Critical analysis of methods for mathematical modelling of wind turbines

Accurate modelling is crucial in designing an optimum system. Wind speed distribution of selected site, hub height and power output curve of chosen wind turbine, are the main factors which influence the performance of wind turbines, and therefore, these must be properly accounted for during modelling of the wind turbines.This paper presents comparative study of various methods for mathematical modelling of wind turbines, with reference to three commercially available wind turbins, with the help of an algorithm developed.It has been found that modelling methods, based on fundamental equations of power available in the wind, are cumbersome to use and do not correctly replicate the behaviour of actual wind turbines.Models based on a presumed shape of power curve, though simple to use, also lack the desired accuracy; however, they give satisfactory response for higher annual average wind speeds.Modelling methods in which actual power curve of a wind turbine is used for developing characteristic equations, by utilising curve fitting techniques of method of least squares and cubic spline interpolation, give accurate results for wind turbines having smooth power curve; whereas, for turbines having not so smooth power curve, model based on method of least squares is best suited.

► Methods for modelling of wind turbines are compared by using developed algorithm.
► Models based on power available in the wind are inaccurate and cumbersome to use.
► Models based on presumed shape of power curve are simple but lack desired accuracy.
► For non-smooth power curve turbines model using method of least squares is accurate.
► For smooth power curve least square and cubic spline interpolation models are suited.