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I am going to design 10 kw, Permanent Magnet, Direct Drive Wind Turbine Generator. The main problem is, how to determine the rotational speed of the Wind Turbine. This is important for me because I have to design the PMG and its rated rpm values.

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The Power captured by Rotor blades from Wind is given by formula :-

Cp = Power coefficient of turbine

r = radius = length of the blade

v = velocity of wind.

Also, Power in any rotational object is given by formula :-

τ = Torque

ω = Angular Velocity of the rotating blades.

If we equate both the equations, then still Torque and angular velocity is unknown. Then how can we calculate angular velocity ? unless we know Torque ?

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We know that Kinetic Energy of the rotating Blade is given by formula :-

I = Moment of Intertia of Rotating Blades

i.e. I = 1/3 * n * M * r^2 where M = Mass of blades;

r = length of blade;

n = number of blades

Can Kinetic Energy of rotating Turbine be equated with Power in the Rotating Turbine multiplied by Time ?

i.e. K.E. = P x Time ??????

Putting Power equation in the above formula :-

K.E. = 1/2*Cp*ρ*(πr^2)*v^3 x Time

Please correct if I am wrong in my assumption. Also please suggest me a better calculation to determine RPM of Wind Turbine if input Wind Power is known.

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__First calculation:__

The Power captured by Rotor blades from Wind is given by formula :-

**P = 1/2*Cp*ρ*(πr^2)*v^3**Cp = Power coefficient of turbine

r = radius = length of the blade

v = velocity of wind.

Also, Power in any rotational object is given by formula :-

**P = τ * ω**τ = Torque

ω = Angular Velocity of the rotating blades.

If we equate both the equations, then still Torque and angular velocity is unknown. Then how can we calculate angular velocity ? unless we know Torque ?

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__Alternate calculation is given below. I may be wrong here :-__

We know that Kinetic Energy of the rotating Blade is given by formula :-

**K.E. = 1/2 * I * ω^2**I = Moment of Intertia of Rotating Blades

i.e. I = 1/3 * n * M * r^2 where M = Mass of blades;

r = length of blade;

n = number of blades

Can Kinetic Energy of rotating Turbine be equated with Power in the Rotating Turbine multiplied by Time ?

i.e. K.E. = P x Time ??????

Putting Power equation in the above formula :-

K.E. = 1/2*Cp*ρ*(πr^2)*v^3 x Time

Please correct if I am wrong in my assumption. Also please suggest me a better calculation to determine RPM of Wind Turbine if input Wind Power is known.

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