Towards the multi-scale Kalman filtering of dynamic wake models: observing turbulent fluctuations and wake meandering

When dynamic wake models are augmented with a Kalman filter, they can provide dynamic estimates of the turbine inflows. Such estimators -especially when implemented through readily available operational data- can support a variety of practical applications in wind farm operation and monitoring, power forecasting, and others. The present work represents a first step towards a multi-scale approach for the filtering of dynamic wake models, aimed at estimating both small-fast and large-slow scales in the flow. The small-fast scales are caused by flow turbulence, which in turn also causes wake meandering, whereas the large-slow ones represent the propagation of macroscopic changes of ambient conditions (e.g., the passing of a wind direction change front throughout a farm). It is argued that the small-fast-scale problem is more difficult to address, because of the lack of measurements between turbines, and it is therefore the focus of this paper. An ensemble Kalman filter is developed that, based exclusively on power measurements from the turbines, estimates small-fast changes in wind speed and wake position. CFD simulations are used to characterize the performance of the proposed approach. Results indicate that - notwithstanding the lack of measurements of the flow as it travels from one turbine to the other- the filter is still able to provide for reasonable estimates of the inflow at the downstream machine. Additionally, it is shown that the filter typically distinguishes between effects caused by ambient flow changes from those due to wake meandering.