# Variability of the Wind Turbine Power Curve

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Collective Interactions Unit, Okinawa Institute of Science and Technology, Onna, Okinawa 9040495, Japan

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Department of Engineering & Public Policy and Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA

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Author to whom correspondence should be addressed.

Academic Editor: Frede Blaabjerg

Received: 9 July 2016 / Revised: 8 September 2016 / Accepted: 8 September 2016 / Published: 14 September 2016

(This article belongs to the Special Issue Advancing Grid-Connected Renewable Generation Systems)

Wind turbine power curves are calibrated by turbine manufacturers under requirements stipulated by the International Electrotechnical Commission to provide a functional mapping between the mean wind speed $\overline{v}$ and the mean turbine power output $\overline{P}$ . Wind plant operators employ these power curves to estimate or forecast wind power generation under given wind conditions. However, it is general knowledge that wide variability exists in these mean calibration values. We first analyse how the standard deviation in wind speed ${\mathsf{\sigma}}_{v}$ affects the mean $\overline{P}$ and the standard deviation ${\mathsf{\sigma}}_{P}$ of wind power. We find that the magnitude of wind power fluctuations scales as the square of the mean wind speed. Using data from three planetary locations, we find that the wind speed standard deviation ${\mathsf{\sigma}}_{v}$ systematically varies with mean wind speed $\overline{v}$ , and in some instances, follows a scaling of the form ${\mathsf{\sigma}}_{v}=C\times {\overline{v}}^{\mathsf{\alpha}}$ ; C being a constant and $\mathsf{\alpha}$ a fractional power. We show that, when applicable, this scaling form provides a minimal parameter description of the power curve in terms of $\overline{v}$ alone. Wind data from different locations establishes that (in instances when this scaling exists) the exponent $\mathsf{\alpha}$ varies with location, owing to the influence of local environmental conditions on wind speed variability. Since manufacturer-calibrated power curves cannot account for variability influenced by local conditions, this variability translates to forecast uncertainty in power generation. We close with a proposal for operators to perform post-installation recalibration of their turbine power curves to account for the influence of local environmental factors on wind speed variability in order to reduce the uncertainty of wind power forecasts. Understanding the relationship between wind’s speed and its variability is likely to lead to lower costs for the integration of wind power into the electric grid.

*Keywords:*wind power; power curve; variability