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## Week 10 Power: Energy Options for a Global Society

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**Week 10Power: Energy Options for a Global Society**Renewable Energy Principles and Applications II: Wind & Geothermal Power**Wind**Modern wind technology is already competitive with fossil fuels. Its ultimate limitations are only due to its intermittency. • Resource Potential • Power • Swept Area • Rotor Design • Wind Speed Distributions • Power Increase with Height**Wind Resource Potential is Currently Being Mapped at Very**High Resolution Old Map New Map**Wind Power**• The power in the wind is: Power = ½ rA V3 • Using the density of air at sea level: Power = 0.6125 AV3 (metric) Power = 0.00508 AV3 (mph, ft)**Example**• Calculate how much more power is available at a site where the wind speed is 12 mph than where it is 10 mph • P ~ V3 • P2/P1 = (V2/V1)3 • P2 = (12/10)3P1 = 1.73 P1 1.7 x the power (almost a factor of 2 increase), with only 2 mph increase in wind speed!**Swept Area**• Power in the wind is also proportional to the swept area A = pR2 • Increase the radius from 10 m to 12 m: A2 = (R2/R1)2 A1 A2 = (12/10)2 A1 = 1.44A1 Nothing tells you more about a wind turbine’s potential than the rotor radius.**Rotor Designs**• Two blades are cheaper but do not last as long • Three blades are more stable and last longer • Options include: • Upwind vs downwind • Passive vs active yaw • Common option chosen is to direct the rotor upwind of thetower with a tail vane**Darrieus Vertical Axis**Fan Mill Horizontal Axis**Specifications**Vestas V82 (V66) • Two Speed Cut-in Wind Speed: 2.5-3.5 m/s (7 mph)Rated Power: 900 KW - 1.65 MWCut-out Wind Speed: 32 m/s (75 mph) • Type: 3 Blade UpwindRotor Diameter: 82 m (270 ft.) Swept Area: 5281 m2 Rotor Speed: 10.8-14.4 rpm**The lift force (only) turns windmill blades for useful power**output • Can think of a windmill as a fan running backwards. • The pitch of the blade causes a difference in air pressure on either side. • This difference in air pressure is what provides the “lift force” (similar to aircraft), and causes the rotors to turn.**Wind Drag**• If the angle of attack of a blade is too large, the wind simply pushes against the blade, exerting a drag force but no lift. When the drag is too great, a stall occurs. • Wind mills are designed to operate in winds up to 35 mph, but must be able to survive 100 mph gales. • Random turbulent winds create strong torques that can fatigue the structure.**Wind Speed Frequency Distribution**• Wind speeds occur at different values • Total energy from a turbine depends heavily on the maximum speeds because Power increases with the cube of the speed “The average of the cubes is greater than the cube of the average.”**Approximating Wind Distribution Using Rayleigh Distribution**• Suppose we only know average speed • e.g. 12.8 MPH (5.7 m/s) • Wind has been observed to follow a Rayleigh distribution in many places, i.e. Prob. (Windspeed < v) = 1 – exp[(-/4)(v/vaverage)2] e.g. P (0) = 0, P (300 MPH) = 1**Wind Power**• The power in the wind is: Power = ½ rA V3 • Using the density of air at sea level: Power = 0.6125 AV3 (metric) Power = 0.00508 AV3 (mph, ft)**A Utility-Grade 1.65MW Turbine A = 5281 m2**• @4.5 m/s • Power = 0.6125 AV3 = 295 KW • @5.5 m/s • Power = 0.6125 AV3 = 538 KW • @ 6.5 m/s • Power = 0.6125 AV3 = 888 KW**Wind Speed Frequency Distribution**Total energy from a turbine depends heavily on the maximum speeds because Power increases with the cube of the speed**Wind Speed & Power Curves**Rayleigh Distribution Turbine Power Profile Cut-in Speed**Wind Speed & Power Curves**Total Energy in 1 Year: ~1.7 million kWh Blades will be turning: 80-90% of time Cut-in Speed 2.5 m/s (5.6 mph) Cut-out Speed 32 m/s (72 mph)**Vestas V82 Power Profile**Wind Speed m/s**Power Increases With Height**V2 = (H2/H1)aV1**How to calculate wind speed increase with height**• Conservative Approximation: V2 = (H2/H1)aV1 • a is the Roughness exponent • Smooth terrain value (water or ice): 0.10 • Rough terrain value (suburb woodlands): 0.25 • Grasslands: 0.14**Example**• Consider doubling the height of your tower from 10 m to 20 m. V2 = (H2/H1)aV1 = (20/10).14 V1 = 1.1V1 • The power available increases to: P2 = (H2/H1)3aP1 = (2)3aP1 = 1.34P1 • If you multiply height by a factor of 5: P2 = (H2/H1)3aP1 = (5)3aP1 = 1.97P1**Example**• You live in a forested area. Calculate how much more power you can get from a turbine at 87meters than a turbine at 30meters. V2 = (H2/H1)aV1 = (87/30).25 V1 = 1.3V1 • The power available increases to: P2 = (H2/H1)3aP1 = (2.9)3(.25)P1 = 2.22P1**Efficiency**• Small wind turbines can seldom deliver more than 30% of the energy in the wind • Most people live where average wind speeds are 4-5 m/s (9-11 mph) • Strangely, at extremely windy sites small wind turbines produce more energy but are less efficient at capturing the energy in the wind (10%) • Very important to locate turbines where winds speeds are highest and turbulence is at a minimum**High technology large turbines can achieve up to 46%**efficiency • The spinning of a windmill causes a “backwind” which is maximum at the blade tip. • This affects the efficiency of the turbine. • Thus, one factor in the design is the tip speed vs. wind speed ratio.**Wind Power Resource Potential**• Potential includes all the • factors we’ve covered: • wind speed • wind speed distribution • roughness of terrain • height of rotors • wind turbulence • etc. • Most turbines do not operate • at full capacity – 20% is typical**Factors to Consider When Designing a Wind System:**• Company specs relevant to the machine only • Company specs may claim 2.4 KW • But does the wind carry that much power? • The site must be tested for wind speed optimization, turbulence minimization • Height of turbine • Design of turbine • Wind speed at which the rotor furls**Hybrid**Systems • Wind turbines effective at night and in stormy weather • Both effective on a windy day • Solar effective on a clear windless day**Wind Farms**• Wind farms funded in the 1980s helped tremendously to mature the technology to make wind power competitive with traditional fuels • California gave huge tax incentives for wind farms • Largest turbine produced 3.2 MW**Colorado**Europe California**1. Madison Windpower, LLC**• Town: Madison • County: Madison • Project Owner: PG&E Generating • # of Turbines: 7 • Turbine type: Vestas V66- 1,650kW • Rotor Diameter: 66m • Hub Height: 67m • Total Capacity (MW): 11.55 • Annual Expected Energy (MWh): 24,000**2. Wethersfield**• Town: Wethersfield • County: Wyoming • Project Owner: CHI Energy, Inc. • # of Turbines: 10 • Turbine type: Vestas V47-660kW • Rotor Diameter: 47m • Hub Height: 65m • Total Capacity (MW): 6.6 • Annual Expected Energy (MWh): 19,000**3. Fenner Windpower, LLC**• Town: Fenner • County: Madison • Project Owner: CHI Energy Inc. • # of Turbines: 20 • Turbine type: GE Wind- 1,500kW • Rotor Diameter: 70.5m • Hub Height: 65m • Total Capacity (MW): 30 • Annual Expected Energy (MWh): 89,000**More about Fenner**• Noise from individual turbines: 50 dbA (as measured from closest non-site owned area) • Comparable to hearing airplane in distance • Area: 2000 acres • Average wind speed: 17mph • Total height: 328 feet • Weight: 375,000 pounds • Resident response: mostly positive: educational, clean, approve of appearance,**4. Calverton**• Town: Calverton • County: • Project Owner: Long Island Power Authority • # of Turbines: 1 • Turbine type: AOC 15/50 • Rotor Diameter: • Hub Height: • Total Capacity (MW): 0.5 • Annual Expected Energy (MWh):**5. Lorax-Energy**• Town: • County: • Project Owner: Harbeck Plastics • # of Turbines: 1 • Turbine type: Fuhrlaender 250 • Rotor Diameter: • Hub Height: • Total Capacity (MW): 0.25 • Annual Expected Energy (MWh):**Tax Incentives**• The Renewable Energy Production Incentive entitles Wind and PV systems to annual incentive payments of 1.5 cents per kilowatt-hour (1993 dollars and indexed for inflation) for the first ten year period of their operation, subject to the availability of annual appropriations in each Federal fiscal year of operation. - www.dsireusa.org. • For our turbine, this could mean 1.7 million kWh * 1.5 cents/kWh = $25,500 per year