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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.

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slide1

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

slide2

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

slide3

Average wind power in the US

http://rredc.nrel.gov/wind/pubs/atlas/maps.html

slide4

Average wind power in Europe

http://www.geni.org/globalenergy/library/renewable-energy-resources/europe/Wind/Wind%20Map%20of%20Western%20Europe_files/euromap.gif

slide5

Generators: Synchronous machine

  • Output: ac. Electric frequency depends on the rotor angular speed.
  • Requires a dc input.
  • Ideally Pmec,in = Pelect,out
slide6

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
slide7

Brushless/Permanent magnet generators

  • Output: ac. Electric frequency depends on the rotor angular speed.
  • No issues with brushes
  • Ideally Pmec,in = Pelect,out
slide8

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.
slide9

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,
slide10

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

slide11

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

slide12

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
slide13

Conversion efficiency

  • Then
  • The rotor efficiency is maximum when λ 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

slide14

Conversion efficiency

From the course’s recommended book

slide15

Variable rotor speeds

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

From the course’s recommended book

slide16

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.
slide17

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