31:T6fe,{ var data = [ { y: calmonthlyFDCs.map(month=>month.flows[25]), x: calmonthlyFDCs.map(month=>month.waterMonth), mode: 'lines', name:'P25', hoverinfo:'none', line: {shape: 'spline',color: colr_b(4),dash:'dashdot', width:0.5}, type: 'scatter' }, { y: calmonthlyFDCs.map(month=>month.flows[50]), x: calmonthlyFDCs.map(month=>month.waterMonth), text: calmonthlyFDCs.map(month=>formatFlow(month.flows[50])), mode: 'lines+markers', name:'Median (P50)',hoverinfo:'text', line: {shape: 'spline', width:3}, marker: {color: colr_b(3), size:7}, type: 'scatter' }, { y: calmonthlyFDCs.map(month=>month.flows[75]), x: calmonthlyFDCs.map(month=>month.waterMonth), mode: 'lines', name:'P75',hoverinfo:'none', line: {shape: 'spline',color: colr_b(4),dash:'dashdot', width:0.5}, type: 'scatter' }]; var layout = { width: width>700?670:width-30, height: 200, margin:{t:10,b:30,l:70,r:5}, font: font, showlegend: true, legend: {x: 1,xanchor: 'right',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: 'Flow (m\u00B3/s)', zeroline: false, showline: false, separatethousands:true, } }; const div=container(`Fig 1. Average (P50), P25 and P75 flow for the Zambezi River at Ngonye Falls by month. In an average year the flow varies by over one order of magnitude from around 150${cumec} in September, October and November to nearly 3,000${cumec} in April.`) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }32:T431,{ var data = [{ x: flood_return.filter(fr=>fr.ReturnYears<=200).map(fr=>fr.ReturnYears), y: flood_return.filter(fr=>fr.ReturnYears<=200).map(fr=>fr.Flow), textposition: 'top', showlegend:false, marker: {color: colr_b(2), size: 15}, type: 'scatter', mode: 'markers+text', textfont: {color:'rgb(10,10,10)', size: 12}}, ]; var layout = { width: width>800?770:width-30, height:250, font: font, showlegend: true, margin:{t:10,b:50,l:70,r:5}, legend: {x: 1, xanchor: 'right', y: 1}, xaxis: { type: 'log', title: 'Return Period - Years (log scale)', showgrid: false, zeroline: false, ticks:'outside', }, yaxis: { title: 'Flow (m\u00B3/s)', zeroline: false, tickformat: ',.2r', showline: false } }; const div=container(`Fig 2. Annual maximum flood flows by return period for the Zambezi River at Ngonye Falls. The 200 year return flood is over 10,000${cumec}.`) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }33:T518,html`A small power station with low capacity that is limited to the flows available in the drought months will produce lower energy, will not be able to take advantage of the higher flows when they occur and will be inefficient at converting the available energy resource into electricity. For example a ${capacities_models[0].capacity}MW plant would waste ${d3.format(',.0%')(capacities_models[0].missed_resource_pct)} of all the water passing the Ngonye Falls in an average year.

In theory it is possible to produce significant power using flood flows. For example a plant with capacity for the mean maximum April flow of 3,000${cumec} could produce nearly 600MW of power while the flow of water in the river is above 3,000${cumec}.

Fig 3 is the Flow Duration Curve (FDC) for the Zambezi River at Ngonye Falls, showing the proportion of time (hours in an average year) that any particular flow is achieved or exceeded. From the FDC we can see that a flow of 3,000${cumec} is only exceeded for 9% of the time. This means that a power station with enough turbines and other machinery to generate a maximum of 600MW would only actually produce this power for 9% of its life and at all other times would be producing significantly less power and much of the plant would sit idle.`34:T619,{ var data = [{ y: fdc.map(f=>f.flow), x: fdc.map(f=>f.exceedance), text: fdc.map(f=>d3.format(',.0%')(f.Exceedance) + ', ' + format_flow(f.flow)), mode: 'lines', hoverinfo:'text', line: {shape: 'spline', color: colr_b(3), width: 3}, type: 'scatter' },{ y: [100, 1130], x: [0.3, 0.3], mode: 'lines', hoverinfo:'text', line: {width: 1, color: colr(2)}, type: 'scatter' },{ y: [1130, 1130], x: [0, 0.3], mode: 'lines', hoverinfo:'text', line: {width: 1, color: colr(2)}, type: 'scatter' }]; var layout = { height: 280, margin:{t:10,b:50,l:70,r:50}, width: width>800?770:width-30, font: font, showlegend: false, legend: {x: 1,xanchor: 'right',y: 1}, xaxis: { showgrid: true, zeroline: false, tickformat: ',.0%', ticks:'outside', title:'Exceedance' }, yaxis: { title: 'Flow (m\u00B3/s)', type:'log', zeroline: false, showline: false, separatethousands:true, } }; const div=container(`Fig 3. Flow Duration Curve - FDC or Exceedance curve for the Zambezi River at Ngonye Falls showing the proportion of time in each year that flow exceeds the given value. The flow exceeds ${d3.format(',.3r')(fdc.filter(f=>f.exceedance>=0.29)[0].flow)} m\u00b3/s for 30% of all days in the year on average. Median flow (P50) is ${d3.format(',.3r')(fdc.filter(f=>f.exceedance>=0.50)[0].flow)} m\u00b3/s`) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }35:T6bf,{ var data = [ { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>f.annual_energy), text: capacities_models.map(f=>d3.format(',.0f')(f.annual_energy) + 'GWh'), hoverinfo:'text', name:'Annual Energy', marker: {color: capacities_models.map(f=>f.capacity==180?make_trans(colr(5),0.8):make_trans(colr(2),0.6))}, type: 'bar', }, { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>(f.capacity_factor)), text: capacities_models.map(f=>d3.format(',.0%')(f.capacity_factor)), mode: 'lines+markers', name:'Capacty Factor',hoverinfo:'text+name', line: {shape: '', color: colr(6), dash:''}, type: 'scatter',yaxis: 'y2', } ]; var layout = { height: 240, margin:{t:10,b:50,l:70,r:50}, width: width>800?770:width-30, font: font, showlegend: true, legend: {orientation:'h', x: 0,xanchor: 'left',y: -0.15}, xaxis: { showgrid: true, zeroline: false, ticks:'outside', title:'Capacity MW', range:xRange,dtick: 45, }, yaxis: { showgrid: false, title: 'Annual Energy
(GWh)', tickformat:',.0f', }, yaxis2: { showgrid: false, title: 'Capacity Factor', tickformat:',.0%', overlaying: 'y', side: 'right' } }; const div=container(`Fig 4. Median (P50) annual energy produced by the Ngonye Falls plant with increasing power station size (bars) and corresponding plant Capacity Factor (line). 45MW increments of capacity correspond with bulb turbine units recommended for the head-flow conditions at Ngonye Falls.`) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }36:T598,{ var data = [ { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>(f.missed_resource_pct)), text: capacities_models.map(f=>d3.format(',.0%')(f.missed_resource_pct)), name: 'Proportion of Water Wasted',hoverinfo:'text+name', marker: {color: capacities_models.map(f=>f.capacity==180?make_trans(colr(5),0.8):make_trans(colr(2),0.6))}, type: 'bar' } , { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>(f.capacity_factor)), text: capacities_models.map(f=>d3.format(',.0%')(f.capacity_factor)), mode: 'lines+markers', name:'Capacty Factor',hoverinfo:'text+name', line: {shape: '', color: colr(6), dash:''}, type: 'scatter', } ]; var layout = { height: 230, width: width>800?770:width-30, font: font, showlegend: true, margin:{t:10,b:50,l:70,r:50}, legend: {orientation:'h', x: 1,xanchor: 'right',y: 1}, xaxis: { showgrid: true, zeroline: false, dtick:45, ticks:'outside', title:'Capacity MW', range:xRange }, yaxis: { showgrid: false, tickformat:',.0%', } }; const div=container(`Fig 5. The proportion of all of the water flowing through the Ngonye Falls not used for power generation (bars) and the Capacity Factor (line) for increasing power station sizes.`) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }37:T946,{ var data = [ { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>(f.costs.epc.civils.total)), mode: 'lines', stackgroup:'one', hoverinfo:'none',line:{width:0}, type: 'scatter', name: 'Civils' }, { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>(f.costs.epc.mech.total)), mode: 'lines', stackgroup:'one', hoverinfo:'none',line:{width:0}, type: 'scatter', name: 'Hydro & elect' }, { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>(f.costs.epc.tline)), mode: 'lines', stackgroup:'one', hoverinfo:'none',line:{width:0}, type: 'scatter', name: 'T-Line' }, { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>(f.costs.epc.eam)), mode: 'lines', stackgroup:'one', hoverinfo:'none',line:{width:0}, type: 'scatter', name: 'Eng, admin & manag' }, { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>(f.costs.other.total)),line:{width:0}, mode: 'lines', stackgroup:'one', hoverinfo:'none', type: 'scatter', name: 'Other' }, { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>(f.costs.financing)),line:{width:0}, mode: 'lines', stackgroup:'one', hoverinfo:'none', type: 'scatter', name: 'Financing' } ,{ x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>(f.costs.total)), text: capacities_models.map(f=>(f.capacity + 'MW, $' + d3.format('.0f')(f.costs.total) + 'm')), mode: 'lines', hoverinfo:'text', line:{color:colr(6)}, type: 'scatter', name: 'Total' } ]; var layout = { height: 300, width: width>800?770:width-30, font: font, showlegend: true, margin: {t:10,b:0,l:70,r:50}, legend: {orientation:'h', x: 0, y:-0.47, xanchor: 'left',yanchor: 'bottom'}, xaxis: { showgrid: true, zeroline: false, ticks:'outside', range:xRange,dtick: 45, }, yaxis: { title: 'Cost ($m)', zeroline: false, showline: false, range:[0,1200], separatethousands:true, } }; const div=container(`Fig 7. Project cost components and total project cost for the Ngonye Falls power station with increasing power station capacity.`) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }38:T69c,{ var data = [ { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>d3.format('.2f')(f.costs.specific_capacity)), text:capacities_models.map(f=>'$' + d3.format('.2f')(f.costs.specific_capacity) + 'm/MW'), name: 'Capacity unit cost',hoverinfo:'text+name', marker: {color: capacities_models.map(f=>f.capacity==180?make_trans(colr(5),0.8):make_trans(colr(2),0.6))}, type: 'bar' }, { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>(f.capacity_factor)), text: capacities_models.map(f=>d3.format(',.0%')(f.capacity_factor)), mode: 'lines+markers', name:'Capacty factor',hoverinfo:'text+name', line: {shape: '', color: colr(6), dash:''}, type: 'scatter',yaxis: 'y2', } ]; var layout = { height: 220, width: width>800?770:width-30, font: font, showlegend: true, margin: {t:10,b:50,l:70,r:50}, legend: {x: 1,xanchor: 'right',y: 1}, xaxis: { showgrid: true, zeroline: false, dtick:45, ticks:'outside', title:'Capacity MW', range:xRange }, yaxis: { title: 'Unit Cost
($m/MW)', zeroline: false, showline: false, showgrid: false, separatethousands:true, }, yaxis2: { showgrid: false, title: 'Capacity Factor', tickformat:',.0%', overlaying: 'y', side: 'right' } }; const div=container(`Fig 8. Construction cost per MW of installed capacity (bars) and Capacity Factor (line) for the Ngonye Falls power station with increasing installed capacity.`) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }39:T572,relativeCostChart={ var data = [ { x: capacities_models.map(f=>f.capacity), y: capacities_models.map(f=>d3.format('.2f')(f.costs.specific_annual_energy)), text: capacities_models.map(f=>'$' + d3.format('.2f')(f.costs.specific_annual_energy) + 'm'), mode: 'lines', fill:'tozeroy', hoverinfo:'text', marker: {color: capacities_models.map(f=>f.capacity==180?make_trans(colr(5),0.8):make_trans(colr(2),0.6))}, type: 'bar' } ]; var layout = { height: 250, margin: {t:10,b:50,l:70,r:50}, width: width>800?770:width-30, font: font, showlegend: false, legend: {x: 1,xanchor: 'right',y: 1}, xaxis: { showgrid: true, zeroline: false,dtick:45, ticks: 'outside', title: 'Capacity MW', range: xRange }, yaxis: { title: 'Relative Cost
of Electricity', zeroline: false, showticklabels: false, showline: false, separatethousands: true, range: [0.75,1.04] } }; const div=container(`Fig 9. Relative cost of electricity for increasing installed capacity for the Ngonye Falls power station. Calculated by dividing the project cost for the capacity by the median average annual energy generated by that capacity (P50 energy). Proportional to the required electricity tariff.`) plt.newPlot(div, data, layout,{displayModeBar: false}); return div }3a:Tbc1,{ const mod = capacities_models[3] return html `

Appendix 1 - Cost Model

EPC Costs - Subject to Tender			${mod.capacity}MW
	Headworks and ancillary infrastructure	Fixed $42m	${forM(mod.costs.epc.civils.fixed)}
	Canal and forebay	$30m plus $0.156m per MW	${forM(mod.costs.epc.civils.capacity)}
	Powerhouse	$25m plus $5m per unit	${forM(mod.costs.epc.civils.powerhouse)}
	EPC Civils P&G	${d3.format(',.0%')(costParams.pg_pct)} of EPC Civils	${forM(mod.costs.epc.civils.pg)}
	Total Civil Costs		${forM(mod.costs.epc.civils.total)}
	Electromechanical - turbines and generators	17 + (4.6826*capacity^0.5849)	${forM(mod.costs.epc.mech.electro)}
	Hydromechanical equipment - gates and racks	10 + 0.163 * capacity	${forM(mod.costs.epc.mech.hydro)}
	Total electro and hydromechanical		${forM(mod.costs.epc.mech.total)}
	T-Line Cost	Fixed cost of 110km of 330kV	${forM(mod.costs.epc.tline)}
	EPC Engineering Administration and Management	${d3.format(',.0%')(costParams.eam_pct)} of EPC Costs	${forM(mod.costs.epc.eam)}
Total EPC Cost			${forM(mod.costs.epc.total)}
Construction Contingency		${d3.format(',.0%')(costParams.contingency_pct)} of EPC Costs	${forM(mod.costs.other.contingency)}
Construction Supervision		${d3.format(',.0%')(costParams.supervision_pct)} of EPC Costs	${forM(mod.costs.other.supervision)}
Other Costs		RAP and ESIA costs, supervision, development and insurance	${forM(mod.costs.other.total-mod.costs.other.contingency-mod.costs.other.supervision)}
Financing Costs Costs		Tax, interest during construction, working capital	${forM(mod.costs.financing)}
TOTAL COST			${forM(mod.costs.total)}

`}3b:T462,capacities_models = capacities.map(cap => { const eff = 0.93 const maxUnitSize = 45 const model = { capacity: cap, units: d3.max([Math.ceil(cap / maxUnitSize),1]), canal_capacity: cap/9.81/eff/19*1000 } model.max_river_flow=grossFlow(model.canal_capacity) model.annual_energy = fdc.reduce((en, ex) => { const generation_flow = (ex.flow < model.max_river_flow)?availableFlow(ex.flow):model.canal_capacity return en + (generation_flow * 9.81 * head(ex.flow) * eff / 1000) * (365*24/1001) },0) / (fdc.length-1) model.missed_resource_pct = fdc.reduce((en, ex) => { const generation_flow = (ex.flow < model.max_river_flow)?availableFlow(ex.flow):model.canal_capacity return en + ((ex.flow - generation_flow) * (60*60*24*(365/1000)))/1000000 },0)/total_resource if (model.capacity==45) {model.annual_energy = d3.min([model.annual_energy,379])} model.capacity_factor = model.annual_energy / (model.capacity * 365 * 24 / 1000) model.costs = projectCost(cap,model.units) model.costs.specific_annual_energy=model.costs.total/model.annual_energy return model }) 3c:T606,projectCost = function (capacity, units) { const costs = { epc: { civils: { fixed: 42, capacity: 30 + 0.156 * capacity, powerhouse: 25 + 5 * units, }, mech: { electro: (4.6826*capacity**0.5849)+17, hydro: 10 + 0.163 * capacity }, tline: 40 } } costs.epc.civils.total = costs.epc.civils.fixed + costs.epc.civils.capacity + costs.epc.civils.powerhouse costs.epc.civils.pg = costs.epc.civils.total * costParams.pg_pct costs.epc.civils.total += costs.epc.civils.pg costs.epc.mech.total = costs.epc.mech.electro + costs.epc.mech.hydro costs.epc.works = costs.epc.mech.total + costs.epc.civils.total + costs.epc.tline costs.epc.eam = costs.epc.works * costParams.eam_pct costs.epc.total = costs.epc.eam + costs.epc.works costs.other={} costs.other.rap_esia = 11 costs.other.dev = 38 costs.other.contingency = costs.epc.total * costParams.contingency_pct costs.other.supervision = costs.epc.total * costParams.supervision_pct costs.other.project_company = 9 costs.other.insurance = costs.epc.total * costParams.insurance_pct costs.other.total = costs.other.rap_esia + costs.other.dev + costs.other.contingency + costs.other.supervision + costs.other.project_company + costs.other.insurance costs.construction = costs.other.total + costs.epc.total costs.financing = costs.construction * costParams.finance_pct costs.total = costs.construction + costs.financing costs.specific_capacity = costs.total/capacity return costs }3d:T46a,chartA = function(marginData, xAxisRange) { var data = [{ x: marginData.map(f=>f.capacity), y: marginData.map(f=>f.energy_pct), name:'Energy', textposition: 'auto', textfont:{size:11}, type: 'bar', marker:{ color: make_trans(colr(2),0.6), }, },{ x: marginData.map(f=>f.capacity), y: marginData.map(f=>f.cost_pct), name:'Cost', textposition: 'auto', textfont:{size:11}, type: 'bar', marker:{ color: make_trans(colr(4),0.6), }, }]; var layout = { height: 230, width: width>800?770 : width-30, font: font, showlegend: true, margin: {t:10, b:50, l:70, r:50}, legend: {x: 1, y: 1, xanchor: 'right'}, xaxis: { showgrid: true, zeroline: false, ticks: 'outside', title: 'Capacity MW', range: xAxisRange, dtick: 45, }, yaxis: { title: 'Incremental Energy
and Cost', tickformat:'%.0f', zeroline: false, showline: false, separatethousands:true, } }; const div=DOM.element('div') plt.newPlot(div, data, layout,{displayModeBar: false}); return div }3e:[{"id":"27450b7c388fa717f49c2626cb2b6c6f6d32e1c5ff0fcd2d0b8fda7ca7e6d9d8eded261f1184525aa6874b0d15fe46722ec5591bfaee78b8ba022b258686dfe6","href":"https://static.observableusercontent.com/files/27450b7c388fa717f49c2626cb2b6c6f6d32e1c5ff0fcd2d0b8fda7ca7e6d9d8eded261f1184525aa6874b0d15fe46722ec5591bfaee78b8ba022b258686dfe6","name":"Screenshot 2023-02-28 112549.png","type":"image/png","lastModified":1677582107679.319,"size":52327},{"id":"00f9a762cbe409ef6057bca0678849431018baa8f52a49eb4311a908f8ccf20cc254e2fc0f5fc694a51395e240b3f6e1ff9fd713e6d3ae90f7d32e7db83e4563","href":"https://static.observableusercontent.com/files/00f9a762cbe409ef6057bca0678849431018baa8f52a49eb4311a908f8ccf20cc254e2fc0f5fc694a51395e240b3f6e1ff9fd713e6d3ae90f7d32e7db83e4563","name":"LayoutComponents.png","type":"image/png","lastModified":1668584422992.269,"size":138543}] 2f:{"title":"Techno-economic Optimisation","cells":[{"id":0,"value":"

Techno-economic Optimisation

Ngonye Falls Hydroelectric Project

\n${book_index('technoeconomic-optimisation')}\n\nThe Ngonye Falls Hydroelectric Project is a run-of-river electricity generation project on the Zambezi River currently under development by Western Power Company. It seeks to utilise the potential of the Ngonye Falls by diverting water from above the falls and passing it through hydropower turbines before returning water to the river four kilometres downstream.\n","pinned":false,"hidden":false,"mode":"html"},{"id":1483,"value":"

Introduction

","pinned":false,"hidden":false,"mode":"html"},{"id":1237,"value":"The size in MW of run-of-river hydroelectric power stations, such as Ngonye Falls, needw to be optimised to balance the financial economies-of-scale afforded by building larger sized plants with the diminishing return in additional energy production of larger plants.\n

\nThis process, a techno-economic optimisation, has been completed for the proposed Ngonye Falls power station by the design engineering consultants, Mott MacDonald, to establish an optimum plant size of 180MW, balancing electricity production with project capital cost.","pinned":false,"hidden":false,"mode":"html"},{"id":1493,"value":"

First Pass Analysis

","pinned":false,"hidden":false,"mode":"html"},{"id":1503,"value":"Prior to undertaking a detailed techno-economic optimisation it is usual to complete a first pass assessment of the hydropower resource to determine the likely range for optimum installed capacity.","pinned":false,"hidden":false,"mode":"html"},{"id":1507,"value":"In their report Hydroelectric Power - A Guide for Developers and Investors, the IFC recommend that run-of-river power stations such as Ngonye Falls should be sized based on a design discharge equal to P30 river flow (flows that are exceeded for 30% of the time).","pinned":false,"hidden":false,"mode":"html"},{"id":1509,"value":"{\n const div=container(``)\n div.prepend(html`

`)\n return div\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1538,"value":"Fig 3. below, the flow duration curve (FDC) shows that the P30 river flow at Ngonye is 1,130 ${cumec}.","pinned":false,"hidden":false,"mode":"html"},{"id":1156,"value":"

Hydrology and Power & Energy

","pinned":false,"hidden":false,"mode":"html"},{"id":1176,"value":"The output electrical power in megawatts (MW) of any hydroelectric power station is proportional to the flow of water through the generators and the head (difference in height) at the power station.\n

\nThe Ngonye Falls hydroelectric power station is \"run-of-river\" which means it has no dam and no storage reservoir holding water. This means that the flow of water for power generation can only come from the flow of water in the river at any given time and will vary through the year with the annual cycle of rain in the upstream river catchment.\n

\nFig 1. shows that in an average year the flow of water in the Zambezi River at Ngonye Falls varies from less than 200${cumec} in October to nearly 3,000${cumec} in April. The flood frequency analysis in Fig 2. shows that in the most extreme flood years the flow in the river can reach nearly 10,000${cumec}. ","pinned":false,"hidden":false,"mode":"html"},{"id":721,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":1192,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":1224,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":758,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":1252,"value":"Fig 4. shows the amount of energy (GWh) that would be produced by the Ngonye Falls plant in an average year for increasingly large power stations with higher installed capacity. Each step of increase in installed capacity produces more electricity in an average year by allowing the power station to utilise more of the flood flows. However, as these flood flows occur for shorter and shorter periods there is a diminishing return of increased energy production.","pinned":false,"hidden":false,"mode":"html"},{"id":545,"value":"$35","pinned":false,"hidden":false,"mode":"ojs"},{"id":1408,"value":"The extent to which the power station operates at full capacity is given by the plant's capacity factor. A capacity factor of 100% means the plant is running at full output all of the time in an average year. No run-of-river hydroelectric power station has a capacity factor of 100% as this would be extreamely inefficient in water resources and financial capital.\n

\nFig 5. shows the proportion of all water flowing over the Ngonye Falls in an average year that would be wasted without producing electricity for increasing power station installed capacity. Even large plant sizes cannot utilise the very high flood flows and a significant proportion of the water is not used for generation.","pinned":false,"hidden":false,"mode":"html"},{"id":1371,"value":"$36","pinned":false,"hidden":false,"mode":"ojs"},{"id":1158,"value":"

Capacity and Project Cost

","pinned":false,"hidden":false,"mode":"html"},{"id":1428,"value":"The cost of electricity produced by hydroelectric power stations is almost entirely due to the construction cost of the plant as there are no fuel costs and operations and maintenance costs (O&M) are relatively low.\n

\nThe construction cost can be split into fixed costs - which are the same no matter what capacity of power station is built - and partially variable costs - with a fixed component and a component that varies depending on the capacity and size of the plant. \n

\nFig 6. shows a view of the Ngonye Falls power station highlighting those elements of the infrastructure with fixed costs and those with fixed and variable cost components. For example headworks (weirs, embankments and barrage) must be constructed in exactly the same way and at exactly the same size for a 45MW plant as for a 360MW plant. However, the power canal which conveys the water to the powerhouse for generation will increase in size as the capacity of the power station increases.","pinned":false,"hidden":false,"mode":"html"},{"id":1144,"value":"{\n const div=container(`Fig 6. Layout and primary infrastructure elements of the Ngonye Falls power station. Infrastructure elements marked in red have a fixed cost irrespective of the installed capacity. Those marked in green have a fixed cost and a cost component that increases with increasing installed capacity.`)\n div.prepend(html`

`)\n return div\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1439,"value":"Appendix 1 - Cost Model shows how the project cost for the project is estimated based on the installed plant capacity. In Fig 7. the estimated total project cost is shown for increasing power station size.","pinned":false,"hidden":false,"mode":"html"},{"id":460,"value":"$37","pinned":false,"hidden":false,"mode":"ojs"},{"id":1451,"value":"Fig 8. Shows the construction cost per MW of installed capacity as the size of the plant increases. Total project cost rises with the plant capacity but the combination of fixed costs and costs proportional to capacity means that the cost rises more slowly than the capacity giving rise to economies of scale.\n

\nAlthough total average annual energy production increases with increasing capacity of plant (Fig 4.) it does so at a decreasing rate giving rise to a diminishing return in energy production.","pinned":false,"hidden":false,"mode":"html"},{"id":703,"value":"$38","pinned":false,"hidden":false,"mode":"ojs"},{"id":1164,"value":"

Cost of Electricity and Optimisation

","pinned":false,"hidden":false,"mode":"html"},{"id":1458,"value":"Fig 9. shows, for increasing plant sizes, the construction cost of the power station (Fig 7.) divided by the average annual energy production for that size of plant (Fig 4.) This gives a measure of the relative cost of the electricity produced and has a minimum at an installed capacity of 180MW.\n

\nAt plant sizes below 180MW the natural energy resource of the river and financial investment are being inefficiently applied for energy generation leading to higher costs.\n

\nAt plant sizes above 180MW the plant is under-utilised for too much of the time and a higher cost of electricity results.\n","pinned":false,"hidden":false,"mode":"html"},{"id":145,"value":"$39","pinned":false,"hidden":false,"mode":"ojs"},{"id":1468,"value":"Fig 10. shows the percentage increase in both project cost and energy for each incremental increase in capacity. For example, increasing the plant size from 45MW to 90MW leads to a 60% in annual energy production for only a 15% increase in project costs. Increasing the plant size from 225MW to 270MW requires 8% more investment but only yields 5% more energy.\n

\nFrom Fig 10. is is apparent that increasing the plant size from 135MW to 180MW is economic as it produces 11% more energy for a 10% increase in investment. However, adding an additional 45MW of capacity to 225MW is not economic as it requires a 9% increase in cost for only 8% additional energy.","pinned":false,"hidden":false,"mode":"html"},{"id":928,"value":"{\n const div=container(`Fig 10. Additional energy produced and cost required for each additional 45MW of generation capacity added to the Ngonye Falls power station. The top chart shows the full range of capacities and the bottom chart only 90 to 270MW for clarity.`)\n div.prepend(chartA(JSON.parse(JSON.stringify(margins)).slice(2,6), xRange))\n div.prepend(chartA(margins, xRange))\n return div\n}\n\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":615,"value":"$3a","pinned":false,"hidden":false,"mode":"ojs"},{"id":1477,"value":"","pinned":false,"hidden":false,"mode":"ojs"},{"id":1030,"value":"

\n

Setup

","pinned":false,"hidden":false,"mode":"html"},{"id":1472,"value":"import {book_index} from \"@westernpower/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":1028,"value":"

Model Functions

","pinned":false,"hidden":false,"mode":"html"},{"id":767,"value":"margins = {\n return capacities_models.map((model, index) => {\n const ret = {\n capacity:model.capacity\n }\n if (index>0) {\n const prev = capacities_models[index-1]\n ret.energy = model.annual_energy - prev.annual_energy\n ret.cost = model.costs.total - prev.costs.total\n ret.energy_pct = ret.energy/prev.annual_energy\n ret.cost_pct = ret.cost/prev.costs.total\n } else {\n ret.energy_pct = 1\n ret.cost_pct = 1\n }\n return ret\n })\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":340,"value":"$3b","pinned":false,"hidden":false,"mode":"ojs"},{"id":1340,"value":"total_resource =fdc.reduce((en, ex) => {\n return en + ((ex.flow) * (60*60*24*(365/1000)))/1000000\n },0)","pinned":false,"hidden":false,"mode":"ojs"},{"id":334,"value":"capacities = Array.from(Array(8).keys()).map(c=>c*45 + 45) //Array.from(Array(25).keys()).map(c=>c*10 + 70)","pinned":false,"hidden":false,"mode":"ojs"},{"id":588,"value":"costParams={\n return {\n pg_pct: 0.23,\n eam_pct:0.25,\n contingency_pct:0.075,\n supervision_pct: 0.04,\n insurance_pct: 0.01,\n finance_pct: 0.23\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":223,"value":"$3c","pinned":false,"hidden":false,"mode":"ojs"},{"id":59,"value":"tailwater=function(q) {\n const lQ = Math.log10(q)\n if (lQ > 3.8) {\n return (-21.429 * lQ**2) + (182.03 * lQ) + 597.15\n }\n if (lQ<=3.8 && lQ > 2.3) {\n return (6.5299 * lQ**2 - 30.155 * lQ) + 999.52\n }\n if (lQ<= 2.3) {\n return (-2.6828 * lQ**2) + (11.265 * lQ) + 952.68\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":68,"value":"headpond = function (q) {\n if (q < 5000) {\n return 990\n }\n if (q < 7500) {\n return (0.000081370 * q) + 989.6\n }\n return (0.000240 * q) + 988.4\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":187,"value":"availableFlow = function(q) {\n if (q>400) {\n return q*0.7\n } \n return q*0.7\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":367,"value":"grossFlow = function(q) {\n if (q>400) {\n return q/0.7\n } \n return q/0.7\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":70,"value":"headloss = function (q) { return q / 1300 }","pinned":false,"hidden":false,"mode":"ojs"},{"id":163,"value":"head = function(q) {\n return headpond(q) - tailwater(q) - headloss(q)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1024,"value":"

Load Data

","pinned":false,"hidden":false,"mode":"html"},{"id":1195,"value":"flood_return = (await d3.csv(server + '/other/ngonye_floods.csv?' + Math.floor(Math.random() * 1000),d3.autoType))","pinned":false,"hidden":false,"mode":"ojs"},{"id":1599,"value":"calmonthlyFdc_raw = (await d3.csv( hydrologyFolder + \"\tcalMonthlyFlowExceedance.csv?\" + Math.floor(Math.random() * 1000),d3.autoType))","pinned":false,"hidden":false,"mode":"ojs"},{"id":1601,"value":"calmonthlyFDCs = Array.from({ length: 12 }, (v, i) => {\n return {\n waterMonth: i+1,\n flows: calmonthlyFdc_raw.map(l=>l[i+1]),\n exceedance: calmonthlyFdc_raw.map(l=>l.exceedance),\n }\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"fdc = (await d3.csv(hydrologyFolder + 'fdc.csv?' + Math.floor(Math.random() * 1000),d3.autoType))","pinned":false,"hidden":false,"mode":"ojs"},{"id":1580,"value":"hydrologyFolder = `${server}/syntheticFlowSeries/${hydrologySet}/processed/`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1578,"value":"hydrologySet='2024'","pinned":false,"hidden":false,"mode":"ojs"},{"id":1576,"value":"server='https://data.westernpower.org'","pinned":false,"hidden":false,"mode":"ojs"},{"id":1006,"value":"

Formatting and helper functions

","pinned":false,"hidden":false,"mode":"html"},{"id":1593,"value":"function formatFlow(flow) {\n return d3.format(',.2r')(flow) + ' m\\u00b3/s'\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":888,"value":"$3d","pinned":false,"hidden":false,"mode":"ojs"},{"id":783,"value":"xRange=[20,380]","pinned":false,"hidden":false,"mode":"ojs"},{"id":17,"value":"import {plotTitle} from \"@andyflem/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":752,"value":"import {format_flow} from \"@westernpower/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":15,"value":"import {margin} from \"@andyflem/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":961,"value":"container = function(captionText) {\n const div=DOM.element('div')\n div.setAttribute(\"class\",\"border m-2 p-2\")\n div.setAttribute(\"style\",`width: ${width>800?800:width}px`)\n if (captionText) {\n const caption=DOM.element('figcaption')\n caption.append(captionText)\n div.append(caption)\n }\n return div\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"import {font} from \"@andyflem/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"import {colr} from \"@andyflem/commonlibrary\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":1551,"value":"function colr_b(i = 1, a = 1) {\n return d3hsv.hsv(215, 1, ((6 - i + 1.5) * 15)/120, a).toString();\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1001,"value":"cumec=`m\\u00b3/s`","pinned":false,"hidden":false,"mode":"ojs"},{"id":982,"value":"html`\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":809,"value":"make_trans=function(col,opacity) {\n let c=d3.color(col)\n c.opacity=opacity\n return c.formatRgb()\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":633,"value":"forM=function(val) {\n return '$' + d3.format(',.0f')(val)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":967,"value":"style=html`css `","pinned":false,"hidden":false,"mode":"ojs"},{"id":1011,"value":"

Import Libraries

","pinned":false,"hidden":false,"mode":"html"},{"id":9,"value":"d3 = require(\"d3@5\",\"d3-hsv@0.1\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"plt = require(\"https://cdn.plot.ly/plotly-latest.min.js\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":1553,"value":"d3hsv = require(\"d3-hsv@0.1\")","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W3e","stdlib":"1","titling":"auto"}