Low-power wind generation

1
Low-power wind generation

• Power output of each generation unit in the
  order of a few kW. Power profile is predominately
  stochastic.
• Originally they were used for nautical and rural
  applications with dc generators. Cost is
  relatively low.
• More modern systems use permanent-magnet
  generators.

SW Windpower Whisper 200 1 kW Rotor diameter 2.7
m
Air-X 400 400 W Rotor diameter 1.15 m
LNP 6.4-5000 5 kW Rotor diameter 6.4 m
2
Low-power wind generation
Bergey Excel 7.5 kW Rotor diameter 6.4 m
SW Windpower Whisper 500 3 kW Rotor diameter 4.5
m
Solerner 3 kW
YM-CZ3kW 3 kW
Wind generators In Tokyo
3
Average wind power in the US
http//rredc.nrel.gov/wind/pubs/atlas/maps.html
4
Average wind power in Europe
http//www.geni.org/globalenergy/library/renewable
-energy-resources/europe/Wind/Wind20Map20of20We
stern20Europe_files/euromap.gif
5
Generators Synchronous machine

• Output ac. Electric frequency depends on the
  rotor angular speed.
• Requires a dc input.
• Ideally Pmec,in Pelect,out

6
Generators Dynamos (Brushed dc generator)

• Output ac dc. AC component electric frequency
  depends on the rotor angular speed.
• Important maintenance and reliability issues
  caused by the brushes
• Ideally Pmec,in Pelect,out

7
Brushless/Permanent magnet generators

• Output ac. Electric frequency depends on the
  rotor angular speed.
• No issues with brushes
• Ideally Pmec,in Pelect,out

8
Wind generators model

• The output in all types of generators have an ac
  component.
• The frequency of the ac component depends on the
  angular speed of the wind turbine, which does not
  necessarily matches the required speed to obtain
  an output electric frequency equal to that of the
  grid.
• For this reason, the output of the generator is
  always rectified.
• The rectification stage can also be used to
  regulate the output voltage.
• If ac power at a given frequency is needed, an
  inverter must be also added.
• There are 2 dynamic effects in the model the
  generator dynamics and the wind dynamics.

9
Wind power

• Consider a mass m of air moving at a speed v.
  The kinetic energy is
• Then power is
• The last expression assumes an static wind
  behavior (i.e. v is constant)
• The mass flow rate dm/dt is
• Thus,

10
Typical Power-speed characteristics
SW Windpower Whisper 200 1 kW Rotor diameter 2.7
m
SW Windpower Whisper 500 3 kW Rotor diameter 4.5
m
11
Conversion efficiency

• In the previous slide, power does not varies
  with the cube of the wind speed. Why?
• Because not all the wind power is transmitted
  through the blades into the generator.
• Consider the next figure

vb
Downwind
vd
Upwind
Rotor area A
vu
12
Conversion efficiency

• The wind energy absorbed by the wind turbine
  rotor equals the kinetic energy lost by the wind
  as it pass through the blades. Hence, the energy
  transmitted by the wind to the rotor blades is
  the difference between the upwind and the
  downwind kinetic energies
• In the last equation it is assumed that there is
  no turbulence and the air passes through the
  rotor as a steady rate.
• If it is assumed that vb is the average between
  vu and vd, then the mass flow rate is
• If we define the ratio

13
Conversion efficiency

• Then
• The rotor efficiency is maximum when ? is 1/3.
  For this value, Cp is 0.593.
• Still, we still need to know how much of the
  absorbed power by the blades is transmitted to
  the generator. This conversion stage is
  characterized based on the tip-speed ration (TSR)

Power in the wind
Fraction extracted
Rotor efficiency Cp
14
Conversion efficiency
From the courses recommended book
15
Variable rotor speeds

• The maximum power point changes as the rotor
  speed changes.

From the courses recommended book
16
Wind stochastic nature

• Wind speed probability (then generated power,
  too) is an stochastic function.
• Wind speed probability can be represented using
  a Rayleigh distribution, which is a special case
  of a Weibull distribution.
• The Rayleigh distribution appears when a
  2-dimentional vector has characteristics that
• are normally distributed
• are uncorrelated
• have equal variance.
• A typical probability density distribution
• for wind speed is shown next. Rayleigh
• distributions approximates these curves.

17
Wind stochastic nature

• The Rayleigh probability density function is
  given by
• where c is a parameter.
• The average value of the random variable (wind
  speed v) is
• The average power is
• If
• Then