Modelling Wind Turbine Power Curves based on Frank’s copula

Abstract

In  the  study  of  wind  turbines,  one  of  the  most  relevant  and  useful  indicators  is  the  power  curve.  It  has  been  shown  to  be  of  paramount  importance  in  evaluating  turbine  performance  and  therefore  reducing  operation  and  maintenance  (O&M)  costs.  Various  techniques  can  be  applied  to  model  and  obtain the shape of this curve, which relates the electrical power generated  by  a  turbine  to  the  wind  speed.  Statistical  copulas  are  used in this paper, a tool used in other fields such as econometrics, and  whose  potential  lies  in  its  ability  to  capture  the  complex  dependency  between  the  variables  involved.  In  particular,  the  Frank  copula  is  applied  to  obtain  a  probabilistic  model  of  the  power curve of a wind turbine. This model is compared with the Gaussian  Mixture  Model,  a  technique  widely  used  to  obtain  parametric probabilistic models. As a result of this comparison, it is observed that the Frank copula model fits the power curve of the wind  turbine  with  greater  precision  and  reliability,  which  would  allow its use for prediction and fault detection.