1. Cost of Wind 1 James McCalley Harpole Professor of Electrical & Computer Engineering

2. Discount rate 2 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.

3. Moving single amounts in time 3 “Present” amount of money “Future” amount of money 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.

4. Annuitizing 4 “Annual” amount of money 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.

5. Inflation 5 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.” N=m-n

6. Inflation and discounting 6 The discount rate in the absence of inflation is called the “real” discount rate, i r. The discount rate accounting for inflation is called the “nominal” discount rate, i n. Current dollar amount at year N (accounting for inflation) Constant dollar amount at year N (without inflation)

7. Levelized cost of energy DataWind Turbine Purchase cost$1820/kW Installation cost$600000 Levelized fixed charge rate 20% Plant rating1.5 MW Capacity factor0.35 Nominal discount rate 8% Levelized fixed charge rate: Capital cost Return on investment Depreciation Fed and state income taxes Property tax Insurance costs 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 7

8. Levelized cost of energy DataWind Turbine Purchase cost$1820/kW Installation cost$600000 Levelized fixed charge rate 11.6% Plant rating1.5 MW Capacity factor0.35 Nominal discount rate 8% Levelized fixed charge rate: Return on investment Depreciation Fed and state income taxes Property tax Insurance costs 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 8

9. Levelized cost of energy DataWind Turbine Purchase cost$1820/kW Installation cost$600000 Levelized fixed charge rate 20% Plant rating1.5 MW Capacity factor0.40 Nominal discount rate 8% Levelized fixed charge rate: Return on investment Depreciation Fed and state income taxes Property tax Insurance costs 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 9

10. Levelized cost of energy DataWind Turbine Purchase cost$1820/kW Installation cost$600000 Levelized fixed charge rate 11.6% Plant rating1.5 MW Capacity factor0.40 Nominal discount rate 8% Levelized fixed charge rate: Return on investment Depreciation Fed and state income taxes Property tax Insurance costs 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 10

11. Levelized cost of energy ResourceLCOE PC plant$59.94/MWhr NGCC plant$99.64/MWhr Nuclear plant$66.49/MWhr Wind, CF=0.35, FCR=20%$143.51/MWhr Wind, CF=0.35, FCR=11.6%$83.24/MWhr Wind, CF=0.40, FCR=20%$125.58/MWhr Wind, CF=0.40, FCR=11.6%$72.83/MWhr

12. Levelized cost of energy 12 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 AOE is generally only about 2% of the purchase cost. The above expression is sometimes expressed as: which implies AOE is given in $/MWhr.

13. Levelized cost of energy 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. www.nei.org/resourcesandstats/documentlibrary/newplants/graphicsandcharts/the-cost-of-new-generating-capacity-in-perspective Data from Electric Power Research Institute

14. Levelized cost of energy 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. www.nei.org/resourcesandstats/documentlibrary/newplants/graphicsandcharts/the-cost-of-new-generating-capacity-in-perspective Data from US DOE Energy Information Administration

15. Levelized cost of energy 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. www.nei.org/resourcesandstats/documentlibrary/newplants/graphicsandcharts/the-cost-of-new-generating-capacity-in-perspective National Research Council (National Academies of Science and of Engineering)

16. Representative split – capital costs 16 Source: P. Jamieson, “Innovation in wind turbine design,” Wiley, 2011. Note – this book has an entire chapter dedicated to “Cost of Energy.” ComponentCost fraction Blades0.177 Hub0.077 Gearbox0.143 Generator0.076 Yaw system0.019 Nacelle cover0.020 Nacelle structure0.040 Tower0.219 Variable speed system0.073 Pitch system0.043 Rotor brake0.006 Couplings0.003 Shaft0.041 Other0.063 Total turbine1.00 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.

17. Representative split - LCOE 17 Source: P. Jamieson, “Innovation in wind turbine design,” Wiley, 2011. Note – this book has an entire chapter dedicated to “Cost of Energy.” Initial capital costsTurbineRotorRotor lock0.0057 0.8200.569Blades0.1037 Hub0.0142 Nacelle systemsGearbox0.0961 Generator0.0378 Rotor brake0.0085 Nacelle cover0.0142 Nacelle structure0.0193 Couplings0.0057 Shaft0.0171 Yaw system0.0171 Bearings0.0171 Electrics and controlPitch system0.0365 Variable speed system0.0551 Tower0.0896 Other0.0313 Balance of plantRoads & civil works0.0221 0.251Electrics and grid con0.0761 Assembly & insttlltn0.0073 Transportation0.0365 Foundations0.0675 Financial and legal0.0414 O&M0.180Labor0.0792 0.180Parts0.0630 Operation0.0216 Equipment0.0090 Facilities0.0072