Wind Turbine Power Output

Everybody talks about wind turbine power output, however; few people know what wind turbine output power really means or "how to calculate wind turbine power output". Formula for calculating output power of wind turbine is a simple equation given towards the end, but general explanation about wind turbine power output will be explained first.

 

Wind Turbine Power Output Overview

The output power of a wind turbine has to be one of the most misunderstood and over quoted aspects of a wind turbine. In order to shed some light on this subject you have to know that wind turbines convert kinetic energy (rotational energy) to mechanical energy and the mechanical energy will be transformed to electrical energy.

In other words, when the alternator (also known as generator) spins and rotate, power will be produced. This is usually typical for all power generating equipments whether it is used for renewable energy or conventional energy such as the alternator that charges your car’s battery (Note: Car's alternator shouldn't be used as a wind turbine alternator without modifications).

However, this does not mean that the alternator can run at any speed and produce the same output power; there is a limitation to how much each and every generator can produce.

Power Output Production and Speed:

When the alternator starts spinning, very little power will be produced. With increased speed, the output power increases and a point will be reached where the power output will be the rated power of the alternator. However, the wind turbine generator can spin faster than its rated power and can produce much more output power.

Eventually, a shutdown value will be reached at higher speed which is usually assigned by the wind turbine alternator manufacturer and will force the generator to stop delivering output power by applying the internal breaking system in order to slowdown the wind turbine and prevent damage to the alternator.

How to Calculate Wind Turbine Power Output?

The wind turbine power output can be calculated using one formula that relates the wind turbine blade diameter (swept area) to the wind speed. You don’t have to concern yourself with how this equation was derived which will be explained somewhere else, however; you can use it to calculate the wind turbine power outlet of three bladed wind turbine.

Formula for Calculating Wind Turbine Power Output

Example: Calculating Wind Turbine Power Output:

Assume you have the below data and you want to calculate the output power of your wind turbine.

Wind speed (V): 3 m/s

Air density (ρ): 1.23 Kg/m3

Betz limit (Cp): 35% (for a good design)

Swept area (A): 5.73 m2

If you plug these values in the power equation, your calculated wind turbine power output would be:

Power Output= ½ (1.23) (.35) (5.73) (3x3x3) = 33.2 Watts

The power output is really too low for you to use, the 3 m/s is usually around the cut-in wind speed, however; if the wind speed was 7 m/s then the wind turbine power output would increase dramatically and can be calculated with the same equation and would produce:

Power Output = ½ (1.23) (.35) (5.73) (7x7x7) = 421.6 Watts

So your turbine can extract about 423.05 watts when the wind speed is 7 m/s which would lead to about 12.8 times more power. However, what would you get if the wind speed was 12 m/s?

Plugging the values in the previous equation while changing only the wind speed value, the wind turbine power output equation yields:

Power Output = ½ (1.23) (.35) (5.73) (12x12x12) = 2,123.8 Watts

What is unique about wind turbine power output is that doubling the wind speed will give 8 times power output while tripling the wind speed will give 27 times the power output and so on. Why is that? It is basically because the wind speed (velocity) is cubed in the power formula. 

Below the graph represents the wind turbine power output curve at different wind speed. The values plotted where taken from the above power equation formula.

 

Data for Calculating Wind Turbine Power Output:

 

Wind Turbine Power Output Data
Wind Speed (m/s)	1	2	3	4	5	6	7	8	9	10	11	12	13
Power Output (Watts)	1.2	9.8	33.2	78.7	153.6	265.5	421.6	629.3	896.0	1,229.1	1,635.9	2,123.8	2,700.3

Data Plot: Wind Turbine Power Output Curve

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