Engineering, Policy, Finance Wind Energy Basics Engineering, Policy, Finance

“Lift Force”

“Lift Force” Land sailer record: https://www.youtube.com/watch?v=TRFRQXPtXTs

How Do You Figure Out How Much Power A Wind Turbine Will Produce? Pwind = (1/2) ρ A V3 Pwind = Power in the wind (watts) Note: 1 Watt = 1 kg-m² / s³ ρ = Air density (kg/m3) = 1.225 kg/m³ at sea level A = Rotor swept area = π r2 r = Radius of turbine rotor (meters) or length of the turbine blade = ½ the rotor diameter V = Velocity of the wind (meters /second) But the net power actually produced from a wind turbine will be slightly less than ½ of the available power in the wind. Will discuss this in more detail later. r

Wind Shear Snyder Wind Farm 100 m hub height 10 mps 14

Average Wind Speed vs Height TTU 200 Meter Tower Data 16

Estimating Wind Speeds Wind speed is best estimated with a Rayleigh/Weibull distribution function

Wind Rose: Shows Direction of Wind 18

Wind Rose: Showing Energy in the Wind P = (1/2) ρ A V3 19

Pitch of Blades Changes Wind Speed (meters per second) Many Utility-Scale Turbines Begin to Produce Power at ~ 3 m/s They May Reach Rated Capacity at ~ 15 m/s, & Shut Down at ~ 25 m/s Blades at Full Feather Blades Fixed at 0 to 1° Pitch of Blades Changes Rated Capacity = 2,300 kW Wind Speed At Rated Capacity Cut-In Speed Cut-Out Speed Wind Speed (meters per second) Region I Region II Region IV Region III

Gross vs. Net Capacity Factors Gross Capacity Factor Capacity Factor of a single wind turbine without any reductions for electrical losses, wake losses, turbulence losses, maintenance outages, transmission outages or curtailments, icing, blade soiling. Gross Capacity Factor at excellent wind sites can be around 50%. Net Capacity Factor Capacity Factor of a group of wind turbines which does include losses within the project Reflects actual energy sold at meter of customer as percentage of Maximum Production Net Capacity Factor at excellent wind sites around 40%

Types of Losses to Account For Turbine unavailability 3 to 5% Power curve 0 to 2% Substation unavailability 0.2 to 0.5% Transmission outages / maintenance 0.1 to 0.5% Transmission curtailment 0 to 30% Electrical losses 2 to 3% Wake effect 2 to 4% Turbulence 1 to 2% Blade contamination 0.5 to 1% Icing 0.5% to 2%

Calculating Total Loss Factor Losses Are Not Additive! Gross Capacity = Expected Production w/o Losses per Time Period x 100 Factor (in %) Maximum Production Maximum Production in One Year = MW x 365 days x 24 hours/day = MWH Net Capacity Factor = Gross Capacity Factor x (1 – Total Loss Factor) Losses Are Not Additive! Turbine Unavailability Factor: 2.0% 1-0.02 = 0.980 Substation Unavailability Factor: 0.2% 1-.002 = 0.998 Transmission Unavailability Factor: 1.4% 1-0.14 = 0.986 Electrical Loss Factor: 3.5% 1-.035 = 0.965 Wake and Turbulence Loss Factor: 5.0% 1-0.05 = 0.950 Blade Contamination / Icing Loss Factor: 1.5% 1-.015 = 0.985 Total Loss Factor = [1 – (0.98*0.998*0.986*0.965*0.95*0.985)] = 0.1292 = 12.92%

Investment Problem Assume the following: Upfront cost per MW is $1,150,000 Energy sales taxed at 10% Net Capacity Factor (calculated from data) Total Capacity is 275 MW 20 year project life span Discount Rate of 8% Find the minimum (break-even) PPA price If the PPA price is $35, what is the NPV and IRR?

Investment Problem (extensions) Debt/Equity Ratio and loan repayment (cost) MACRS depreciation (benefit) Tax Credits (benefit) Royalty payments to landowners (cost) Land lease payments (cost) Energy price escalation (*) PVWatts for solar