I want to calculate the power of wind turbine, the result should be between cut in and cut out speed, above or below equal to zero.
I found two equations for this purpose which are:
1-p=0.5*r*a*cf*v^3
2- p=prated*(vbins.^2 - vin^2)/(vr^2 - vin^2);
but the result is completely different even if I used the same spread sheet for the speed, which contains 8760 hours for a year.
Dear Rahil,
with these two equations, you'll calculate only the wind power in watt [W] at time "t". I thinks that the first one is more accurate, where you have direcly the power coefficient at wind speed "v" specified for each wind turbine by the power coefficient curve, and the second one includes many wind turbines.
exple: you can have many wind turbines with the same rated capacity and same wind speeds cut, in and rated but you will have a wind turbine which will give you a better result for a wind speed "v".
other mark, I think that the coefficient on the second equation is not "2" but "k" the shape Weibull parameter, but I'm not sure.
Good luck.
Dear Boudia
first, thanks for your help
i just calculate the power with different value of speed with other constant values(swept area, cut in ,cut out, rated speed & power and capacity factors)
my question can i use these equation to the same purpose
Dear,
look this article
Y. Xia, K.H. Ahmed, B.W. Williams, „Wind Turbine Power Coefficient Analysis of a New Maximum Power Point Tracking Technique“, IEEE Trans. Ind. Electr, Vol. 60, No. 3, march 2013, pp. 1122-1132.
Martin
Dear Abdulla,
Power available in a particular swept area at a particular speed of a wind is given by:
P(available in wind)= 0.5x air density x Swept Area x wind velocity cubed
Cp value is the wind turbine power coefficient. It is basically the efficiency of the turbine.
P(wind turbine) = P(available in wind) x Cp ,OR;
P(wind turbine) = 0.5 x air density x swept area x wind velocity cubed x Cp
However, these formulas do not have any boundaries, i.e. cut-in or cut-out.
Remember that these are power(watts) at a particular time. They are not energy yield formulas. The Energy yield(Joules or WHrs) would be the sum of all "Power x Time" where power is calculated for each velocity for the duration.
For your second equation, see the link.
scroll down to the section for: Defining the Turbine Power Curve
http://www.mathworks.com/examples/matlab/3412-wind-turbine-data-analysis
Dear Rahil,
With the first equation you are calculating the wind power associated with certain velocity. With second equation, you are calculating the available power between cutin and cutout speed. The accurate method would be:
1) First with the historical data, you evaluate the probability distribution function it follows. This graph will tell you about the wind power density of location. It is not what you can harness.
2) Next, you need to fit the power curve of turbine against the predicted power curved of location. With cutin speed, cut out speed, rated speed and actual efficiency known, you can evaluate what a turbine's output would be.
Since, the wind velocity will be different at different time, you can't simply evaluate the power with one velocity.
http://xn--drmstrre-64ad.dk/wp-content/wind/miller/windpower%20web/en/tour/econ/oandm.htm
Power output is calculated as follows: power = [(air density) times (swept area of blades) times (wind speed cubed)] divided by 2. The area is in meters squared, air density is in kilograms per meters cubed and wind speed is in meters per second.
Like what others have said, the first formula does not consider cut-in and cut-out speed....and it simply estimate the wind power not the actual usable electrical power.
Formula 2 is suitable when you have the details for a specific wind turbine product which can be obtained from the manufacturer data... With the availability of historical data, consideration of uncertainties, and wake effects (for multiple wind turbines) formula 2 is preferable
Most of the wind turbine specifications do not have the rated wind speed. Then how I can estimate the probable power generation?
In calculation of wind power extracted Coefficient of Power (Cp) is the major factor after the wind velocity. As Cp is a function of Pitch angle (beta) and tip speed ratio (gamma), it varies with wind speed. So using a particular Cp value for every wind speed will generate error. Also, if the Generation of one day is calculated then taking average wind speed for that day for calculation will also cause reduced accuracy. Wind speed for each and every interval say per hour should be taken and the cumulative energy generation will be accurate.
P= 0.5*Area*air density*(wind velocity)^3 *Cp
Area = pi*r^2
Air density @15°C = 1.225kg/m^3
Cp = 0.35-0.45 max =0.59
Energy gen = pow*generation hours
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