2c:null 2d:["$","title",null,{"children":"Power and Energy | Western Power | Observable"}] 32:T523,html`

Introduction

The Power and Energy (P&E) Model takes the total flow of water in the river and, with reference to the design and operation of the plant, calculates the instantaneous power output (in megawatts) of the proposed powerstation.

By using the entire available historic record of river flows as the input to the P&E model, the production of the power station can be simulated as if had been built and continuously operated since 1924.

Assuming that, on average and over the long term, the pattern of flows in the river will be the same in the future as they have been in the past then we can analyse these modelled, simulated energy results based on the historic record of river flows to understand the performance of the power station once it is built.

The impact of possible cycles or permanent changes in the pattern of river flow, for example due to climate change, can also be investigated by modifying the historic flow record to simulate these changes into the future and then using this modified flow data as the input to the P&E model. `33:T5bf,html`

	Turbne Unit	Plant
Units		4
Nominal Power	${d3.format('.0f')(model.Capacity/4)}MW	${d3.format('.0f')(model.Capacity)}MW
Minimum Head	${model.MinimumHead}m
Rated Head	${model.RatedHead}m
Minimum Flow	${format_flow(model.MinimumFlowUnit)}
Rated Flow	${format_flow(model.RatedDischarge)}
Maximum Load	${d3.format('.0f')(model.MaximumLoadFactor*100)}% of rated flow
Maximum Flow	${format_flow(model.RatedDischarge*model.MaximumLoadFactor)}	${format_flow(model.RatedDischargemodel.MaximumLoadFactor4)}
Rated Turbine Efficiency	${d3.format('.1f')(model.RatedTurbineEfficiency*100)}%
Rated Generator Efficiency	${d3.format('.1f')(model.RatedGeneratorEfficiency*100)}%
Rated Power	${d3.format('.1f')(model.RatedPower)}MW
Maximum Power	${d3.format('.1f')(model.Power_Turbine1_max)}MW	${d3.format('.1f')(model.Power_max)}MW

`34:T57e,{ var data = [ { x: pefdc.map(ex=>ex.Flow), y: pefdc.map(ex=>ex.HeadTurbine1), mode: 'lines', line: {shape: 'spline', color: colr(1)}, type: 'scatter' }, { x: [5300,8900,8900,5300], y: [10,10,0,0], fill: 'toself', mode:'none', fillcolor: 'rgba(220,120,120,0.3)', showlegend:false, type: 'scatter' } ]; var layout = { width: width*.8, height:200, font: font, title: plotTitle('Net Head'), margin: { l: 90, r: 90,b: 50, t: 30 }, showlegend: false, annotations: [ { x: 6500, y: 5, text: 'Low-head Shutdown', showarrow: false, }], xaxis: { showgrid: false, zeroline: false, ticks:'outside', title: 'River Flow (m\u00B3/s)', }, yaxis: { title: 'Net Head (m)', zeroline: false, showline: false, separatethousands:true, } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{staticPlot: true}); return html`

${div}

Fig 1. Net head decreases with increasing flow of water in the river as the downsteam gorge tends to flood at higher flows and the water elevation rises at the power station tailrace. Above 5,300 m\u00b3/s the net head falls below 10m and their is not enough head to operate the turbines.

` }35:T6f1,{ var total_energy=d3.sum(calmonths.map(mnth=>mnth.Energy_median)) var sum; var data = [ { name:'Median Energy Production', x:calmonths.map(mnth=>mnth.WaterMonth), y:calmonths.map(mnth=>Math.round(mnth.Energy_median/1000)), //text:calmonths.map(mnth=>Math.round(mnth.Energy_median/1000)), type: 'bar', mode: 'markers+text', textfont: { color:'rgb(10,10,10)', size: 12, }, textposition:'outside', showlegend:true, marker: {color:colr(1,0.6)} }, { name:'Cumulative Energy %', x: calmonths.map(mnth=>mnth.WaterMonth), y: cum_energy, text:cum_energy.map(pct=>pct+'%'), textposition:'top', yaxis: 'y2', hoverinfo:'none', mode: 'text+markers', line: {shape: 'spline'}, textfont: { color:'rgb(10,10,10)', size: 12, }, marker: {color: 'black'}, type: 'scatter' } ]; var layout = { width: width*.8, height:350, font: font, barmode:'overlay', margin: margin(true), title:plotTitle('Median Monthly Energy and Flow'), showlegend: true, legend: {x: 0,xanchor: 'left',y: 1}, xaxis: { showgrid: false, zeroline: false, ticks:'outside', tickvals: [ 1,2,3,4,5,6,7,8,9,10,11,12 ], ticktext:['Oct','Nov','Dec','Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep'], }, yaxis: { title: 'Energy (GWh)', range:[0,150], zeroline: false, showline: false, separatethousands:true }, yaxis2: { visible:false, overlaying: 'y', side: 'right' } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div} ` }36:T7ce,{ var total_energy=d3.sum(calmonths.map(mnth=>mnth.Energy_median)) var sum; var data = [ { name:'Median Power', x:calmonths.map(mnth=>mnth.WaterMonth), y:calmonths.map(mnth=>Math.round(mnth.Power_median)), //text:calmonths.map(mnth=>Math.round(mnth.Energy_median/1000)), type: 'bar', mode: 'markers+text', textfont: { color:'rgb(10,10,10)', size: 12, }, textposition:'outside', showlegend:true, marker: {color:colr(1,0.6)} }, { x:flow_calmonths.map(mnth=>mnth.WaterMonth), y:flow_calmonths.map(mnth=>mnth.Flow_median), yaxis: 'y3', mode:'lines', name: 'Median River Flow', line: {shape: 'spline',color:colr(5)}, }, ]; var layout = { width: width*.8, height:350, font: font, barmode:'overlay', margin: margin(true), title:plotTitle('Median Monthly Power'), showlegend: true, legend: {x: 0,xanchor: 'left',y: 1}, xaxis: { showgrid: false, zeroline: false, ticks:'outside', tickvals: [ 1,2,3,4,5,6,7,8,9,10,11,12 ], ticktext:['Oct','Nov','Dec','Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep'], }, yaxis: { title: 'Power (MW)', range:[0,200], zeroline: false, showline: false, separatethousands:true }, yaxis3: { showgrid: false, zeroline: false, showline: false, title: 'Flow (m\u00B3/s)', separatethousands:true, tickformat: ',.2r', overlaying: 'y', side: 'right' } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 2. Median energy and flow by month (top) and power (bottom). Shows how the output of the run-of-river power station is governed by the seasonal change in river flow. Note the use of a 'water year' from October to September.

` }37:T4e8,{ var data = [ { y: calmonths.map(m=>m.Energy_coefvar*100), x: calmonths.map(m=>m.WaterMonth), mode: 'lines', line: { shape: 'spline' }, marker: { color: colr(1,0.8) }, type: 'bar' } ]; var layout = { width:width*.7, height: 260, font: font, showlegend: false, margin: margin(true), legend: { x: 1, xanchor: 'right', y: 1 }, title: plotTitle('Monthly Variability in Energy Production'), xaxis: { showgrid: true, zeroline: false, ticks: 'outside', tickvals: [ 1,2,3,4,5,6,7,8,9,10,11,12 ], ticktext:['Oct','Nov','Dec','Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep'], }, yaxis: { title: 'Coefficient
of Variation %', zeroline: false, showline: false } }; const div = DOM.element('div'); plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 3. The coefficient of variation (standard deviation divided by mean) in energy production by month. Higher flow months show less variation except March and April where tailrace flooding and headloss can cause production to drop.

` }38:T64e,{ var sum; function trace(name, field, colour, trans) { return { name: name, x:calmonths.map(mnth=>mnth.WaterMonth), y:calmonths.map(mnth=>(mnth[field]/1000)), text:calmonths.map(mnth=>(d3.format('.0f')(mnth[field]/1000))), type: 'scatter', mode: field=='Energy_P90'?'lines+markers+text':'lines+markers', textposition:'outside', hoverinfo: 'x+y', showlegend:true, fill: field=='Energy_P95'?'':'', line: {shape: 'spline', color: make_trans(colour,trans)}, marker: {color: make_trans(colour, trans), size: 8}, textposition:'top-right' } } var data = [ trace('P95', 'Energy_P95', colr(7, 1), 0.3), trace('P90', 'Energy_P90', colr(5, 1), 0.6), trace('P50', 'Energy_median', colr(1, 1), 0.9) ] var layout = { width: width*.8, height:350, font: font, barmode:'overlay', margin: {l: 65,r: 10,b: 45,t: 40}, showlegend: true, legend: {x: 0,xanchor: 'left',y: 1}, xaxis: { showgrid: false, zeroline: false, ticks:'outside', tickvals: [ 1,2,3,4,5,6,7,8,9,10,11,12 ], ticktext:['Oct','Nov','Dec','Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep'], }, yaxis: { title: 'GWh', range:[0,150], zeroline: false, showline: false, separatethousands:true, tickformat: '.0f' } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 4. Monthly energy probabilities show how higher flow months produce more energy on average.

` }39:T68e,{ var sum; function trace(name, field, colour, trans) { return { name: name, x:calmonths.map(mnth=>mnth.WaterMonth), y:calmonths.map(mnth=>(mnth[field])), text:calmonths.map(mnth=>(d3.format('.0f')(mnth[field]))), type: 'scatter', mode: field=='Power_P90'?'lines+markers+text':'lines+markers', textposition:'outside', hoverinfo: 'x+y', showlegend:true, fill: field=='Power_P95'?'':'', line: {shape: 'spline', color: make_trans(colour,trans), dash: field=='Power_max'?'dashdot':''}, marker: {color: make_trans(colour, trans), size: 8}, textposition:'top-right' } } var data = [ trace('P90 (MW)', 'Power_P90', colr(5, 1), 0.6), trace('P50', 'Power_median', colr(1, 1), 0.9), trace('Max', 'Power_max', colr(9, 1), 0.3) ] var layout = { width: width*.8, height:350, font: font, barmode:'overlay', margin: {l: 65,r: 10,b: 45,t: 0}, showlegend: true, legend: {x: 0,xanchor: 'left',y: 1}, xaxis: { showgrid: false, zeroline: false, ticks:'outside', tickvals: [ 1,2,3,4,5,6,7,8,9,10,11,12 ], ticktext:['Oct','Nov','Dec','Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep'], }, yaxis: { title: 'MW', range:[0,210], zeroline: false, showline: false, separatethousands:true, tickformat: '.0f' } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 4. Monthly energy (top) and power (bottom) probabilities show how higher flow months produce more energy on average.

` }3a:T7ee,{ var energy_mean = d3.mean(yearly.map(yr => yr.Energy / 1000)); var data = [ { x: [1924, 2016], y: [model.P50/1000, model.P50/1000], name:'Median (P50) Annual', mode: 'lines', line: { color: 'rgba(100,100,100,1)', dash: 'dot', width: 1.5 } }, { x:[1924,2016], y:[model.P90/1000,model.P90/1000], line:{color:'rgba(100,100,100,1)', dash: 'dashdot', width: 1}, name:'P90 Annual', mode:'lines', }, { x:[1924,2016], y:[model.P75/1000,model.P75/1000], line:{color:'rgba(100,100,100,1)', dash: 'dash', width: 1}, name:'P75 Annual', mode:'lines', }, { y: yearly.map(yr => yr.Energy / 1000), x: yearly.map(yr => yr.WaterYear), showlegend: false, name: '', marker: {color: colr(1,0.5)}, type: 'bar' }, { y: movingAverage(yearly.map(yr => yr.Energy / 1000), 10), x: yearly.map(yr => yr.WaterYear), name: '10yr moving average', mode: 'lines', line: { color: 'rgba(50,50,50,1)', dash: 'dashdot', width: 1.5 }, type: 'scatter' } ]; var layout = { width: width, height: 350, font: font, showlegend: true, margin: { l: 90, r: 30, b: 50, t: 50 }, legend: { orientation:'h' }, title: plotTitle('Simulated Annual Energy'), xaxis: { showgrid: false, zeroline: false, ticks: 'outside', range: [1923, 2017] }, yaxis: { title: 'Energy (GWh)', zeroline: false, tickformat: ',.2r', showline: false, range: [400, 1100] } }; const div = DOM.element('div'); plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 5. Total annual energy production for each of the ${yearly.length} years of the historic flow record when passed through the P&E model. The 10 year moving average, overall median (P50), the P75 and P90 values are shown.

` }3b:T81e,{ var data = [ { x: yearly.map(yr => yr.Energy / 1000), type: 'histogram', marker: { color: colr(1,0.7), size: 5 } } ]; var layout = { showlegend: false, width: 550, height: 300, font: font, title:plotTitle('Histogram Annual Energy'), margin: margin, yaxis: { title:'count (n:' + yearly.length + ')', }, xaxis: { separatethousands: true, title:'Energy (GWh)' } }; const div = DOM.element('div'); plt.newPlot(div, data, layout, { staticPlot: true }); return html`

${div}

Fig 6. Histogram of modelled annual energy for the ${yearly.length} years of the historic flow record.

Energy Summary

Mean - ${d3.format(',.0f')(model.Mean / 1000)} GWh
Median P50 - ${d3.format(',.0f')(model.P50 / 1000)} GWh
P75 - ${d3.format(',.0f')(model.P75 / 1000)} GWh
P90 - ${d3.format(',.0f')(model.P90 / 1000)} GWh
Max - ${d3.format(',.0f')(model.Max / 1000)} GWh
Min - ${d3.format(',.0f')(model.Min / 1000)} GWh
P95 'Firm' Energy - ${d3.format(',.0f')( edc[19]['Energy'] / 1000 )} GWh

Power Summary

Nominal - ${d3.format(',.0f')(model.Capacity)} MW
Max - ${d3.format(',.0f')(model.Power_max)} MW
P95 'Firm' Power - ${d3.format(',.1f')( power_exceed.filter(e => e.Exceedance >= 0.95)[0].Power )} MW
Capacity Factor (nominal) - ${d3.format(',.1f')(model.CapFactor * 100)}%
Capacity Factor (max) - ${d3.format(',.1f')(model.CapFactor_Power_max * 100)}%

` }3c:T68b,{ let correls= Object.values(autocorrel[0]).filter((a,i)=>i<=10) let lims=Object.values(autocorrel[1]).filter((a,i)=>i>0 && i<=10).map(s=>s.replace(' ',',')).map(l=>JSON.parse(l)) var data = [ { y: correls, x: [...Array(11).keys()], name: 'Correlation coefficient', marker: { color: [...Array(11).keys()].map(i=>i==0?colr(1,0.4):colr(1,0.8)) }, type: 'bar' }, { x: [...Array(11).keys()].slice(1), y: lims.map((l,i)=>l[1]-correls[i+1]), fill: 'tozeroy', name:'95% Confidence interval', line: {color: 'rgba(0,0,0,0)'}, fillcolor: 'rgba(0,0,0,0.2)' }, { y: correls, x: [...Array(11).keys()], showlegend:false, marker: { color: [...Array(11).keys()].map(i=>i>0 && i<3 ?colr(1,0.8):'rgba(0,0,0,0)') ,size:10}, mode:'markers', type: 'scatter' }, ]; var layout = { height: 330, width:width, font: font, showlegend: true, bargap :0.9, margin: margin, //legend: {x: 1, xanchor: 'right', y: 1,}, title: plotTitle('Annual Energy Autocorrelation'), xaxis: { showgrid: true, zeroline: false,dtick:1,ticks: 'outside', title: 'Lag (years)' }, yaxis: { title: 'Correlation',zeroline: false,showline: false, } }; const div = DOM.element('div'); plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 7. Autocorrelation plot for annual energy. Significant autocorrelation for lags of 1 and 2 years shows that years with above or below average yield may follow each other consecutively.

` }3d:T632,{ var data = [ { y: edc.map(f => d3.format(',.0f')(f.Energy / 1000)), x: edc.map(f => Math.round(f[''] * 100)), mode: 'lines', name:'Energy', line: { shape: 'spline' }, marker: { color: colr(1) }, type: 'scatter' }, { y: [d3.format(',.0f')(edc[19]['Energy'] / 1000)], x: [edc[19][''] * 100], mode: 'markers+text', marker: { color: colr(5), size: 10 }, type: 'scatter' } ]; var layout = { height: 360, width:width*.8, font: font, showlegend: false, margin: margin, legend: { x: 1, xanchor: 'right', y: 1 }, annotations: [ { y: edc[19]['Energy'] / 1000, x: 95, text: "P95 'Firm' Energy - " + d3.format(',.0f')(edc[19]['Energy'] / 1000) + ' GWh', showarrow: true, arrowhead: 2, ax: -90, ay: 50, xref: 'x', yref: 'y' } ], title: plotTitle('Annual Energy Exceedance'), xaxis: { showgrid: true, zeroline: false, dtick: 10, ticks: 'outside', title: 'Exceedance %' }, yaxis: { title: 'Energy (GWh)', zeroline: false, showline: false, separatethousands: true } }; const div = DOM.element('div'); plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 8. Annual energy production shown on an exceedance basis. P50 median energy production is ${d3.format(',.0f')(model.P50 / 1000)} GWh and P95 energy is ${d3.format(',.0f')(edc[19]['Energy'] / 1000)} GWh.

` }3e:T569,{ var data = [ { x:[10,40], y:[180,180], text:['',' Installed Capacity'], textposition:'middle-left', mode:'lines+text', line:{color:'black',width:0.5} }, { y: pe_fdc.map(f => d3.format(',.0f')(f.Power)), x: pe_fdc.map(f => Math.round(f['Exceedance'] * 100)), mode: 'lines', name: 'Power', line: { color: colr(1) }, type: 'scatter' } ]; var layout = { width:width*.8, height: 330, font: font, showlegend: false, margin: margin, legend: {x: 1,xanchor: 'right',y: 1 }, title: plotTitle('Power by Flow'), annotations: [ { y: 20,x: 5,text:' Increasing Flow', showarrow: true, arrowhead: 2,ax: -300,ay:0,xref: 'x',yref: 'y' }, { y: 40,x: 65,text:' Increasing Head',showarrow: true, arrowhead: 2,ax: 300,ay:0,xref: 'x',yref: 'y' } ], xaxis: { showgrid: true, zeroline: false, dtick: 10, range:[100,0], ticks: 'outside', title: 'Flow Exceedance %' }, yaxis: { title: 'Power (MW)', zeroline: false, showline: false, separatethousands: true } }; const div = DOM.element('div'); plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div} ` }3f:T5bb,{ var data = [{ y: pe_fdc.map(f => d3.format(',.0f')(f.Power)), x: pe_fdc.map(f => Math.round(f['Flow'])), mode: 'lines', name: 'Power', line: {color: colr(1) }, type: 'scatter' }]; var layout = { width:width*.8, height: 260, font: font, showlegend: false, annotations: [{ y: 20,x: 5000,text:' Increasing Flow', showarrow: true, arrowhead: 2,ax: -250,ay:0,xref: 'x',yref: 'y' }, { y: 40,x: 1000,text:' Increasing Head',showarrow: true, arrowhead: 2,ax: 250,ay:0,xref: 'x',yref: 'y' }], margin: { l: 90,r: 90,b: 90,t: 5}, legend: {x: 1,xanchor: 'right',y: 1 }, xaxis: { showgrid: false, zeroline: false, ticks: 'outside', title: 'Flow (m\u00b3/s)' }, yaxis: { title: 'Power (MW)', zeroline: false, showline: false, separatethousands: true } }; const div = DOM.element('div'); plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 9. Plots of power output against river flow and flow exceedance. Power is lower at high flow (lower exceedance values) because high flow causes a reduciton in head. Power is lower at low flow (higher exceedance) due to lack of flow for generation. Peak power is higher than the installed capacity because the turbines can overdriven with excess flow under certain conditions.

` }40:T61a,{ var data = [ { y:power_exceed.map(v => v.Power), x: power_exceed.map(v => v.Exceedance), mode: 'lines', name: 'Power', line: { shape: 'spline',color: colr(1) }, type: 'scatter' }, { y: [ d3.format(',.1f')( power_exceed.filter(e => e.Exceedance >= 0.95)[0].Power ) ], x: [0.95], mode: 'markers', marker: { color: colr(5), size: 10 }, type: 'scatter' } ]; var layout = { height: 330, width:width*.8, font: font, showlegend: false, margin: margin, legend: { x: 1, xanchor: 'right', y: 1 }, annotations: [ { y: power_exceed.filter(e => e.Exceedance >= 0.95)[0].Power, x: 0.95, text: "P95 'Firm' Power - " + d3.format(',.1f')( power_exceed.filter(e => e.Exceedance >= 0.95)[0].Power ) + ' MW', showarrow: true, arrowhead: 2, ax: -40, ay: -70, xref: 'x', yref: 'y' } ], title: plotTitle( 'Power Exceedance'), xaxis: { showgrid: true, zeroline: false, ticks: 'outside', title: 'Exceedance %', tickformat:'%.0f' }, yaxis: { title: 'Power (MW)', zeroline: false, showline: false, separatethousands: true, range: [0, 200] } }; const div = DOM.element('div'); plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div} ` }41:T71f,{ var data = [ { y: pe_fdc.map(f => d3.format(',.1f')(f.Power)), x: pe_fdc.map(f => Math.round(f['Exceedance'] * 100)), mode: 'lines', name: 'Power', line: { shape: 'spline',color: colr(1) }, type: 'scatter' }, { y: [ d3.format(',.1f')( power_exceed.filter(e => e.Exceedance >= 0.95)[0].Power ) ], x: [95], mode: 'markers', marker: { color: colr(5), size: 10 }, type: 'scatter' } ]; var layout = { height: 330, width:width*.8, font: font, showlegend: false, margin: margin, legend: { x: 1, xanchor: 'right', y: 1 }, annotations: [ { y: power_exceed.filter(e => e.Exceedance >= 0.95)[0].Power, x: 95, text: "P95 'Firm' Power - " + d3.format(',.1f')( power_exceed.filter(e => e.Exceedance >= 0.95)[0].Power ) + ' MW', showarrow: true, arrowhead: 2, ax: -40, ay: -70, xref: 'x', yref: 'y' } ], title: plotTitle( 'Power by Flow Exceedance'), xaxis: { showgrid: true, zeroline: false, dtick: 10, ticks: 'outside', title: 'Flow Exceedance %' }, yaxis: { title: 'Power (MW)', zeroline: false, showline: false, separatethousands: true, range: [0, 200] } }; const div = DOM.element('div'); plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 10. Plant power output shown on an exceedance (top) and time of flow exceedance (bottom) basis. The P95 'firm' power is ${d3.format(',.1f')(power_exceed.filter(e => e.Exceedance >= 0.95)[0].Power)} MW

` }42:T4ee,html`

Low Head and Low Flow Shutdown

Under both the most extreme high flow and low flow events (floods and droughts) there are conditions where the power station cannot operate.

The minimum flow required to operate one turbine is ${format_flow(50)}. Where the whole river flow falls below approximately ${format_flow(120)} and depending on the month and therefore the required environmental flows then there may not be sufficient flow to operate a single turbine and the power station will be shut down. Prior to a low flow shutdown the power station will already be generating very little energy - approximately 11MW. In the simulation of power generation against the historic flow series there is only a single low flow shutdown event which continued for 10 days. This is approximately a 1 in 100 year event.

Because of the impact of flooding on the narrow downstream gorge, generation head decreases with increasing river flow. The power generating turbines are only able the operate down to a minimum net head of 10m which corresponds to whole river flow of ${format_flow(5350)} equivalent to a 5-year return flood event. At flows above this level there is insufficient head and the power station cannot operate. `43:T582,{ var data = [ { y: yearly.map( yr => ((yr.Energy / 1000 - summary.EnergyAdjustedMean) / summary.EnergyAdjustedMean) * 100 ), x: yearly.map(yr => yr.WaterYear), showlegend: true, name: 'Annual Energy', marker: { color: colr(1) }, type: 'bar' }, { y: flow_yearly.map(yr => yr.Flow_mean_pct_var), x: flow_yearly.map(yr => yr.WaterYear), marker: { color: 'rgba(0,0,0,0.4)' }, name: 'Mean Annual Flow', type: 'bar' } ]; var layout = { bargap: 0, width: width, height: 350, font: font, showlegend: true, margin: margin, legend: { x: 1, xanchor: 'right', y: 1 }, title: plotTitle('Annual Flow and Energy - Variation from the Mean'), xaxis: { showgrid: false, zeroline: false, ticks: 'outside', range: [1923, 2017] }, yaxis: { title: '% Variation From Mean', zeroline: false, tickformat: ',.2r', showline: false } }; const div = DOM.element('div'); plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 11. Total annual energy and mean flow as a percentage variation from their long term average. The percentage variation for mean annual flow is significantly higher than for total annual energy.

` }44:T4ab,{ var data = [ { x: flow_yearly.map(yr => yr.Flow_mean_pct_var), type: "histogram", name: "Mean Annual Flow", opacity: 1, marker: { color: 'rgba(0,0,0,0.4)' } }, { x: yearly.map( yr => ((yr.Energy / 1000 - summary.EnergyAdjustedMean) / summary.EnergyAdjustedMean) * 100 ), type: "histogram", name: "Annual Energy", opacity: 1, marker: { color: colr(1) } } ]; var layout = { width:width*.7, height: 300, font: font, title: plotTitle('Annual Flow and Energy - Variation from the Mean'), margin: margin(true), barmode: "overlay", yaxis: { title: 'Years (n:93)' }, xaxis: { title: '% Variation from Mean' } }; const div = DOM.element('div'); plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 12. Histograms of percent variaiton from the overall mean for annual energy and mean annual flow. The histogram for variation of mean annual flow is significantly wider than the histogram for variation of annual energy.

` }45:T543,{ var data = [ { y: years.map(f => Math.round(f.Energy / 1000)), x: years.map(f => Math.round(f.Flow_mean)), name: 'Mean Annual Flow', mode: 'markers', marker: { color: colr(1), symbol: 'x' }, type: 'scatter' }, { y: years.map(f => Math.round(f.Energy / 1000)), x: years.map(f => Math.round(f.Flow_median)), name: 'Median Annual Flow', mode: 'markers', marker: { color: colr(5), size: 4 }, type: 'scatter' } ]; var layout = { height: 350, width:width/5*4, font: font, showlegend: true, margin: { l: 90, r: 90, b: 50, t: 100 }, title: { text: 'Annual Flow and Energy Correlation', font: { size: 18 } }, xaxis: { showgrid: true, zeroline: false, ticks: 'outside', separatethousands: true, title: 'Flow (m\u00b3/s)' }, yaxis: { title: 'Annual Energy (GWh)', zeroline: false, showline: false, separatethousands: true } }; const div = DOM.element('div'); plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

Fig 13. Plots of mean and median annual flow against total annual energy for the simulated output over the historic flow series show poor correlation.

` }46:T465,function histo(monthNo) { let xs = monthly.filter(v => v.Month===monthNo) var data = [{ x: xs.map(v => v.Energy/1000), marker: {color: colr(2,0.8)}, type: 'histogram', hoverinfo: 'x+y', showlegend:false, name: '', histnorm: 'probability', }] var layout = { height: 170, width: width * 0.38, font: font, barmode:'overlay', showlegend: true, legend: {orientation:'v',xanchor: 'left', x:0, y: 1}, margin: {l: 65,r: 10,b: 45,t: 0}, xaxis: { showgrid: true, zeroline: false, ticks:'outside', title: 'GWh', range: [0,160]}, yaxis: { showgrid: false, zeroline: true, tickformat: '%,.2f', ticks:'outside', }}; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return html`

${div}

${monthNames[monthNo-1]}
Mean: ${d3.format(',.0f')(d3.mean(xs, v => v.Energy)/1000)} GWh
P50: ${d3.format(',.0f')(d3.quantile(xs, 0.5, v => v.Energy)/1000)} GWh

` }47:Te1c,function compare_years(year1, year2) { var data = [ { y: monthly .filter(mn => mn.WaterYear == year1) .map(mn => mn.Energy / 1000), x: monthly .filter(mn => mn.WaterYear == year1) .map(mn => mn.WaterMonth * 30), marker: { color: colr(1,0.5) }, yaxis: 'y2', showlegend: false, name: '', type: 'bar' }, { y: monthly .filter(mn => mn.WaterYear == year2) .map(mn => mn.Energy / 1000), x: monthly .filter(mn => mn.WaterYear == year2) .map(mn => mn.WaterMonth * 30), marker: { color: colr(5,0.5) }, yaxis: 'y2', showlegend: false, name: '', type: 'bar' }, { x: weekly.filter(yr => yr.WaterYear == year1).map(mn => mn.WaterWeek * 7), y: weekly.filter(yr => yr.WaterYear == year1).map(mn => mn.Flow), mode: 'lines', name: year1, type: 'scatter', line: { shape: 'spline', color: colr(1), width: 2 } }, { x: weekly.filter(yr => yr.WaterYear == year2).map(mn => mn.WaterWeek * 7), y: weekly.filter(yr => yr.WaterYear == year2).map(mn => mn.Flow), mode: 'lines', name: year2, type: 'scatter', line: { shape: 'spline', color: colr(5), width: 2 } } ]; var layout = { height: 300, margin: { l: 70, r: 70, b: 50, t: 50 }, legend: { x: 0, xanchor: 'left', y: 1 }, title: { text: year1 + ' and ' + year2 + ' Flow and Energy', font: { size: 18 } }, font: font, xaxis: { showgrid: false, zeroline: false, ticks: 'outside', //range: [0, 53], tickvals: [ 30.00, 60.00, 91.00, 122.00, 150.00, 181.00, 211.00, 242.00, 272.00, 303.00, 334.00, 364.00 ], ticktext: [ 'Oct', 'Nov', 'Dec', 'Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep' ] }, yaxis: { title: 'Flow (m\u00B3/s)', zeroline: false, tickformat: ',.2r', showline: false }, yaxis2: { showgrid: false, zeroline: false, showline: false, title: 'Energy GWh', separatethousands: true, tickformat: ',.0f', overlaying: 'y', side: 'right', range: [0, 300] } }; const div = DOM.element('div'); plt.newPlot(div, data, layout, { staticPlot: true }); return html`

${div}

	${year1}	${year2}
Mean Flow	${format_flow( flow_yearly.filter(y => y.WaterYear == year1)[0].Flow_mean )}	${format_flow( flow_yearly.filter(y => y.WaterYear == year2)[0].Flow_mean )}
Energy	${format_energy( yearly.filter(y => y.WaterYear == year1)[0].Energy / 1000 )}	${format_energy( yearly.filter(y => y.WaterYear == year2)[0].Energy / 1000 )}

`; }48:[{"id":"05209d4325f35da787fbdbeed4e682732b220a63b6f574624f28139ef85d00a276797fa2936db164ed386f37a08c5e5e04c5b353bd4f9d96510c7e9d6f60b0fa","href":"https://static.observableusercontent.com/files/05209d4325f35da787fbdbeed4e682732b220a63b6f574624f28139ef85d00a276797fa2936db164ed386f37a08c5e5e04c5b353bd4f9d96510c7e9d6f60b0fa","name":"power_and_energy_model.png","type":"image/png","lastModified":1582101937656.958,"size":49751}] 30:{"id":"4789fd723cf1fccd","slug":"power-and-energy","title":"Power and Energy","thumbnail":"f3ccf10e21db85c139a3d9db8ceebd90b11956f6ee3b5480de6c73c8af7b1466","access_level":"public","create_time":"$D2020-02-18T12:22:19.649Z","update_time":"$D2024-05-23T19:35:02.581Z","view_time":null,"first_public_time":"$D2020-02-21T09:14:49.346Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"3aaf4970407a12be","login":"westernpower","name":"Western Power","avatar_url":"https://avatars-next.observableusercontent.com/0c11a3086911e8caa71a7767a24de09ff93d85f36798166fa6c2d0b61107b761","tier":"starter_2024"},"version":2221,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"96924893937b5930","login":"andyflem","name":"Andy Fleming","avatar_url":"https://avatars-next.observableusercontent.com/fd3844143a4c29872f0df28a8ebce77bb56cebf2fa74bb669872e4def82ad809","tier":null}],"members":[{"type":"team","id":"3aaf4970407a12be","login":"westernpower","name":"Western Power","avatar_url":"https://avatars-next.observableusercontent.com/0c11a3086911e8caa71a7767a24de09ff93d85f36798166fa6c2d0b61107b761","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":3,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Power and Energy","cells":[{"id":0,"value":"html`\n

Power and Energy

Ngonye Falls Hydroelectric Project

\n
\n${book_index('power-and-energy')}\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":114,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2111,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1431,"value":"html`\n

Energy Generation

\nThe run-of-river hydroelectric power station will generate electricity by the action of water, diverted from the Zambezi river, turning hydropower turbines connected to electrical generator units.\n

\nAt any time, the power output of the station is proportional to the flow of water through the turbines - generation flow - and the difference in elevation between the inlet and outlet sides of the turbines - net head.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1669,"value":"tex.block`\n\nPower\\,MW \\:{\\displaystyle \\propto }\\: Generation\\,Flow * Head\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1673,"value":"html`\n\n\nThe maximum generation flow is set by the flow capacity of the canal which carries the water from the headworks, in the river upstream of the power station, to the powerhouse and turbines.\n

\nIn the case of the Ngonye Falls power station the narrow, constrained gorge downstream of the falls means that the net head varies with the total flow of water in the river. As river flow increases, the gorge fills with water and the elevation at the outlet side of the turbines (the tailrace) also rises, leading to lower net head.\n

\nThe effect of the net head increasing as flow decreases is that the power station produces proportionally more energy under lower flow conditions than other run-of-river power stations. However, this can also mean that under the highest flow conditions, net head can be insufficient to operate the turbines and the power stations must be shut down.\n`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1452,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":129,"value":"md`\n## Average Year Energy Generation\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":282,"value":"html`\nThe average (mean or P50 - median) pattern of generation through the year follows the pattern of rising and falling flows in the river.\n

\nHowever, there is a reduction in average energy production in the peak flow month of April because higher average flows lead to lower net head as explained in the section above.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":147,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2105,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":343,"value":"html`\n

Variation in Monthly Energy

\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1425,"value":"html`\nThe variation in energy output from year to year for a particular month is less in high flow months where there is generally sufficient water to fully use the power canal and run all four turbines. In March and April however, there may be so much flow that the downstream gorge floods and output is curtailed, by reduced head, so there is greater variability in production for these months.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1390,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2130,"value":"$38","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2166,"value":"$39","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2191,"value":"html`\n

${histo(1)}

${histo(2)}

${histo(3)}

${histo(4)}

${histo(5)}

${histo(6)}

${histo(7)}

${histo(8)}

${histo(9)}

${histo(10)}

${histo(11)}

${histo(12)}

\n \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":693,"value":"md`\n## Annual Energy\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":931,"value":"html`\nFigure 5 shows the total annual (October to September water year) energy which would have been produced by the power station operating across all of the period of the historic flow record. Each year from the historic flow record has a different hydrograph shape - including the timing of the onset of the flood and drought periods and the maximum and minimum flows - and each year therefore produces a different total energy yield.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":682,"value":"$3a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1895,"value":"html`\nFor the historic flow record, the highest annual energy production is ${d3.format(',.0f')(model.Max / 1000)} GWh from the 1963-64 water year and the lowest ${d3.format('.0f')(model.Min / 1000)} GWh from 1995-96.\n

\nThe lowest three energy production years from the historic record are highlighted in Figure 5. The 1948 water year yield of ${d3.format(',.0f')(yearly.filter(y=>y.WaterYear==1948)[0].Energy/1000)} GWh is more than 2 standard deviations from the mean. The two lowest energy yield years, 1994 (${d3.format(',.0f')(yearly.filter(y=>y.WaterYear==1994)[0].Energy/1000)} GWh) and 1995 (${d3.format(',.0f')(yearly.filter(y=>y.WaterYear==1995)[0].Energy/1000)} GWh), which are more than 3 standard deviations below the mean, are also consecutive. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1803,"value":"$3b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1650,"value":"$3c","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1050,"value":"$3d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1511,"value":"md`\n## Power Output\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1687,"value":"html`\nPlotting the plant's power output in megawatts against river flow or flow exceedance probability - the percentage of time that a particular flow is exceeded - shows how power reduces with very high flow, as the head decreases, as well well as at lower flows. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1310,"value":"$3e","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1535,"value":"$3f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1703,"value":"html`\nThe plot of power exceedance shows that the median power output is ${d3.format('.0f')(power_exceed.filter(e => e.Exceedance >= 0.5)[0].Power)}MW and the P95 'Firm' Power output - the power which is met or exceeded for 95% of the time - is ${d3.format('.0f')(power_exceed.filter(e => e.Exceedance >= 0.95)[0].Power)}MW. The 5% of the time where output is lower than the firm power is not evenly distributed across all years however and in the historic record of 94 years, power would not have dropped lower than this at all in ${d3.format('.0f')(100-yearly.filter(y=>y.Power_min e.Exceedance >= 0.95)[0].Power).length/yearly.length*100)}% of years. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2088,"value":"$40","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1330,"value":"$41","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1962,"value":"$42","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1985,"value":"table = {\n const avloss=d3.mean(lowhead.map(y=>y.Days*y.Month_power_max*24/1000));\n \n const tbl = d3.select(html`

`);\n\n //headers\n tbl\n .append('thead')\n .selectAll('td')\n .data(lowhead_display.columns)\n .join('td')\n .attr('class', 'header')\n .attr('style',(d,i)=>'width:' + lowhead_display.widths[i] + 'px')\n .text(d=>d);\n\n //rows\n const rows = tbl\n .selectAll('tr')\n .data(lowhead_display)\n .join('tr')\n .attr('class', 'row');\n\n const cells = rows\n .selectAll('td')\n .data(d => Object.entries(d))\n .join('td')\n .attr('class', d => d[0])\n .text(d => (isNaN(d[1]) ? d[1] : Math.round(d[1])));\n\n return html `\n\n ${tbl.node()}\n

Table 1. List of 13 flood events from the historic flow series which would have led to power station shut down due to low head.

\n `\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2069,"value":"text={\n const avloss=d3.mean(lowhead.map(y=>y.Days*y.Month_power_max*24/1000));\n return html`\nTable 1 shows the 13 flood events from the historic flow series which would have led to power station shut down due to low head. The shutdowns last on average ${d3.format('.0f')(d3.mean(lowhead.map(l=>l.Days)))} days (min 3, max 60 days). \n\n

\nThe low head shutdowns cause estimated average lost generation of ${d3.format('.0f')(avloss)} GWh, equivalent to ${d3.format('.0%')(avloss/838)} of P50 annual energy (min 13 GWh, max 159 GWh).\n`\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":997,"value":"md\n`\n## Variation in Energy and Flow\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":711,"value":"$43","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":862,"value":"$44","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1213,"value":"html`\n

Correlation in Energy and Flow

\nThe annual energy yield of the power station depends on the overall shape of the annual hydrograph and not on any simple measure of annual flow including mean, median or maximum flow.\n

\nFor this reason it is difficult to forecast with any certainty the future energy production of the power station by forecasting mean or median flow or any othe simple measure of the hydrograph. \n

\nFigure 13 shows the poor correlation between mean and median flow and energy yield for simulated production over the historic flow series. Figures 14 and 15 show hydrographs and monthly energy yield for two pairs of years which have similar mean flow and very different total energy yield or similar energy yield but very different mean flow.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1244,"value":"$45","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1124,"value":"html`\n

\n ${compare_years(1981,1944)}\n

Fig 14. Comparison of flow (lines) and modelled energy (bars) for 1944 and 1981. The mean flow for 1944 is nearly twice the mean flow of 1981 but the modelled energy output for the two years is almost identical. More energy would have been generated from the 'shoulder months' in 1944 particularly February and June but in April more energy would have been generated in 1981 because the very high flows in 1944 flood the gorge around the powerhouse and reduce the generation head.

\n ${compare_years(1960,1978)}\n

Fig 15. Comparison of flow (lines) and modelled energy (bars) for 1960 and 1978. The mean flow for the two years is almost identical but the modelled energy production is significantly higher for 1978 than for 1960. The energy production in 1960 is increased by the higher flows in all of the 'shoulder years' in the first half of the season - October to February.

Next: 5. Selected Years Simulations

Appendix

\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2193,"value":"$46","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":794,"value":"md`\n## Models\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":807,"value":"model_name='Base Case'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":805,"value":"model=models.filter(md=>md.ModelName==model_name)[0]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":802,"value":"models = (await d3.csv(\"https://gis.westernpower.org/data/input_data/models.csv?\" + Math.floor(Math.random() * 1000),d3.autoType))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":798,"value":"md`\n## Summary\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":41,"value":"summary={\nreturn {\n DebtEnergy_mean: d3.mean(sims_summary.map(s=>s.DebtEnergy)),\n DebtDiscountedEnergy_mean: d3.mean(sims_summary.map(s=>s.DebtDiscountedEnergy)), \n EquityEnergy_mean: d3.mean(sims_summary.map(s=>s.EquityEnergy)),\n EquityDiscountedEnergy_mean: d3.mean(sims_summary.map(s=>s.EquityDiscountedEnergy)), \n EnergyMean:d3.mean(yearly.map(yr=>yr.Energy/1000)),\n EnergyAdjustedMean: d3.mean(\n yearly.map(yr=>{\n if (yr.WaterYear==1994 || yr.WaterYear==1995 || yr.WaterYear==1948){\n return null \n } else{\n return yr.Energy/1000 \n }\n }))\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"md`## Load Data`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1987,"value":"lowhead_display = {\n const d = lowhead.map((y,i) => {\n return [\n i+1,\n d3.timeFormat('%d-%b-%Y')(y.StartDate),\n y.Days,\n y.Month_power_max,\n y.Days*y.Month_power_max*24/1000, \n ];\n });\n d['columns'] = [\n 'No',\n 'Date',\n 'Days of Shutdown',\n 'Average Power before Shutdown (MW)',\n 'Lost Energy Estimate (GWh)'\n ];\n d['widths'] = [1,20,20,40,40];\n return d;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1981,"value":"lowhead = await d3.csv(\"https://gis.westernpower.org/data/output_data/\" + model.OutputPrefix + \"lowheadshutdowns.csv?\" + Math.floor(Math.random() * 1000),d3.autoType)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1641,"value":"autocorrel = await d3.csv(\"https://gis.westernpower.org/data/output_data/\" + model.OutputPrefix + \"_pe_autocorrel.csv?\" + Math.floor(Math.random() * 1000),d3.autoType)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1325,"value":"power_exceed = await d3.csv(\n \"https://gis.westernpower.org/data/output_data/\" +\n model.OutputPrefix +\n \"_pe_power_exceed.csv?\" +\n Math.floor(Math.random() * 1000),\n d3.autoType\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1312,"value":"pe_fdc = await d3.csv(\n \"https://gis.westernpower.org/data/output_data/\" +\n model.OutputPrefix +\n \"_pe_fdc.csv?\" +\n Math.floor(Math.random() * 1000),\n d3.autoType\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1247,"value":"years = yearly.map(y => {\n return {\n WaterYear: y.WaterYear,\n Energy: y.Energy,\n Flow_mean: flow_yearly.filter(f => f.WaterYear == y.WaterYear)[0].Flow_mean,\n Flow_median: flow_yearly.filter(f => f.WaterYear == y.WaterYear)[0]\n .Flow_median,\n Flow_max: flow_yearly.filter(f => f.WaterYear == y.WaterYear)[0].Flow_max\n };\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":522,"value":"yearly = await d3.csv(\n \"https://gis.westernpower.org/data/output_data/\" +\n model.OutputPrefix +\n \"_pe_yearly.csv?\" +\n Math.floor(Math.random() * 1000),\n d3.autoType\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1073,"value":"weekly = await d3.csv(\n \"https://gis.westernpower.org/data/output_data/\" +\n model.OutputPrefix +\n \"_pe_weekly_slim.csv?\" +\n Math.floor(Math.random() * 1000),\n d3.autoType\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":309,"value":"monthly = (await d3.csv(\"https://gis.westernpower.org/data/output_data/\" + model.OutputPrefix + \"_pe_monthly.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":170,"value":"cum_energy={\n var total_energy=d3.sum(calmonths.map(mnth=>mnth.Energy_median))\n var sum=0;\n return calmonths.map(mnth=>{sum+=mnth.Energy_median;return Math.round(sum/total_energy*100);})\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1054,"value":"edc=(await d3.csv(\"https://gis.westernpower.org/data/output_data/\" + model.OutputPrefix + \"_pe_percentiles.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":143,"value":"calmonths=(await d3.csv(\"https://gis.westernpower.org/data/output_data/\" + model.OutputPrefix + \"_pe_calmonthly.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"sims_summary = (await d3.csv(\"https://gis.westernpower.org/data/output_data/\" + model.OutputPrefix + \"_pe_sims_summary.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"sims=(await d3.csv(\"https://gis.westernpower.org/data/output_data/\" + model.OutputPrefix + \"_pe_sims.csv?\" + Math.floor(Math.random() * 1000),d3.autoType))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1454,"value":"pefdc = (await d3.csv(\"https://gis.westernpower.org/data/output_data/\" + model.OutputPrefix + \"_pe_fdc.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":824,"value":"md`\n## Flow\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":822,"value":"flow_yearly = (await d3.csv(\"https://gis.westernpower.org/data/output_data/ngonye_flow_yearly.csv?\" + Math.floor(Math.random() * 1000),d3.autoType))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":284,"value":"flow_calmonths = (await d3.csv(\"https://gis.westernpower.org/data/output_data/ngonye_flow_calmonthly.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":359,"value":"fdcs = (await d3.csv(\"https://gis.westernpower.org/data/output_data/ngonye_vicfalls_fdcs.csv?\" + Math.floor(Math.random() * 1000), d3.autoType))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2195,"value":"monthNames = ['Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec']","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"md` ## Styling`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"import {font} from \"@andyflem/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1144,"value":"function format_energy(energy) {\n return d3.format(',.0f')(energy) + 'GWh';\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1138,"value":"function format_flow(flow) {\n return d3.format(',.0f')(flow) + 'm\\u00b3/s';\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1994,"value":"commonStyle","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2134,"value":"make_trans=function(col,opacity) {\n let c=d3.color(col)\n c.opacity=opacity\n return c.formatRgb()\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1199,"value":"md`\n## Builders\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1070,"value":"$47","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"md`## Libraries`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1992,"value":"import {commonStyle} from \"@andyflem/commonlibrary\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1839,"value":"import {book_index} from \"@andyflem/commonlibrary\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1369,"value":"import {plotTitle} from \"@andyflem/commonlibrary\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1366,"value":"import {margin} from \"@andyflem/commonlibrary\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1362,"value":"import {colr} from \"@andyflem/commonlibrary\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":689,"value":"import {movingAverage} from \"@andyflem/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"d3 = require(\"d3@5\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"plt = require(\"https://cdn.plot.ly/plotly-latest.min.js\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W48","stdlib":"1"}} 31:"$30:body"