Modelling of cup anemometry and dynamic overspeeding in average wind speed measurements
Authors: Pedersen Troels Friis , Dahlberg Jan-Åke 
Published: March 2024

Abstract. Cup anemometers measure average wind speed in the atmosphere and have been used for one and a half centuries by meteorologists. Within the last half century, cup anemometers have been used extensively in wind energy to measure wind resources and performance of wind turbines. Meteorologists researched cup anemometer behaviour and found dynamic overspeeding to be an inherent and significant systematic error. The wind energy community has strong accuracy requirements for power performance measurements on wind turbines, and this led in the last 2 decades to new research on cup anemometer characteristics, which was taken to a new level with the development of improved calibration procedures, cup anemometer calculation models and classification methods. Research projects in wind energy demonstrated, by field and wind tunnel measurements, that angular response was a significant contributor to uncertainty and that dynamic overspeeding was a significant but less important contributor. Earlier research was mainly made on cup anemometers with hemispherical cups on long arms, ​​​​​​​and dynamic overspeeding was considered an inherent and high uncertainty error for cup anemometers. Research on conical cups on short arms has now shown that zero or low overspeeding is present on a well-designed cup anemometer, providing a much lower overspeeding uncertainty error. Different cup anemometer calculation models were investigated in order to find derived overspeeding characteristics. The general and often used parabolic torque coefficient model showed that zero overspeeding is present when the speed ratio roots of the torque coefficient curve go through the equilibrium speed ratio and zero. The two-cup drag model is a special case of the parabolic torque coefficient model but with the second root being reciprocal to the equilibrium speed ratio. The drag model always results in a positive maximum overspeeding of the order of 1.1 times the turbulence intensity squared. A linear torque coefficient results in maximum overspeeding levels equal to the turbulence intensity squared. Torque characteristics of a cup anemometer with hemispherical cups fit slightly well to the drag model, but a cup anemometer with conical cups does not fit to the drag model nor the parabolic model; it fits better to a partial linear model and even better to an optimized torque model. The most accurate modelling of cup anemometer characteristics is at present made with the ACCUWIND model (Dahlberg et al., 2006). This model uses tabulated torque coefficient and angular response data measured in a wind tunnel. The ACCUWIND model is found in International Electrotechnical Commission (IEC) wind turbine power performance standards, where it is used in a classification system for estimation of operational uncertainties. For an actual comparison of two cup anemometers, with respectively hemispherical and conical cups, the influence of dynamic overspeeding was found to be relatively low compared to angular response, but for conical cups it was specifically low.