Fundamentals of Wind Energy Paul Gipe, wind-works.org Power in the Wind P1AV 3 2 Where is air density (kg/m3), A is area (m2), and V is velocity (m/s); thus 2V3 = 8P Paul Gipe, wind-works.org Energy in the Wind Annual Energy Output (AEO) Annual Energy Production (AEP) AEO = 1/2 ρ A V 3 ή (8,760 hrs/year) Air Density Efficiency Swept Area Paul Gipe, wind-works.org Seasonal Wind Distribution Avg. Monthly Wind Speed (mph) 18 16 ! ! ! ! ! 14 ' & ' & ! ' &! ' ! ! ! & ! & ' ! 12 & & ' 10 ' & & & && ' ' 8 ' ' ' 6 ! Amarillo, Texas 4 & Erie, Penn. ' San Francisco, Calif. 2 0 Jan Feb March April May June July Aug Sept Oct Nov Dec Month Paul Gipe, wind-works.org Rayleigh Wind Speed Distribution Frequency of Occurrence % 0.16 0.14 5 m/s 6 m/s 0.12 7 m/s 0.1 0.08 0.06 0.04 0.02 0 01234567891011121314151617181920 Wind Speed Bin Paul Gipe, wind-works.org Speed, Power, & Height α V/Vo = (H/Ho) 3α P/Po = (H/Ho) Where α is the surface friction coefficient. • 1/7 (0.14), Low Grass Prairies • 1/4 (0.25), Suburbs • 0.40, Urban Paul Gipe, wind-works.org Increase in Wind Speed with Height " V=Vo (H/Ho) 1.6 Wind Shear Exponent 1.5 , 0.1) 0.14 (1/7)& 0.2* 0.25 * * 1.4 * * & & * & 1.3 & * ) & ) ) 1.2 * & ) ) , , & ) , , * ) , 1.1 & , ) , , 1 &),* 1 1.5 2 2.5 3 3.5 4 4.5 5 H/Ho Paul Gipe, wind-works.org Increase in Power with Height 3" P=Po (H/Ho) 3.5 * Wind Shear Exponent * 3 , 0.1) 0.14 (1/7)& 0.2* 0.25 * * & 2.5 & * & & 2 * ) & ) ) * & ) ) , , 1.5 & ) , , , * ) , & , ,) 1 &),* 1 1.5 2 2.5 3 3.5 4 4.5 5 H/Ho Paul Gipe, wind-works.org Change in Wind Speed & Power with Height 2 X Height 5 X Height 25 to 50 m 10 to 50 m Wind Speed 1.1 1.25 Wind Power 1.35 1.99 1/7 (0.14), Low Grass Prairies Paul Gipe, wind-works.org Vegetative Indicators--Wind Throw Paul Gipe, wind-works.org Aude, France Increase in Wind Speed Over Ridges Paul Gipe, wind-works.org Paul Gipe, wind-works.org Resource Maps • 80 m or higher • Drill Down • More Wind than we once thought Paul Gipe, wind-works.org Central California Resource Paul Gipe, wind-works.org Annual Energy Output (AEO) Estimating Methods • Back-of-the-Envelope (Swept Area) Simple Approximation • Power Curve & Speed Distribution Method Used by the Pros Accuracy Dependent Upon Data • Manufacturers’ Tables Must be Certified • Software Must Know Assumptions Used (RETScreen) Paul Gipe, wind-works.org Rotor Dimensions Paul Gipe, wind-works.org Medium-Size & Large Wind Turbines Swept Area (m²) 5000 Rotor Diameter (m) 4000 80 3000 2000 70 2000 1500 60 1000 50 0 1000 15 25 40 60 70 80 40 Diameter (meters) 30 500 20 250 10 50 0 Paul Gipe, wind-works.org Conversion Efficiency Medium Size Wind Turbines Measured Efficiency 0.5 0.4 0.3 Efficiency 0.2 0.1 0 0 2 4 6 8 10 12 14 16 18 20 Wind Speed (m/s) bk1/medturbeffic.wb3 L 18/80 S31 E40 V47 Paul Gipe, wind-works.org Tararua New Zealand Yields Tararua Wind Plant New Zealand Specific Yields Vestas V47 Diameter Swept Area Specific Yield kWh/yr m m2 kWh/m2/yr Approximate Low 1,457,901 47 1,735 840 800 Median 2,500,000 47 1,735 1,440 1,500 High 3,050,622 47 1,735 1,760 1,800 WindStats, Spring 2005, Vol. 18, No. 2, pg 13. Paul Gipe, wind-works.org AEO Medium & Large Turbines Paul Gipe, wind-works.org Power Curve Calculation V80, 1.8 MW, 7 m/s Avg. Kilowatts 2000 1500 1000 500 0 012345678910111213141516171819202122232425 Wind Speed m/s Paul Gipe, wind-works.org Power Curve Calculation V80, 1.8 MW, 7 m/s Avg. Hours per Year 1000 800 600 400 200 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Wind Speed m/s Paul Gipe, wind-works.org Power Curve Calculation V80, 1.8 MW, 7 m/s Avg. kWh/year (Thousands) 800 5.4 million kWh/yr 600 400 200 0 024681012141618202224 Wind Speed (mph) Paul Gipe, wind-works.org Estimated AEP for Bergey’s Excel 6 in kWh Standard m/s AEP Measured AEP Extrapolated Uncertainty in AEP 4 5,522 721 5,522 5 9,919 1,034 9,919 6 14,940 1,287 14,967 7 19,777 1,445 19,944 8 23,749 1,516 24,298 9 26,523 1,521 27,740 10 28,096 1,482 30,200 11 28,657 1,417 31,745 Paul Gipe, wind-works.org Measures of Productivity • Capacity (Plant) Factor Misleading Indicator Used for Fossil-Fired Plants Not Suited for Wind Energy Use • kWh/kW/yr (for Planning Purposes) When Sufficient Data is Unavailable • Annual Specific Yield (kWh/m2/yr) The Only Measure Specific to Wind Energy Paul Gipe, wind-works.org Measures of Cost • $/kW of Installed Capacity Often a Misleading Indicator • $/m2 of Installed Swept Area Most Useful When Resource is Unknown • $/kWh/yr of Annual Generation Most Important Criteria in the End Paul Gipe, wind-works.org Representative Installed Cost Representative Relative Installed Wind Turbine Costs Relative Installed Cost* Low High Size $/m2 $/m2 Micro 1,500 2,500 Mini 1,250 2,500 Household 1,250 2,250 Small Commercial 800 1,250 Large** 400 600 *Gross approximation only. **Several turbines in small clusters. Paul Gipe, wind-works.org Large Wind Turbine Component Cost Sample Cost Estimate for a Large Wind Turbine Relative to Total Installed Cost As a Percentage of Total Cost Project Size 1 MW 100 MW Pre Development Engineering, Site Assessment and Land Acquisition 9% 5% Site Engineering and Equipment Selection 5% 6% Blade Procurement 16% 17% Turbine/Generator/Nacelle Procurement 21% 22% Tower Fabrication and Delivery 18% 19% Electrical Control Panels 3% 3% Unit Transformer 3% 3% Site Works including Switchyard 14% 15% Foundation for Tower including Reinforcing 5% 5% Crane Service and Turbine Erection Cost 1% 1% Commissioning, Warranty and Interest During Construction 6% 4% Source: APPrO, Ontario Wind Power Task Force, February 2002, pages 93 & 94. Economies-of-Scale Variable & Uncertain Paul Gipe, wind-works.org Relative Operating Cost Relative Costs for GE 1.6 MW Platform Adapted from Ryan Wiser LBNL 2012 Standard Low Wind Platform MW 1.62 1.62 Diameter m 82.5 100 Operating Costs $/kW/yr $60 $60 Relative Installed Cost $/kW $1,600 $1,850 Derived Swept Area m2 5,346 7,854 Operating Costs of Installed Cost 3.8% 3.2% Relative Cost per Swept Area $/m2 500 400 http://emp.lbl.gov/sites/all/files/wind-energy-costs-2-2012_0.pdf Paul Gipe, wind-works.org Sample Cash Flow Sample Cash Flow for Single Large Wind Turbine in Commercial Application Before Tax Assumptions: Rotor Diameter 100 Swept Area 7,854 Avg. wind speed 7 Yield 800 Net Generation 6,283,185 Installed Cost 3,500,000 Annual Reoccurring Costs $140,000 Tariff or PPA Rate $0.10 Inflation Rate 2% Loan Term 10 Loan Interest 7.50% Annual Cumulative Gross Annual Loan Loan Revenue Revenue Year Revenue Reocurring Costs Interest Principal (Loss) (Loss) 0 1 $628,319 ($140,000) ($262,500) ($247,401) ($21,582) ($21,582) 2 $640,885 ($142,800) ($243,945) ($265,956) ($11,816) ($33,398) 3 $653,703 ($145,656) ($223,998) ($285,902) ($1,854) ($35,252) 4 $666,777 ($148,569) ($202,556) ($307,345) $8,307 ($26,945) 5 $680,112 ($151,541) ($179,505) ($330,396) $18,671 ($8,274) 6 $693,714 ($154,571) ($154,725) ($355,176) $29,242 $20,968 7 $707,589 ($157,663) ($128,087) ($381,814) $40,025 $60,993 8 $721,740 ($160,816) ($99,451) ($410,450) $51,024 $112,017 9 $736,175 ($164,032) ($68,667) ($441,234) $62,242 $174,259 10 $750,899 ($167,313) ($35,574) ($474,326) $73,685 $247,944 11 $765,917 ($170,659) $595,258 $843,202 12 $781,235 ($174,072) $607,163 $1,450,364 13 $796,860 ($177,554) $619,306 $2,069,670 14 $812,797 ($181,105) $631,692 $2,701,363 15 $829,053 ($184,727) $644,326 $3,345,688 16 $845,634 ($188,422) $657,212 $4,002,901 17 $862,547 ($192,190) $670,357 $4,673,258 18 $879,798 ($196,034) $683,764 $5,357,021 19 $897,394 ($199,954) $697,439 $6,054,461 20 $915,341 ($203,954) $711,388 $6,765,848 $6,765,848 For illustrative purposes only. Paul Gipe, wind-works.org Wind Energy Software • Spreadsheets Fully Integrated (RETScreen) • Wind Farm Design Tools WAsP (Risø) WindFarm (ReSoft) WindFarmer (Garrad Hassan) WindPro (EMD) WindMap (Brower) Paul Gipe, wind-works.org Measured Performance Data • Power Curves • Noise • Power Factor • Flicker Paul Gipe, wind-works.org Wind Turbine Standards • Small Turbines Caveat Emptor (Buyer Beware) IEC-61400-2, SWCC UL--Not a Performance Standard! • Large Turbines Minimum Design Standards Performance Guarantees • Field Experience Always Best Guide Paul Gipe, wind-works.org Small Wind Turbine Certification • Minimum Requirement! Paul Gipe, wind-works.org Sources of Information • Trade Magazines • European Wind Reports • German Market Survey • Books • Web Sites • Workshops Paul Gipe, wind-works.org Wind Works! • But It Must be Done Right Paul Gipe, wind-works.org Paul Gipe, wind-works.org.