (kW): **${pv_size_display}**`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":393,"value":"pv_input = html``\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":494,"value":"md`Battery Size (MW): **${d3.format(\".2n\")(battery_size_display)}**`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":480,"value":"battery_input = html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":601,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1158,"value":"legend = {\n \n const key_map = {\n \"pv_to_project\": \"Photovoltaic to Project\",\n \"battery_to_project\": \"Battery to Project\",\n \"grid_to_battery\": \"Grid to Battery Charging\",\n \"grid_to_project\": \"Grid Electricity to Project\"\n \n }\n \n const svg = d3.select(DOM.svg(960, color.domain().length * 24))\n .style(\"font\", \"11px sans-serif\");\n\n const g = svg.append(\"g\")\n .selectAll(\"g\")\n .data(color.domain().slice().reverse())\n .enter().append(\"g\")\n .attr(\"transform\", (d, i) => `translate(${40}, ${i*24})`);\n\n g.append(\"rect\")\n .attr(\"width\", 20)\n .attr(\"height\",20)\n .attr(\"fill\", color);\n\n g.append(\"text\")\n .attr(\"x\", 30)\n .attr(\"y\", 9.5)\n .attr(\"dy\", \"0.35em\")\n .text(d => key_map[d]);\n \n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1287,"value":"md`Based on this configuration, the annual cost savings for the project would be approximately **${d3.format(\"($,\")(_.round(cost_savings))}**. Refer to the \\`costs()\\` function for utility rate information.` ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1219,"value":"md`The distribution of loads is shown in the graph below. Note how the photovoltaics and batteries are able to reduce the number of high-demand hours throughout the year. To see the original demand distrubtion select \\`Show Original Distribution\\` and to see the optimized load distribution select \\`Show Optimized Distribution\\`. The threshold shown (**${_.round(frequency.threshold/1000, 2)}** MW) is based on the backup system needed for 80% availability.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1277,"value":"viewof data_set = select([\"Show Original Distribution\", \"Distribution With PV and Battery\"])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1238,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1343,"value":"frequency_legend = {\n \n const threshold = frequency.threshold;\n const l = [frequency.percentile, 1 - frequency.percentile];\n \n const colors = [\"#3182bd\", \"#9ecae1\"];\n \n const svg = d3.select(DOM.svg(960, colors.length * 24))\n .style(\"font\", \"11px sans-serif\");\n\n const g = svg.append(\"g\")\n .selectAll(\"g\")\n .data(colors)\n .enter().append(\"g\")\n .attr(\"transform\", (d, i) => `translate(${40},${i * 24})`);\n\n g.append(\"rect\")\n .attr(\"width\", 20)\n .attr(\"height\", 20)\n .attr(\"fill\", d => d);\n\n g.append(\"text\")\n .attr(\"x\", 30)\n .attr(\"y\", 9.5)\n .attr(\"dy\", \"0.35em\")\n .text((d, i) => `${_.round(l[i]*100, 2)}% of Hours ${i === 0 ? \"Above\": \"Below\"} ${_.round(threshold/1000, 2)}MW`);\n \n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1256,"value":"md`The current optimization scenario uses the \\`peak()\\` function to reduce peak demand over a given period of time. Given a load profile over period ${tex`p_0-p_n`}, and battery capacity ${tex`b`}, the program iteratively reduces the peak load by ${tex`r`} such that ${tex`\\sum\\limits_{p=0}^{n} r_{p} < b`}. With this approach, the battery discharge is constrained so that the peak is optimally reduced over each period of time. More information about the peak function is shown below.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":215,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":263,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1521,"value":"md`The peak function optimizes for peak load cost savings. The graph below shows the cost savings and estimated installed costs for the selected configuration of photovoltaics and battery storage. For this anlaysis we used ${d3.format(\"($,\")(_.round(assumptions.pv_cost))}/kW for the installed cost of the photovoltaic system and ${d3.format(\"($,\")(_.round(assumptions.battery_cost))}/kWh for the battery storage. The light blue area represents an optimal range for system payback.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1525,"value":"$38","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1586,"value":"cost_legend = {\n \n const svg = d3.select(DOM.svg(960, 60))\n .style(\"font\", \"11px sans-serif\");\n\n const g = svg.append(\"g\")\n .attr(\"transform\", (d, i) => `translate(${40},${i * 24})`);\n\n g.append(\"circle\")\n .attr(\"cx\", 10)\n .attr(\"cy\", 10)\n .attr(\"r\", 5)\n .attr(\"fill\", \"#3182bd\");\n \n const label = `${pv_size_display} kW PV System | ${d3.format(\".2n\")(battery_size_display)} MW Battery Storage`;\n\n g.append(\"text\")\n .attr(\"x\", 30)\n .attr(\"y\", 9.5)\n .attr(\"dy\", \"0.35em\")\n .text(label);\n \n g.append(\"rect\")\n .attr(\"width\", 20)\n .attr(\"height\", 20)\n .attr(\"y\", 25)\n .attr(\"fill\", \"#9ecae1\")\n .attr(\"opacity\", 0.2);\n \n g.append(\"text\")\n .attr(\"x\", 30)\n .attr(\"y\",35)\n .attr(\"dy\", \"0.35em\")\n .text(\"Optimal Payback Range\");\n \n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1611,"value":"md`The rest of the information in this notebook consists of helper functions for the anlaysis, data variables, external libraries, and other tools that we used in evaluating photovoltaic generation and battery storage. All of the primary assumptions for this analysis are included in the data below.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":748,"value":"keys = [\"grid_to_project\", \"grid_to_battery\", \"battery_to_project\", \"pv_to_project\"];","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":171,"value":"raw = {\n let raw = (await d3.csv(dataset, function(d) {\n\n \n return {\n month: +d.Month,\n day: +d.Day,\n hour: +d.Hour,\n pv_potential: +d[\"PV Potential\"],\n project_demand: +d[\"Project Electricity kWh\"]\n }\n })\n );\n\n const months = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]\n const times = [];\n \n for (const m in _.range(12)) {\n for (const d in _.range(months[m])) {\n for (const h in _.range(24)) {\n times.push({month: +m + 1, day: +d + 1, hour: +h});\n }\n }\n }\n \n raw.map((d, i, arr) => {\n arr[i] = {...d, ...times[i]};\n });\n \n return raw;\n\n } \n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1527,"value":"results = sim(raw, {pv_size: pv_size, battery_size: battery_size, forecast: 1, controls: peak});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1232,"value":"peaks = {\n const nested = d3.nest()\n .key(d => d.month)\n .entries(results)\n .map((d) => {\n let month = +d.key;\n let day = +d.values.reduce((a, b) => {\n return (a.project_demand || 0) > b.project_demand ? a : b;\n }, {}).day;\n let values = results.filter(dd => (dd.month === month && dd.day === day));\n\n return {month: month, day: day, values: values};\n });\n \n \n let peaks = [].concat(...nested.map(d => d.values));\n \n \n peaks.map((d, i, arr) => {\n arr[i] = {...d, index: i};\n });\n \n return peaks;\n\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1618,"value":"max_savings = _.sum(costs(sim(raw, {pv_size: assumptions.pv_max, battery_size: assumptions.battery_max, forecast: 1, controls: peak})).map(d => d.cost_savings))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1620,"value":"max_costs = (assumptions.pv_cost * assumptions.pv_max) + (assumptions.battery_cost * assumptions.battery_max * 4 * 1000)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1284,"value":"cost_savings = _.sum(costs(results).map(d => d.cost_savings))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":344,"value":"$39","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":357,"value":"color = d3.scaleOrdinal()\n .range([\"#3182bd\", \"#6baed6\", \"#9ecae1\", \"#c6dbef\"])\n .domain(keys)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":482,"value":"battery_size = Generators.observe(next => {\n // Yield the input’s initial value.\n next(battery_input.valueAsNumber);\n\n // Define an event listener to yield the input’s next value.\n const inputted = () => {\n return next(battery_input.valueAsNumber);\n }\n\n // Attach the event listener.\n battery_input.addEventListener(\"change\", inputted);\n\n // When the generator is disposed, detach the event listener.\n return () => battery_input.removeEventListener(\"change\", inputted);\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":486,"value":"battery_size_display = Generators.input(battery_input)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":422,"value":"pv_size = Generators.observe(next => {\n // Yield the input’s initial value.\n next(pv_input.valueAsNumber);\n\n // Define an event listener to yield the input’s next value.\n const inputted = () => next(pv_input.valueAsNumber);\n\n // Attach the event listener.\n pv_input.addEventListener(\"change\", inputted);\n\n // When the generator is disposed, detach the event listener.\n return () => pv_input.removeEventListener(\"change\", inputted);\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":491,"value":"pv_size_display = Generators.input(pv_input)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":254,"value":"_ = require(\"lodash\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":615,"value":"parse_date = d3.timeParse(\"%m %d %H\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1519,"value":"assumptions = ({battery_max: 3,\n pv_max: 3000,\n //cost per kwh\n battery_cost: 450,\n //cost per kw\n pv_cost: 2100,\n payback: 43})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1279,"value":"import {select} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W3a","stdlib":"1","titling":"auto"}} 33:"$32:body"