# Variable Speed Fixed Pitch WT blade design

Hello to everybody,
First of all, as I wasn’t sure if this question should go with CONTROL topics or it is more related with AERODYNAMICS I have decided to post it here.
I’m designing a VS-FP (passive stall,10 kW rated) WT blade for my Master Degree Final Project to be placed in a low wind town surroundings (with Weibull parameters k=1.79 and c=5.5). My doubts are the followings:

1. As far as I know, in variable speed turbines we make the rotational speed increase proportionally with wind velocity until a certain point so that we work in the optimum TSR for the turbine. I have seen in some books that the Cp remains constant and Cp=Cpmax within this range of velocities as it can be seen in the attached figure.
My concern is that when I design the blade with BEM corrected method using Matlab I optimize the twist angle of each section of the blade to reach maximum glide ratio (Cl/Cd). I choose a design velocity (the most probable in the emplacement) and this gives a different chordal Re number in each section, so the angle of attack in which the maximum Cl/Cd ratio are evaluated for the precise Re number that occurs in each spanwise point.
Mantaining a constant TSR within a range of velocities will make the angles of attack to remain constant and equal to those of the design, but with different wind velocities (from the velocity used in the design), wouldn`t we have our blade sections working in different reynolds regimes, and therefore nearly optimally (but not exactly)?
2. My second question is directly related to the control system issue. How can I set the limit of the gap where my WT will work in variable speed? I mean, it will start working variable speed with the Cut-in velocity, but how can I establish a criteria to decide at which wind velocity it will switch to constant velocity. Could it be a tip noise matter? Which are the practical drawbacks of being working in VS through a wide range of velocities?
Best regards,
Alvaro Olcoz

Dear Alvaro,

Regarding (1), I’m sure an aerodynamicist can offer more advice, but I agree that an airfoil at a given cross section of a variable speed wind turbine will experience different Reynolds numbers. Due to the often quite high tip-speed ratio, the omega cross radius term tends to dominate the local relative wind velocity rather than the wind speed, so, variable speed rotors will operate with variable Reynolds number.

Regarding (2), often the operational variable-speed range is limited by (a) noise constraints that limit the maximum rotational speed and (b) structural constraints–to avoid having the wind excite natural frequencies in the structure. Reason (b) is often addressed through the use of a Campbell diagram that shows the natural frequencies of the wind turbine as a function of rotor speed. Due to rotational sampling of turbulence, the blades will be excited by 0P, 1P, 2P etc. effects and the support structure will be excited by 0P, 1P, 3P, 6P, etc. effects. Thus, these lines of constant frequency are added to the Campbell diagram to identify areas of potential resonance. The wider the range of rotational speed, the harder it is to avoid resonances in the structural design.

Best regards,

Dear Jason,
Thank you very much for such a quick reply.
I would like to ask you which of your NWTC design codes would be the best one to perform the following:
I have implemented the BEM theory (+ corrections) in Matlab to get the Power-velocity and CP-velocity curves of a WT with the previously designed blades and now I would like to test the results that I got from these simulations with the results of one of your design codes. So, which will be the most appropiate way to perform such a simple analysis (steady wind, no stall delay, no blade mass…)?