TURBINE OPERATION/ENERGY OUTPUT

Power coefficient

Introduction
The power coefficient CP tells how efficiently a turbine converts the energy in the wind to electricity. Very simply, the electrical power output is divided by the wind energy input to measure how technically efficient a wind turbine is. In other words, the power curve is divided by the area of the rotor to get the power output per square metre of rotor area. For each wind speed, the result is then divided by the amount of power in the wind per square metre.
The graph shows a power coefficient curve for a typical wind turbine. It shows the power coefficient as a function of the windspeed of a stall controlled wind turbine. Although the average efficiency for these turbines is somewhat above 20%, the efficiency varies very much with the wind speed. Note that if there are small kinks in the curve, they are usually due to measurement errors.
As it can be shown, the mechanical efficiency of the turbine is largest (in this case 44%) at a wind speed around some 9 m/s. This is a deliberate choice by the engineers who designed the turbine. At low wind speeds efficiency is not so important, because there is not much energy to harvest. At high wind speeds the turbine must waste any excess energy above what the generator was designed for. Efficiency therefore matters most in the region of wind speeds where most of the energy is to be found.

Higher technical efficiency is not necessarily the way forward
It is not an aim in itself to have a high technical efficiency of a wind turbine. What matters, really, is the cost of pulling kWh out of the winds during the next 20 years. Since the fuel is free, there is no need to save it. The optimal turbine is therefore not necessarily the turbine with the highest energy output per year. On the other hand, each square metre of rotor area costs money, so it is of course necessary to harvest whatever energy is possible- as long as the costs per kWh can be kept down. We return to that subject later on the page about optimising wind turbines.

The Cp-λ curve
Once the blade has been designed for optimum operation at a specific design tip speed ratio, which is defined as the ratio between the blade tip speed and the wind speed, the performance of the rotor over all expected tip speed ratios needs to be determined. For each tip speed ratio, the aerodynamic conditions at each blade section need to be determined. From these, the performance of the total rotor can be determined. The results are usually presented as a graph of power coefficient CP versus the tip speed ratio λ. This graph is called the CP-λ curve.

The shape of this curve be made plausible with the following reasoning:
- At λ= 0 the rotor does not rotate and hence cannot extract power from the wind - At very high λ (in this case λ = 12) the rotor runs so fast that it seen by the wind as a completely blocked disc. The wind flows around this "solid" disc (as if it was a solid building), so there is no mass transport (wind) through the rotor, and hence no possiblity to extract energy from a moving mass (the wind).
- Somewhere between λ= 0 and λ= 12 there will be an optimum value, in this case λ= 8 for which the maximum power is extracted. This will be the condition in which the (average) velocity at the rotor disc is 2/3th of the wind speed according to Betz law.
These CP-λ curves are used in wind turbine design to determine the rotor power for any combination of wind and rotor speed. In the next section this is explained in more detail.