How can I calculate the output power of wind turbine ?

Is the power as calculated by the above equation at rated speed very different to the rated power, or just a little?

The equation looks right to me - of course air density and capacity factor are estimates (often good estimates, but not perfect).  The power you calculate by that formula may not match an experimentally measured power at rated speed, but I'd expect the numbers to be "close".

in my case i put some condition which are

if wind speed<cut in then power=0 and if wind speed >cut out then power=0

and from cut in to rated speed , power extracted using the equation above

and from rated to the cut out the power = rated power

but the power still large compare with rated power for the period from cut in to rated speed

Yeah, I understand that, so you have:

        { 0                                   : v_w < cut-in

P =  { 0.5 * A * ρ * cf * v_w³     : cut-in < v_w < cut-out

        { 0                                   : v_w > cut-out

Right?

Presumably, rated-speed is between cut-in and cut-out.  If you calculate P for rated-speed, it should come out ~= rated power.  That's check 1 that I was suggesting above.  If that comes out significantly different, you probably have one of the variables (density, area or cap factor) wrong.  Let's assume it comes out similar...

Now, the function you have for P is monotonically increasing with v_w. Not only that, it increases fast (with v_w³).  So, if rated speed < cut-out speed then you're always going to get a range of v_w (between rated speed and cut-out) for which P_calculated > P_rated.

I have seen people deal with this in my work (caveat: aggregate output simulations only - not research into wind technology in itself) by limiting the power to rated power between rated speed and cut-out.  I guess that is one option - so you get

        { 0                                   : vw < cut-in

P =  { 0.5 * A * ρ * cf * v_w³  : cut-in < v_w < v_rated

        { P_rated                          : v_rated < v_w < cut-out

        { 0                                   : v_w > cut-out

If you need something less crude than that, you will have to go from actual power curves from experiments, I guess.  Depends what you want to use the power curve for.

Abdulla Rahil, you are right in using conditional statements. Just make sure that you Cp and tip speed ratio formulae are generating correctly. Please make sure that you cannot immediately have power of 0 W above the cut out speed. There is still some region in which pitch control is dominant. During this time the WECS will be generating rated power. When the rpm is close to the structural limit and pitch control cannot maintain / regulate rated power, only then the generator is stalled with zero output power.

Dear all, just let me add a picture to illustrate the ideal shape of the power vs wind speed curve of a wind turbine. The sketch is taken from Hugh Piggott's Windpower workshop. To obtain accurately the actual shape.of the curve between the cut-in speed and the rated speed, you should have the curve characterized by means of experimental testing of your turbine or by means of simulations with, for example, FAST & AeroDyn coupled simulation tools for Horizontal Axis Wind Turbines, etc.

Regards,

Jose

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.

Power = 0.5 x Swept Area x Air Density x Velocity3

example calculation :