part 3

• Wind and geothermal energy

  The Green Energy
• A wind turbine obtains its power input by converting the force of the wind into torque (turning force) acting on the rotor blades
• Energy content in wind

  The amount of energy which the wind transfers to the rotor depends on the density of the air, the rotor area, and the wind speed
• Density of air


  • The kinetic energy of a moving body is proportional to its mass (or weight)
  • The kinetic energy in the wind thus depends on the density of the air, i.e. its mass per unit of volume
  • Density also depends on temperature and humidity
• The rotor


  • The rotor area determines how much energy a wind turbine will be able to harvest from the wind
  • Rotor area increases with about the square of the rotor diameter, a turbine which is twice as large will receive 4 times as much energy
• Wind velocity


  Energy in the wind is proportional to the cube of the wind speed
• Power output per m2 of the rotor blade is not linearly proportional to the wind velocity
• It is more profitable to place a wind energy converter in a location with occasional high winds than in a location where there is a constant low wind speed
• Fluctuations in wind speed can cause power output to vary significantly
• Extracting maximum power from wind

  1. Downwind velocity is zero which means that the wind turbine extracts all the wind kinetic energy

  2. Downwind velocity is the same as the upwind velocity and, hence, wind turbine extracts none of the wind kinetic energy

  3. There must be some ideal slowing of the wind velocity so that the turbine can extract the maximum kinetic energy from the wind
• Maximum rotor efficiency (CP)


  The energy extracted by the turbine blades
• Determining the wind speed ratio λ which maximizes the rotor efficiency

  Plug the optimal value for λ = 1/3 back into CP to find the maximum rotor efficiency
• Tip speed ratio

  The ratio (as a scalar) of the circumferential velocity of the rotor at the end of the blade (maximum velocity ue) and the wind velocity v0 in front of the rotor blade
• The tip speed ratio has a strong influence on the efficiency of a wind energy converter
• When the tip speed ratio is small, the circumferential velocity is also small which results in an increase in the angle of attack α
• When the angle of attack increases past a critical angle, the flow breaks from the profile and becomes turbulent, thus dramatically reducing the lift force
• If the tip speed ratio is too large, the lift force will reach its maximum value and decrease afterwards, thus reducing the power efficiency of the converter
• Rotors with two blades reach their maximum efficiency at higher tip speed ratios compared to three blades type
• Relationship between power coefficient and tip-speed ratio


  • Example given
• Given information


  1. 40-m diameter wind turbine with three-blades and 600 kW power output

  2. Wind speed is 14 m/s

  3. Air density (ρ) is 1.225 kg/m3
• Find


  1. RPM of the rotor if the wind turbine operates at a TSR of 4.0

  2. Tip speed of the rotor

  3. Gear ratio needed to match the rotor speed to the generator speed if the generator must turn at 1800 rpm

  4. Efficiency of the wind turbine under these conditions
• Solution provided
• Wind shear


  Wind velocity decreasing closer to ground level
• Studying wind energy site

  1. Measure wind velocity and profile

  2. Arrive at conclusions about the site
• Roughness class


  Measure of surface roughness
• Roughness length


  Measure of surface roughness
• Calculating wind speed at different heights

  1. Given: Wind speed 9 m/s at 50 m height, roughness length 0.1 m

  2. Calculate wind speed at 100 m height
• Weibull distribution


  Continuous probability distribution that models a broad range of random variables, largely in nature of a time to failure or time between events
• Weibull distribution parameters


  • Mean wind speed 7 m/s
  • Shape parameter 2
• Weibull distribution


  • Probability density distribution
  • Area under curve is always 1
  • Median wind speed 6.6 m/s
  • Distribution is skewed, not symmetrical
  • Most common wind speed 5.5 m/s
• Scale parameter


  Governs the shape of the Weibull distribution curve, higher value means distribution is spread over a wider range and the probabilistic average wind velocity has a higher value
• Shape parameter


  Governs the shape of the Weibull distribution curve, higher value (2-3) means distribution is more skewed towards higher wind velocities, lower value (1-2) means distribution is skewed towards lower velocities
• If the shape parameter is exactly 2, the distribution is known as a Rayleigh distribution</b>
• Wind turbine manufacturers often give standard performance figures for their machines using the Rayleigh distribution
• Wind speed of 14 m/s

  Power available is 16 times higher than at 5.5 m/s, but only for 2% of the time
• Components of a wind energy converter


  • Rotor blades
  • Gearbox
  • Generator
  • Tower
  • Miscellaneous parts
• Rotor blades


  • Aerodynamic profile creates low pressure on upper surface, generating lift force perpendicular to wind direction
  • Most modern blades are made of glass fibre reinforced plastics
• Gearbox


  Transfers power from wind turbine rotor to generator
• Wind turbine generator


  Converts mechanical energy to electrical energy, has to work with fluctuating mechanical power from wind turbine rotor
• Tower


  • Needs to be as tall as possible to capture higher wind speeds
  • Can be tubular steel, lattice, or concrete