the physics of wind turbines Harvesting the Wind the physics of wind turbines Kira Grogg Carleton College February 23, 2005

Why Wind-power? Wind-power is clean – wind turbines emits no pollutants and create no other types of waste Wind is renewable – the fuel replenishes itself at a rate comparable to the extracted rate Modern wind turbines can run as efficiently as conventional power plants (~30-40%)

What is a wind turbine? http://www.canren.gc.ca/tech_appl/index.asp?CaID=6&PgID=219

Outline History Origins of wind Power from the wind Aerodynamics of the blades Loads, stress, and fatigue Generators and Electricity Current issues Future developments

History First windmills about 1000 B.C.E. 12th century – horizontal wind mills appear in Europe Water pumping windmills in America 1888 – first experiments with electricity generating wind turbines 1891-1918 – Poul La Cour builds over 100 small wind turbines Increase in production in 1970s due to oil difficulties

The Wind Earth receives 1.74 x 1017 watts from the sun Each year this is 160 times the total energy in the world’s reserves of fossil fuels. 30% radiated out, 47% warming, 23% absorbed by evaporation of water, the remaining goes to plants, wind, and waves 1-2% of the sun’s energy becomes wind energy—100 times the energy in biomass

Forming the Wind Wind begins as the sun heats the air in the atmosphere Uneven heating combined with the Coriolis force lead to geostrophic winds Latitude 90-60°N 60-30°N 30-0°N 0-30°S 30-60°S 60-90°S Direction NE SW SE NW

Finding a Site Landscape Roughness Height vs. wind speed: Sea breezes 10-4 over water to 1 m in cities Height vs. wind speed: Sea breezes Mountains desired height roughness length known velocity at height zref reference height

Wind Speed Distribution

Power in the Wind The power is proportional to the cube of the wind speed: Wind speed data can be misleading : Average wind speed data is too: < U>3 ≠ <U3>

Extracting Power from the Wind Not all of the power in the wind can be turned into useable energy The upper limit on power extracted for a HAWT is ~ 59% (Betz’ Law) Cp = power to rotor / power in wind

Power Curves No system that converts between types of energy can be 100% efficient Actual power output (of electricity) is about 30% of the power in the wind

Wake Rotation Energy and momentum must be conserved Angular velocity added from the turning of the blades, Ω, implies a compensating angular velocity in the wake of the turbine, ω www.windpower.org

Tip Speed Ratio λ λ = ratio of rotor speed to wind speed The tip speed ratio can range from 5 to about 10 for electricity generating applications Equating the thrust equations: Tip speed ratio: λ = ΩR/U where R is the length of the blade

Torque and Power Cp Manwell, et. al (2002)

Induction Factors Tip speed ratio λ= 7.5 Manwell, et. al (2002)

The Blades Lift vs. Drag Lift Thrust Drag Weight Early Persian drag windmill Manwell, et. al (2002)

Airfoils Types of airfoils: Airfoil geometry: Manwell, et. al (2002)

Angles and Relative Winds Angle of attack, α, is usually between 3 - 10 degrees during normal operation The angle of the relative wind is the sum of the angle of attack and the section pitch angle: Hansen (2000)

Manwell, et. al (2002)

Lift and Drag Lift and drag coefficients: Wind tunnel tests of airfoils for lift and drag data Manwell, et. al (2002)

Blade Element Momentum Theory (BEM) BEM uses conservation of momentum and forces on individual elements

Maximizing Power Computational algorithms are employed to determine the most effective blade shape, in terms of chord length and twist (λ = 7, R = 5, Cl =1, α = 70, B =3) A new power coefficient with lift and drag:

Cp -λ Curve Manwell, et. al (2002)

Blade Control Stall Control Pitch Control Active Stall Manwell, et. al (2002)

Yaw Control Wind Rose data No yaw – only VAWTs Tail – water pumping windmills Free/Damped yaw – only downwind HAWTs Active yaw – upwind HAWTs Red section is the power x frequency, Middle section is the wind speed x frequency Outer section is the wind frequency distribution

Loads, Stress, and Fatigue Types of loads: static, steady, cyclic, transient, impulsive, stochastic, and resonance induced Certain loads will occur over 109 times during a 20 year lifetime Testing for fatigue – dynamic and static www.windpower.org

Some Loads Bending Moments: Coning to reduce flapwise bending: Edgewise Coning to reduce flapwise bending: Hansen (2000)

Blade Construction Metal does not work, composites do Glass reinforced plastic (GRP) Carbon fibers Wooded frames Measuring strains

The rotor is about 80m across: This is what excessive loads can do to a WT Hansen (2000)

Inside the Nacelle

Gearbox As the speed increases, torque decreases, so power remains constant The ratio of the speeds is equal to the inverse ratio of the number of teeth The gear ratio of Carleton’s 1.65 MW wind turbine is 1:84.3, so that when the rotor is operating at its rated speed of 14.4 rpm, the generator shaft is turning at about 1214 rpm

Gears vs. Direct Connection Advantages of gearless connection: Cheaper Quieter Fewer losses Disadvantages: Special low-speed generator is costly

Converting Energy Electrical to kinetic conversion in an electrical motor is about 90% efficient, Heat to kinetic conversion of an internal combustion engine is about 10-20% efficient Coal fired power station—chemical to electrical—is about 35-40% efficient Newer wind turbines are 30-40% efficient

Creating Electricity Wind turbines use generators to create electricity Synchronous generators Asynchronous (induction) generators Permanent magnet Compatibility with The Grid

Faraday’s Law of Induction Use a moving part and a magnetic field to create a current Magnetic flux through a loop of wire in a magnetic field: Induced emf: Magnetic field Angle between A and B Area of loop Rotational velocity of loop ω = θt

Magnetic fields and currents Three phase current Coil connections Number of poles N Manwell, et. al (2002) S S N N S

Asynchronous/Induction Generators Usually 4-pole Rotor uses converted DC from grid to generate a magnetic field Stator consists of six coils creating 3-phase current Slip—ratio of the rotating magnetic field speed to the rotor speed

The Parts of the Generator Cage wound rotor Layered stator

Generator Manwell, et. al (2002)

Electronics Every part of the turbine has a sensor monitoring and/or controlling it Every sensor has a duplicate to make sure they are working correctly

Power Quality and Grid Connection Power quality is checked 7680 times per second The current must be in phase with the grid current before connection Thyristors (semi-conducting transistor type controlling devices) allow a ‘soft’ start of a wind turbine

Current Issues Bird and bat deaths Electromagnetic interference Noise Visual appearance

Off-shore Wind Farms Off shore winds are stronger and less turbulent Larger turbines, ~4 MW, are feasible Foundations and transmission are the major obstacles

What Now? Optimization of More testing More wind turbines Blade shape Gearbox Generator Tower height Siting More testing More wind turbines

Acknowledgements To: my advisor, Steve Parker the Carleton physics faculty my fellow physics majors my friends and family the audience