The Price of a Yaw: Optimal Deadbands and Filters for Wind-Turbine Yaw Control, Calibrated on SCADA Data

A wind turbine must keep its rotor facing a wind whose direction never stops moving, and every yaw that realigns it wears the yaw system. Using a year of 10-minute records from the six turbines of the Kelmarsh wind farm, this paper measures what sets the right policy: below rated power the wind direction wanders like a random walk, at 11.2 degrees per square-root hour on average but at a rate that changes with the weather, with 8.2 degrees of fast turbulence on top, and misalignment costs power as $\cos^k$ with $k = 2.59$. With the turbulence idealised as white noise, the optimal controller separates into a Kalman-Bucy filter whose time constant is $\eta\sqrt{2\tau_u}/s$, 3 to 8 minutes for turbulence correlation times of 10 to 60 seconds, and a deadband of half-width $(6Ks^2/a)^{1/4}$ on the filtered misalignment. An ideal band of 8.9 degrees run on the site’s own varying wander reproduces the turbines’ bursts of yaws, 40.9% of them back to back against 41.1% in the records and 12.4% under a steady wander, so their controller behaves like that band. It reveals a price of 2.3 kWh per yaw, at which the cost of misalignment and wear together is 1.0% of below-rated energy; a band that widens with the fourth root of the current wander rate lowers it by 18%, and a 30-second average instead of a filter holds about three times the misalignment for the same number of yaws.