you know "Wind energy explaind" from WILEY ? you would get your help from this book chapter 3.

I guess the formula can be derived with regarding theory of Betz, schmitz ...etc

Hello ,

The following link helped my understand these concepts :

https://community.dur.ac.uk/g.l.ingram/download/wind_turbine_design.pdf

It has all the derivations and final formulae for Cp and Cv using BEM theory

Hope it helps.

Hi,

For any specific shape (or configuration) the Cp vs TSR will be a single curve, even if the wind speed changes. This curve is a "definition" of the aerodynamic characteristics of the wind turbine. Thus, if you change the blade characteristics, say by changing the pitch angle, then you really have a "new turbine". Doing so would then change the Cp vs TSR curve.

The easiest way to understand this curve is first to imagine a wind turbine in a constant wind. Without taking any power out of the shaft (free windmilling state), the Cp would be 0 and the TSR is at maximum value. Then you start to draw out power from the rotating shaft (easiest is by mechanical braking),  The Cp would increase, but the turbine speed would reduce, lowering the TSR (rem. the wind speed is constant).

You could continue drawing power from the shaft The angle of attack at the blades would increase. You could continue until a point where the angle of attack starts to be more than the alpha max - meaning the blade starts to stall. Once this happens, the power that you can draw out of the shaft would start to reduce. Finally you reach the zero power condition when the rotor stopped altogether. This is the point at the origin of the graph.

Note also that if you draw a straight vertical line at Max Cp, the behaviour of the turbine could be divided into two. The right side is stable while the left side would be unstable.

Wan Zaidi 

Wan Zaidi's answer is very good. To summarize, the Cp vs TSR function is standard, and the resulting curve is dependent on, basically, aerodynamical profile, number of blades and pitch.

this curve   explains the Wind turbine control not the performance of Wind turbine  because the Cp  depends to a lot of combained aerodynamic parameters based on BEM theory  in a state of Wind speed with consider the type of design wind turbine (fixed speed-variable speed).

Mohammaed,

We have not gone to the point of controlling the turbine yet. JUst to understand if the Cp is a function TSR. When we want to control the wind turbine, it is totally a different ball game. Although understanding the Cp characteristics is the basis of the design of the control algorithm.

TQ.

Wan Zaidi