Review of power curve modelling for wind turbines

TLDR: In this article, a review of the equations commonly used to represent the power curves of variable speed wind turbine generators (VSWTs) is carried out, which shows that the exponential and cubic approximations give the higher R 2 values and the lower error in energy estimation.

Abstract: Currently, variable speed wind turbine generators (VSWTs) are the type of wind turbines most widely installed. For wind energy studies, they are usually modelled by means the approximation of the manufacturer power curve using a generic equation. In literature, several expressions to do this approximation can be found; nevertheless, there is not much information about which is the most appropriate to represent the energy produced by a VSWT. For this reason, in this paper, it is carried out a review of the equations commonly used to represent the power curves of VSWTs: polynomial power curve, exponential power curve, cubic power curve and approximate cubic power curve. They have been compared to manufacturer power curves by using the coefficients of determination, as fitness indicators, and by using the estimation of energy production. Data gathered from nearly 200 commercial VSWTs, ranging from 225 to 7500 kW, has been used for this analysis. Results of the analysis presented in the paper show that exponential and cubic approximations give the higher R 2 values and the lower error in energy estimation. With the approximate cubic power curve quite high values of R 2 and low errors in energy estimation are achieved, which makes this kind of approximation very interesting due to its simplicity. Finally, the polynomial power curve shows the worst results mainly due to its sensitivity to the data given by the manufacturer.