Transformation of Wind Turbine Power Curves Using the Statistics of the Wind Process

A new methodology is derived to transform between an ideal zero-turbulence power curve and practical power curves representing wind turbine performance in irregular winds. The derivation is based on substituting a theoretical distribution of the wind process in place of a single mean wind speed, truncating the wind-speed distribution at the rated power of the turbine, and then applying random process theory to derive analytical expressions based on the expected power and standard deviation of power of the parts of the distribution above and below the rated speed. The resulting expressions explicitly include the effects of turbulence intensity and can be used with higher statistical moments of the wind. The limited number of parameters needed to develop a practical power curve and to predict the standard deviation of the power can be estimated from limited time-domain simulations or from measured field data. The new methodology can also be used to generate a turbulence-free power curve from power data measured in turbulent winds. The accuracy of the new method is demonstrated by benchmarking expected power and standard deviation of power against predictions based on using direct numerical simulation and against an equivalent power curve resulting from direct field measurement.