Defining Capacity Factor by Weibull Shape Parameter and Mean Wind Speed

Abstract

This workmodels capacity factor in terms of wind turbine operating characteristics, mean wind speed, and shape parameter of Weibull probability density function. The methodology used involves fewer parameters than have been used by other workers. We have used a nondimensional speed parameter ( x) as the ratio of the wind speed ( V) to the mean wind speed ( Vm). The operating characteritics of a megawatt wind turbine cut-in ( Vin), rated ( Vr) and cut-out ( Vout) speeds are divided by Vm, resulting into nondimensional speeds: xin, xr, and xout, respectively. Similarly, the Weibull scale parameter is also transformed by the Vm. The final model of the capacity factor constitutes four variables: xin, xr, xout and k. The analysis of model shows that, in general, low values of nondimensional speed xr results into higher values of capacity factor. The shape parameter also influences the value of capacity factor. High values of shape parameter provides, in general, low value of capacity factor. For example, a turbine designed for shape parameter of about 2 if installed at a site where the shape parameter is about 4 or more than the value of capacity factor may reduce by almost 10%. The analysis also shows that if one wishes to achieve higher values of capacity factor for a turbine desined for k = 2 to k = 4 would necessitate increase in the mean wind speed of the new site ( k = 4).