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Cost of Wind James McCalley Harpole Professor of Electrical & Computer Engineering 1 Discount rate Discount rate, i. • the annual payment as a percentage of the amount owed; • the value given to possession of money now rather than later, since having it now allows it to be invested to earn a return. In this sense, the discount rate is the annual income as a percentage of the amount invested, i.e., average interest rate. 2 Moving single amounts in time “Future” amount of money 1 P F N (1 i ) “Present” amount of money F P (1 i) Monetary Value F P P(1+i) 1 P(1+i)2 2 3 4 Time Period 3 N N Number of time periods Observe that “F” may be a cost or a revenue. In either case, the equivalent amount of money in the present is smaller. • I prefer to incur a $100 cost later than a $100 cost now. • I prefer to obtain a $100 revenue now than a $100 revenue later. Annuitizing “Annual” amount of money i(1 i) N A P (1 i) N 1 A F i (1 i ) N 1 Monetary Value F P A 1 A 2 A 3 A 4 Time Period 4 A A N Note that payment A is made at the end of a period, so there is no payment made at the beginning of period 1, but there is a payment made at the end of period N. Inflation The discount rate does not reflect the effects of inflation. Inflation, e, changes the buying power of money. “Current dollars” are the actual cash flow that would occur during a particular year, m, accounting for inflation. “Constant dollars” are the dollars that would have been required if the cost was paid in the “base year,” n. We refer to this as “n dollars” as in “2012 dollars.” F F (1 e) N 5 N=m-n Inflation and discounting The discount rate in the absence of inflation is called the “real” discount rate, ir. The discount rate accounting for inflation is called the “nominal” discount rate, in. F F 1 F P N N N N (1 in ) (1 ir ) (1 ir ) (1 e) F Current dollar amount at year N (accounting for inflation) F Constant dollar amount at year N (without inflation) N N N (1 in ) (1 ir ) (1 e) (1 in ) (1 ir )(1 e) 6 in (1 ir )(1 e) 1 1 e ir ir e 1 e ir Levelized cost of energy Data Purchase cost Installation cost Levelized fixed charge rate Plant rating Capacity factor Nominal discount rate Wind Turbine $1820/kW $600000 20% 1.5 MW 0.35 Levelized fixed charge rate: • Capital cost • Return on investment • Depreciation • Fed and state income taxes • Property tax • Insurance costs 8% The initial investment is ($1820/kw)*1500kW+600000=$3,300,000 The fixed annual charges are then 0.2*3,300,000=$660,000. This is called the levelized annual revenue requirements (LARR) The average annual energy production is =Capacity*8760hrs/yr*CapacityFactor =1.5MW*8760hrs/yr*.35=4599MWhrs LARR 660000 LCOE $143.51/ MWhr AverageAnn ualEnergyP roduction 4599 7 Levelized cost of energy Data Purchase cost Installation cost Levelized fixed charge rate Plant rating Capacity factor Nominal discount rate Wind Turbine $1820/kW $600000 11.6% Levelized fixed charge rate: • Return on investment • Depreciation • Fed and state income taxes • Property tax • Insurance costs 1.5 MW 0.35 8% The initial investment is ($1820/kw)*1500kW+600000=$3,300,000 The fixed annual charges are then 0.116*3,300,000=$382,800. This is called the levelized annual revenue requirements (LARR) The average annual energy production is =Capacity*8760hrs/yr*CapacityFactor =1.5MW*8760hrs/yr*.35=4599MWhrs LARR 382,800 LCOE $83.24 / MWhr AverageAnn ualEnergyP roduction 4599 8 Levelized cost of energy Data Purchase cost Installation cost Levelized fixed charge rate Plant rating Capacity factor Nominal discount rate Wind Turbine $1820/kW $600000 20% Levelized fixed charge rate: • Return on investment • Depreciation • Fed and state income taxes • Property tax • Insurance costs 1.5 MW 0.40 8% The initial investment is ($1820/kw)*1500kW+600000=$3,300,000 The fixed annual charges are then 0.2*3,300,000=$660,000. This is called the levelized annual revenue requirements (LARR) The average annual energy production is =Capacity*8760hrs/yr*CapacityFactor =1.5MW*8760hrs/yr*.40=5256MWhrs LARR 660000 LCOE $125.58/ MWhr AverageAnn ualEnergyP roduction 5256 9 Levelized cost of energy Data Purchase cost Installation cost Levelized fixed charge rate Plant rating Capacity factor Nominal discount rate Wind Turbine $1820/kW $600000 11.6% Levelized fixed charge rate: • Return on investment • Depreciation • Fed and state income taxes • Property tax • Insurance costs 1.5 MW 0.40 8% The initial investment is ($1820/kw)*1500kW+600000=$3,300,000 The fixed annual charges are then 0.116*3,300,000=$382,800. This is called the levelized annual revenue requirements (LARR) The average annual energy production is =Capacity*8760hrs/yr*CapacityFactor =1.5MW*8760hrs/yr*.40=5256MWhrs LARR 382,800 LCOE $72.83/ MWhr AverageAnn ualEnergyP roduction 5256 10 Levelized cost of energy Resource PC plant NGCC plant Nuclear plant Wind, CF=0.35, FCR=20% Wind, CF=0.35, FCR=11.6% Wind, CF=0.40, FCR=20% Wind, CF=0.40, FCR=11.6% LCOE $59.94/MWhr $99.64/MWhr $66.49/MWhr $143.51/MWhr $83.24/MWhr $125.58/MWhr $72.83/MWhr Levelized cost of energy Additional note: Another term that should be added in is the annual operating expenses (AOE). This includes land lease cost, levelized O&M cost, and levelized replacement cost: AOE=LLC+LOM+LRC with units of $/year. So the expression for LCOE is LARR AOE LCOE AverageAnnualEnergyProduction AOE is generally only about 2% of the purchase cost. The above expression is sometimes expressed as: LARR LCOE AOE AverageAnnualEnergyProduction 12 which implies AOE is given in $/MWhr. Levelized cost of energy Data from Electric Power Research Institute 13 Nuclear Energy Institute, “The cost of new generating capacity in perspective,” Sept., 2011, available online at www.nei.org/resourcesandstats/documentlibrary/newplants/graphicsandcharts/the-cost-of-new-generating-capacity-in-perspective. Levelized cost of energy Data from US DOE Energy Information Administration 14 Nuclear Energy Institute, “The cost of new generating capacity in perspective,” Sept., 2011, available online at www.nei.org/resourcesandstats/documentlibrary/newplants/graphicsandcharts/the-cost-of-new-generating-capacity-in-perspective. Levelized cost of energy National Research Council (National Academies of Science and of Engineering) 15 Nuclear Energy Institute, “The cost of new generating capacity in perspective,” Sept., 2011, available online at www.nei.org/resourcesandstats/documentlibrary/newplants/graphicsandcharts/the-cost-of-new-generating-capacity-in-perspective. Representative split – capital costs This is for capital (investment) costs. It is for a representative wind turbine design, but one should recognize that there are different designs. But it does provide some indication of relative splits among major wind turbine components. Source: P. Jamieson, “Innovation in wind turbine design,” Wiley, 2011. Note – this book has an entire chapter dedicated to “Cost of Energy.” 16 Component Cost fraction Blades 0.177 Hub 0.077 Gearbox 0.143 Generator 0.076 Yaw system 0.019 Nacelle cover 0.020 Nacelle structure 0.040 Tower 0.219 Variable speed system 0.073 Pitch system 0.043 Rotor brake 0.006 Couplings 0.003 Shaft 0.041 Other 0.063 Total turbine 1.00 Representative split - LCOE Initial capital costs Turbine 0.820 0.569 Rotor Nacelle systems Source: P. Jamieson, “Innovation in wind turbine design,” Wiley, 2011. Note – this book has an entire chapter dedicated to “Cost of Energy.” Electrics and control O&M 0.180 17 Rotor lock 0.0057 Blades 0.1037 Hub 0.0142 Gearbox 0.0961 Generator 0.0378 Rotor brake 0.0085 Nacelle cover 0.0142 Nacelle structure 0.0193 Couplings 0.0057 Shaft 0.0171 Yaw system 0.0171 Bearings 0.0171 Pitch system 0.0365 Variable speed system 0.0551 Tower 0.0896 Other 0.0313 Balance of plant Roads & civil works 0.0221 0.251 Electrics and grid con 0.0761 Assembly & insttlltn 0.0073 Transportation 0.0365 Foundations 0.0675 Financial and legal 0.0414 Labor 0.0792 Parts 0.0630 Operation 0.0216 Equipment 0.0090 Facilities 0.0072 0.180