# Determing rated wind speed

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= 0.5
rhoPiR^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

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,