Small Wind Guidebook/How Much Energy Will My System Generate

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How Much Energy Will My System Generate?

RelativeSizeOfSmallWindTurbines.png

According to the AWEA Small Wind Turbine Performance and Safety Standard, the Rated Annual Energy of a wind turbine is the calculated total energy that would be produced during a one-year period with an average wind speed of 5 meters/second (m/s, or 11.2 mph).[1] The following formula illustrates factors that are important to the performance of a wind turbine. Notice that the wind speed (V) has an exponent of 3 applied to it. This means that even a small increase in wind speed results in a large increase in power. That is why a taller tower will increase the productivity of any wind turbine by giving it access to higher wind speeds.

The formula for calculating the power from a wind turbine is:

  • Power = Cp 1/2 ρ A V³

Where:

  • P = Power output, watts
  • Cp = Maximum power coefficient, ranging from 0.25 to 0.45, dimension less (theoretical maximum = 0.59)
  • ρ = Air density, kg/m³
  • A = Rotor swept area, m² or
  • π D² / 4 (D is the rotor diameter in m, π = 3.1416)
  • V = Wind speed, mps[2]

The rotor-swept area (A) is important because the rotor captures the wind energy. So the larger the rotor, the more energy it can capture. The air density, ρ, changes slightly with air temperature and with elevation. The ratings for wind turbines are based on standard conditions of 59° F (15° C) at sea level. A density correction should be made for higher elevations as shown in the Air Density Change with Elevation graph. A correction for temperature is typically not needed for predicting the long-term performance of a wind turbine.

AirDensityChangeWithElevation.png

Although the calculation of wind power illustrates important features about wind turbines, the best measure of wind turbine performance is annual energy output. The difference between power and energy is that power (kilowatts [kW]) is the rate at which electricity is consumed while energy (kilowatt-hours [kWh]) is the quantity consumed. An estimate of the annual energy output from your wind turbine, kWh/year, is the best way to determine whether a particular wind turbine and tower will produce enough electricity to meet your needs. Contact a wind turbine manufacturer, a dealer/installer, or a site assessor to help you estimate the energy production you can expect. They will use a calculation based on the particular wind turbine power curve, the average annual wind speed at your site, the height of the tower that you plan to use, micro-siting characteristics of your site and, if available, the frequency distribution of the wind (an estimate of the number of hours that the wind will blow at each speed during an average year). They should also adjust this calculation for the elevation of your site.

To get a preliminary estimate of the performance of a particular wind turbine, use the formula below.

  • AEO = 0.01328 D² V³

Where:

  • AEO = Annual energy output, kWh/year
  • D = Rotor diameter, feet
  • V = Annual average wind speed, mph[3]

The Wind Energy Payback Period Workbook is a spreadsheet tool that can help you analyze the economics of a small wind electric system and decide whether wind energy will work for you. The spreadsheet can be opened using Microsoft Excel software. It asks you to provide information about how you will finance the system, the characteristics of your site, and the properties of the system you’re considering. It then provides you with a simple payback estimation (assumes no increase in electricity rates) in years. If the number of years required to regain your capital investment is greater than or almost equal to the life of the system, then wind energy will not be practical for you.

References

  1.  "American Wind Energy Association. AWEA Small Wind Turbine Performance and Safety Standard"
  2. Manwell, James. (2010). Wind Energy Explained. John Wiley & Sons Ltd. ISBN 978-0-470-01500-1
  3.  "U.S. Department of Energy. Installing and Maintaining a Small Wind Electric System"