Aug 04
2009

If you read the papers or keep on top of alternative energy news I’m sure that you have seen at least one article, if not many, in the past months about wind farms and/or wind turbine technology being installed in residential applications or in large scale power generation projects. Either way, wind turbines are rapidly being installed in many parts of the world to generate clean electricity. Let’s take a look at the basic principles of Wind Turbines and how they work.
Overview
Wind Turbines make use of the kinetic energy contained within the wind itself to turn a propeller of some kind (there are many different styles) which then turns a generator to create electricity. Electricity created by a wind turbine is typically Direct Current (DC) electricity and is either used to charge batteries and then converted, via an inverter, into Alternating Current (AC) electricity for operation of appliances within a home or business or it is sent directly to an inverter to generate AC electricity for immediate use with no backup storage.
The amount of power, measured in Watts, that a wind turbine can generate is based on a number of factors. One of them is the generator itself and what voltage it generates and at what current. Power can be calculated using a simple formula:
Power = Voltage * Amperage or
P = V * A
So, if a generator connected to a wind turbine can generate 48V at 1A that generator is capable of generating 48W (48V * 1A = 48W) of electricity at its rated speed.
An important factor in determining power is the speed at which the generator rotates. However, since the generator rotation speed is directly affected by the rotation of the turbine we need to look at the factors that affect the turbine rotation. There are a number of factors that affect rotation speed on a wind turbine but there are 2 primary factors; 1) wind speed and 2) swept area of the blades.
Wind Speed
Wind speed is extremely important because the higher the wind speed the more kinetic energy that is applied to the blades to cause the turbine to rotate. Without going too deep into the mathematics behind it wind speed is extremely important because the power curve associated with wind speed is not linear. For example; let’s assume that a certain turbine would generate 100W of power with a wind speed of 5 m/s. If you double the wind speed to 10 m/s the power doesn’t double to 200W, in fact the power jumps to 800W. Every time you double the wind speed the potential power generated increases by a factor of 8. Now you can see how important wind speed is to wind turbines and the power generated.
Swept Area
The swept area is the total surface area that the blades cover as they rotate and as such is the total area in which the kinetic energy of the wind is captured by the wind turbine. The larger the swept area the more kinetic energy that can be harnessed and cause the turbine to rotate. The diameter of the blades affects power consumption in a similar way to wind speed. If you double the blade diameter the potential power from the turbine will actually increase by 4. So, if you had a turbine with a blade diameter of 1m and it generated 100W of power, by increasing the blade diameter to 2m your potential power generation would go from 100W to 400W.
Wind Turbine Power Generation
So you can see the importance of these 2 factors as they apply to increasing power generation on a wind turbine. If a wind turbine with a 1m blade diameter generates 100W at wind speeds of 5 m/s, by doubling the wind speed and the blade diameter you would have 3200W (assuming all other efficiencies etc. of the 2 turbines are equal) of potential power.
There are other factors that affect turbine operation such as the pitch of the blades, atmospheric pressure, and a number of efficiency factors but we won’t spend a lot of time on these but there are a couple other factors we should discuss quickly to help you understand how turbines are rated.
Wind turbines are generally rated at their peek output. A wind turbine that is rated at 1kw will not generate 1kw at all times. As you saw earlier, wind speed plays a significant role in how much power can be generated by a turbine so if the wind is not blowing at the same speed identified for the turbines peek output it will generate less power. Many turbines also have a maximum rotation speed which also limits the power that can be generated so you can just assume that continued increase in wind speed will yield an unending exponential increase in power because the mechanical equipment will fail if some sort of brake (mechanical – known as a furl, or electromechanical etc.) is not used to prevent equipment damage in extremely high winds. So when you are looking for a wind turbine is it important to understand how to read a power curve chart which will show you the expected power output for the turbine at a given wind speed, and it will also show the maximum power output of the turbine as well.
Calculating Total Available Wind Power
The formula for calculating the total potential power from the wind is:
Total Available Wind Power (W) = 0.5 * Air Density * Swept Area * Wind Speed (m/s)^{3}
This formula calculates the potential power (in watts) available in the wind given the parameters specified. This formula does not take into consideration efficiency of the turbine and losses due to mechanical systems and inefficiencies in the turbine design. This is jus the raw potential power (in watts) of the wind at a given speed across a given swept area. Let’s read further to see how some other factors affect calculating actual turbine power.
Air Density
It is important to quickly note Air Density. The higher above sea level you live, the less dense the air is. The less dense the air is the less kinetic energy contained within the air and as such the less energy that is applied to a wind turbine when the wind is blowing. At sea level (at 15 Celsius) air has a density of 1.23 kg/m^{3}. It’s important to understand this since many turbines are rated at see level. But if you live in an area that is 5000 ft above see level your air density factor may be only 1.02. Changes in temperature also affect air density. Try changing air temperature from 40 degrees Celsius to 20 degrees Celsius. There are almost 25 per cent more air molecules in a cubic metre of the cold air than in a cubic metre of the warm air. That would affect power output by about 25% (better in colder temperatures). Moist air is also less dense than dry air. So you can see there are a number of factors that affect air density so using the ratings below is the simplest approach I’ve found. Since air density will change based on moisture, temperature etc. you don’t have to worry about getting this exactly right, because there is no “exactly right” since it changing all the time.
Altitude in Feet above Sea Level Output Correction (rounded) 
Air Density Factor kg/m^{3} 

0 
100% 
1.23 
2500 
91% 
1.12 
5000 
83% 
1.02 
7500 
76% 
0.93 
Turbine Efficiency
Since wind turbines are not 100% efficient there is another factor that needs to be applied to the calculation that will reflect the turbines efficiency and subsequently the power that can be expected to be generated by a given turbine. This factor is known as the Coefficient of Power (CP), or Power Coefficient, and will vary from turbine to turbine. Not only does it vary from design to design, but the power coefficient for a single turbine will vary depending on what speed the turbine is operating at. Generally the faster the rotation the less efficient the turbine. So looking at power coefficient requires that we consider average power coefficient based on the wind speeds in an area since some days you maybe operating at the most efficient wind speeds and on other days at a lower efficiency. Apparently a 30%35% average Coefficient of Power would indicate a very well designed turbine. Let’s use 30% in the example below. So now the formula for determining the potential power from a turbine (not the potential power in the wind) looks like:
Total Available Turbine Power (W) = 0.5 * Air Density * Swept Area * Wind Speed (m/s)^{3} * Coefficient of Power
Let’s try this formula out. Let’s assume an air density of 1.23 (sea level), blade diameter of 5 ft (1.52m) which would have a swept area of 1.81m^{2} , a wind speed of 5 m/s and a Coefficient of Power (CP) of 30%.
Total Available Turbine Power (W) = 0.5 * 1.123 * 1.81 (m^{2) } * 5^{3} (m/s) * 30%
Total Available Turbine Power (W) = 0.5 * 1.123 * 1.81 * 125 * 30%
Total Available Turbine Power (W) = 42W (rounded)
If this turbines peak output rating is calculated at wind speeds of 15m/s the power rating you might see on the marketing materials is:
Total Available Turbine Power (W) = 0.5 * 1.123 * 1.81 (m^{2) } * 15^{3} (m/s) * 30%
Total Available Turbine Power (W) = 0.5 * 1.123 * 1.81 * 3375 * 30%
Total Available Turbine Power (W) = 1127 W (rounded) or 1.1kW
Summary
So, now you can see how important it is to understand how ratings are calculated and even more important to understand how to read a wind turbine power curve chart (which is quite simple) so you can determine the power output you might expect from a turbine based on your local conditions. In addition it doesn’t hurt to talk to an expert in the field as they will understand in even more detail the specifics of the various products they represent. You also now know enough to ask some intelligent questions so you can get data that is more accurate to your area instead of just the “ideal” ratings.