The Physics and Feasibility of WindPowered Electric Generators

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The Physics and Feasibility of Wind-Powered
Electric Generators

• -Matt Wick

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Preview

• Why do we care about windmills?
• How does a wind-powered generator work?
• Are windmills currently an effective replacement
  for coal burning power plants?

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Why Windmills?

• A lot of talk recently about wind farms being
  built in Western Illinois
• My uncle lives off the grid in Northern
  Wisconsin and is currently looking into possible
  sources of renewable energy
• It is intelligent to utilize the kinetic energy
  of the wind to produce electrical power for our
  homes

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Why Windmills?

• Currently, we produce most of our nations power
  by burning coal to heat water
• The water produces steam which is used to turn
  the blades of a large turbine generator
• The wind can turn the blades of the turbine
  without burning coal or producing pollution

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How does a Wind-Powered Generator Work?

• History
• In 1861, Michael Faraday conducted numerous
  experiments on electricity and magnetism

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How does it work?

• Faradays law of Induction
• An EMF, as well as a current, can be induced in a
  circuit by a changing magnetic (B) field
• EMF electromotive force, a potential difference
  in volts
• Ex. In a battery, the emf is the maximum
  possible voltage that the battery can provide
  between its terminals

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Faradays Law of Induction

• IMPORTANT
• In a given circuit, the induced EMF is directly
  proportional to the change in Magnetic Flux (Ø)
  over time!
• This leads us to an equation representing
  Faradays Law of Induction..
• EMF -dØ / dt
• This equation is for the induced EMF in a
  conducting coil with n 1 turns

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Generators

• Turn energy from work into electrical energy!
• The generators used in windmills are alternating
  current (AC) generators
• Basically, they are conductive loops of wire
  rotated in a B field by some external means
  (winds kinetic energy)

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Generators

• According to Faradays Law, the Magnetic Flux (Ø)
  through the area enclosed by the loop changes
  over time as the loop rotates
• Therefore, an EMF and a current is induced in the
  loop!
• The ends of the rotating loop are connected to
  slip rings which rotate along with the loop
• There are stationary brushes in contact with
  the slip rings
• These brushes act as the output terminals of
  the generator

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A More Realistic Generator

• Most generators will have more than 1 loop in its
  coil
• If a coil has N loops with the same area, and if
  it rotates in a B field with constant angular
  speed (w)..
• Then the magnetic flux (Ø) through the loop at
  any time (t) is
• Ø BAcos? BAcoswt
• ? angle between B field and the normal to the
  plane of the loop
• ? wt

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EMF of generator with N turns

• Recall
• EMF -N (dØ / dt)
• And
• Ø BAcoswt
• So.
• EMF -NBA d/dt(coswt) NBAw(sinwt)

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AC generator?

• The fact that our generator follows..
• EMF NBAw(sinwt)
• -shows that our EMF follows a sinusoidal pattern
  over time!
• ?This is why it is called an alternating current
  (AC) generator!
• - Because the current alternates back and forth
  due to the sinusoidal nature of the EMF over time

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Power From an AC Generator

• Most wind generators store their energy in
  batteries, completely disconnected from the grid
• Big Problem!
• Our AC current must be converted to a DC current
  in order to power the batteries!
• Direct Current (DC) a current that is constant
  in direction

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Why Convert AC to DC?

• In a battery in a particular circuit, the battery
  terminals have a constant potential difference,
  and hence a constant EMF
• As a result, the current in the circuit is
  constant in magnitude and direction
• Therefore, we cannot use AC and require DC to
  charge the batteries
• The batteries can then be used to power
  electrical items and provides a source of EMF to
  pump charges around!

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Are Windmills an Effective Source of Power?

• Answer Maybe!
• A windmill is effective only in areas with
  suitable conditions
• A lot of research goes into surveying ones
  situation
• Considerations power ratings, average area wind
  speed, tower height, permits, rotor swept area,
  costs, labor

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Power Ratings

• Many windmill manufacturers provide Power Curve
  graphs
• Allows one to directly compare different models
  and their relative power output vs. wind speed

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Power Curve Graphs

• One must choose the best model for the average
  wind speed in their area
• One must also accommodate for seasons with less
  wind
• Compare power outputs for relative wind speeds to
  your average power use each season

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Notice This!

• 1. At low wind speeds, there is no power output!
• -We need at least a certain wind speed to make
  any usable power!
• ? 2. Wind speed is NOT linear to power!
• - If we double the wind speed, it does not mean
  we double the power!
• - In fact, the relationship between wind speed
  and energy is cubic!
• - If we double the wind speed, we actually get
  23 8 times the power!

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Wind Speed

• One of the most important considerations
• Remember that we need steady wind year round
• Two ways to check the wind speed of your area
• 1. Consult wind maps that are prepared by the
  government and available to the public for the
  area in question
• 2. Pay a company to do a site measurement study
  for a couple of months or longer

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Tower Height

• At greater heights, the speed and smoothness of
  the wind increases
• The higher the tower, the greater the power

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Permits

• Any new construction requires building permits
• Permits vary from county to county and should be
  researched before any investments are made
• Permits can restrict tower height, blade size,
  and placement on property

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Rotor Swept Area

• Bigger blades catch more kinetic energy from the
  wind to convert to electrical energy
• The rotor swept area is directly proportional to
  power output
• If we double the sweep area, we will double the
  power!
• ?The sweep area must be kept in mind when
  comparing different models on a power curve
  graph

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Costs

• Windmills are not cheap!
• We must consider product, labor, permit, and
  evaluation costs
• If on the grid, it is much cheaper to just use
  the coal-generated power (1/watt)
• However, if off the grid, it may be cost
  effective when considering costs to expand
  existing power lines to your home
• The smaller units prove more expensive than large
  units
• More environmentally friendly than coal

Bergey 1kW            16,168            16/watt
Proven 2.5kW         35,774            14/wattA
RE 2.5kW             21,628            8.50/watt
Bergey 10kW          50,056            5/watt
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Labor

• Windmills are not easy to install
• Some counties may require a licensed contractor
  to install the tower
• Besides, the initial building of the wind
  generator, they require periodic maintenance
• Changing bearings, batteries, broken or corroded
  parts, electrical connections, etc
• System also needs constant monitoring in case of
  emergency

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Conclusion

• The wind powered generator is an intelligent
  design for harnessing wind to create electrical
  energy
• However, caution must be taken when considering a
  wind power investment
• Research is necessary in making the correct
  decision and comparing its value to coal-power
• Wind technology is constantly becoming more
  efficient
• On average, it is much more expensive than coal
  power, but creates much less pollution in the
  long run
• What is your priority?

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Thank You!
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An Implication of Faradays Law

• When a magnet is moved toward or away from a
  conducting loop, a current and an EMF is
  established within the loop
• This current is present even in the absence of a
  battery or other source of power
• This current is called an Induced Current
  produced by an Induced EMF

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Magnetic Flux

• An EMF, and hence a current, is produced in a
  circuit when the magnetic flux in the circuit
  changes over time
• Magnetic Flux Ø ?BdA (1 loop)
• B Magnetic Field
• dA A vector perpendicular to surface equal
  to the area

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Faradays Law of Induction

• A more realistic coil would consist of N loops
• EMF -N (dØ / dt)
• This is because the loops are in a series, so
  their EMFs add together
• Assume all loops have the same area
• Ø is still the Magnetic Flux in 1 loop

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What Have We Learned So Far?

• An EMF, which induces a current, can be
  established in a circuit in a number of ways .
• The B field changes with time
• The area enclosed by the loop changes with time
• The angle ? between B and the normal to the loop
  changes with time
• Any combination of the above

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How Convert AC to DC?

• In order to convert AC to DC one must install an
  AC/DC converter in the circuit after the brushes
• Called a Rectifier Bridge

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Rectifier Bridge

• Contains a diode
• Diode a circuit element that conducts current
  in one direction but not the other
• Due to low resistance to current in one direction
• As a result, the AC is converted to the form
  shown by rectifier output graph

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Rectifier Bridge

• If we add a capacitor and a resistor to the
  circuit, it becomes a DC power supply!
• As the current begins to rise at t 0, the
  capacitor charges up
• As the current begins to fall, the capacitor
  discharges through the resistor
• Therefore, the current from the resistor does not
  lower as quickly as the current from the
  transformer