Determing rated wind speed

Wind & Water Rotor Aerodynamics
1

Dear all.

Issue: Difference in the rated wind speed determined using formula (1) and formula (2).

I am working on WP1.5MW turbine. I have generated power curve using OpenFAST using the grid resolution: Tip speed ratio—0.061; Pitch — 0.1 deg.
The optimal point on power surface plot:
Tip speed ratio (lambda_opt) = 7.2082, optimal pitch (beta_opt) = 2.2 deg , and the corresponding the power coefficient C_Popt = 0.48059.
Rated generated sped (Omega_g)_rat = 1800 RPM, Gear ratio:87.965, Radius = 35m, rho = 1.225 kg/m^3.
We know,
lambda = (ROmega/V) ----(1)
P= 0.5rhoPiR^2*V^3*C_P ---- (2)
By substituting the values corresponding to the optimal point in the formula (1), rated wind speed is obtained as V_rat = 10.404 m/s.
By substituting the values corresponding to the optimal point in the formula (2), rated wind speed is obtained as V_rat = 10.980 m/s. This means, the wind turbine cannot produce rated power for any wind speed less than 10.980 m/s. But the value obtained from formula (1) is different. How to understand this difference, if at all it is expected?

Regards,
Kumara

2

Dear Kumara,

Your first formula is correct, but it is not typically the case that a wind turbine operates at lambda_opt at rated speed. Instead, a wind turbine typically operates with a lambda less than lambda_opt at rated conditions to avoid excessively high tip speeds.

Best regards,