Modeling of power curves for industrial wind turbines of specified unit size

Abstract

Based upon the analysis of power curves of 66 wind turbines in megawatt class, a mathematical model of the power curve has been developed, which, contrary to the already existing models, allows determination of the power curves for a wind turbine merely by using its two main parameters: wind-turbine generator nameplate capacity and rotor diameter. It has been proved that the mathematical model of the power curve for a wind turbine of specified unit size presented as a spline can be approximated to the power curve of wind turbine of another unit size by introducing respective scaling factors along Х and Y axes. From the results of the investigation a linear dependence was revealed between scaling factors and respective values of WT generator nameplate capacity, rotor diameter, and respective equations of linear regression were obtained. A statistical analysis based on the results of modeling of the power curves for 66 wind turbines with power ranging from 2.0 to 3.6 MW and rotor diameter from 100 to 140 m showed their high average coefficient of determination R2 = 0.995, and a standard deviation of simulation absolute error is broadly congruent with an error of power curve experimental determination. The developed mathematical model of power curve enables prompt and reliable determining the power curve for a wind turbine of specified unit size, if there is no free access to it, or for the wind turbines being designed.