Energy Production: Donohoe Wind
Donahoe Wind
by Brandee Scheffey, student research assistant
[note: click here for a kids activity page, click here for a connect-the-dots page]
Wind energy is becoming more popular every year as a way to supply energy to homes and businesses, although it has been around for a longer time then you may realize. This type of energy has been used for hundreds of years, since European settlers arrived on wind-powered ships, and windmills were used during colonial times. Modern wind power equipment is very different from those early attempts to harness the power of the air. Most commonly, wind energy systems generate electricity using large wind turbines on top of a hill or mountain ridge or in exposed locations.
The wind turbine installed by Penn State Extension in Greensburg, PA at the Donahoe Center is rated to provide up to 10 kW of 3-phase power to the electrical grid. (The electrical grid is an interconnected system for delivering electricity from suppliers to consumers. It consists of three main components: generating plants that produce electricity, transmission lines that carry electricity to demand centers, and transformers that reduce voltage so distribution lines can deliver power to consumers.) A wind turbine is basically the opposite of a fan. Instead of using electricity to make wind, wind turbines use wind to make electricity. Simply stated, wind pushes and turns the blades, which spin a shaft. The shaft is connected to a generator that makes electrical energy.
You might think that wind turbine blades are similar to airplane propellers because of how they operate, but in fact the composition and aerodynamics of the blade are much more like the wings of an airplane. In cross section, an airplane wing looks like an irregularly shaped teardrop. When a plane flies, its wings slice through the air, creating a lifting force on the wing. Because of the curve on the upper surface of the wing, wind must flow faster to get around it, relative to the flat bottom surface. Because of the difference in speed, the air above the wing has lower air pressure than the air below the wing. The difference in pressure creates lift that is perpendicular to the direction of the moving air, allowing the plane to fly.
The same principle applies to wind turbine blades. Wind turbines extract energy by slowing down the wind. For a wind turbine to be 100% efficient it would need to stop 100% of the wind - but then the rotor would have to be a solid disk, and air would "pile up" at the location of the wind turbine, because it wouldn't have any kinetic energy to move away from the turbine. On the other extreme, if you had a wind turbine with just one rotor blade, most of the wind passing through the area swept by the turbine blade would miss the blade completely and so the kinetic energy would be kept by the wind. Albert Betz was a German physicist who in 1919 concluded that no wind turbine can convert more than 59.3% of the kinetic energy of the wind into mechanical energy turning a rotor. To this day this is known as the Betz Limit.
This limit has nothing to do with inefficiencies in the generator, but in the very nature of wind turbines themselves. The theoretical maximum power efficiency of any design of wind turbine is 0.59. Once you also factor in the engineering requirements of a wind turbine, the real world limit has values of 0.35-0.45. By the time you take into account other inefficiencies in a complete wind turbine system - e.g. the generator, bearings, power transmission and so on - only 10-30% of the power of the wind is ever actually converted into usable electricity. (http://www.reuk.co.uk/Betz-Limit.htm)
Those that can take full advantage of wind energy are farmers who own land that is suitable for wind farming and can use their location to install their own wind turbine. People in remote areas where electrical wiring would be expensive, or those with large, flat areas of land would also benefit greatly from wind energy. A location must be VERY windy to be commercially desirable for wind power. In Pennsylvania, this means that only the highest ridge tops and the shore of Lake Erie are the most practical spots for wind turbines. A graph below shows the relationship between wind speed and power production at the Donahoe Center wind turbine. Notice how, on the windy day, the wind speed is higher and the amount of wind power produced is higher as well. On calm days, the opposite happens. Notice how the relationship is not linear - low wind speeds produce extremely little power, and only relatively high windspeeds generate a significant amount.
The sporadic nature of wind speed and direction near the ground means that wind energy is most ideal for locations far above ground level level to maximize available wind.
Activity:
Given that the maximum amount of energy that the Donahoe turbine can produce is 10 kW at a design wind speed of 16 meters per second, calculate the maximum power efficiency of the Donahoe wind turbine. The diameter of the turbine is 7 meters and the density of air is 1.2 kg/m3.
Need a few hints? Here's how to go about it.
1) Figure out how much energy is in the wind at 16 m/s velocity. Use the following equations:
E = ½ m * v^2
E = energy in the wind (watts)
m = mass flow rate of air through the turbine's "swept area" (kilograms per second)
v = wind speed (meters per second)
m = h * A * v
m = mass flow rate of air through the turbine's "swept area" (kilograms per second)
h = air density (kilograms per cubic meter)
A = "swept area" of the wind turbine blades (square meters)
v = wind speed (meters per second)
A = p * r^2
A = "swept area" of the wind turbine blades (square meters)
p = 3.14159
r = radius = length of turbine blade (meters)
2) Figure out the theoretical maximum amount of energy that can be removed from the wind by the turbine. Use the following equation:
Max = 0.593 * E
Max = maximum energy that can be removed from the wind (watts)
E = energy in the wind (watts)
3) Calculate the efficiency (%) of the turbine based on its actual output. Use the following equation:
% = (10 kW ÷ Max) * 100
% = percent efficeincy of the turbine
Max = maximum energy that can be removed from the wind (watts)
Note that the asterix symbol (*) is used to mean "multiplied by" and the carat symbol (^) is used to mean "to the power of". For example, 2 * 4^2 means "two multiplied by four squared".