Network based estimation of wind farm power and velocity data under changing wind direction

This paper describes an estimation algorithm for velocity and power output signals in a wind farm under changing wind direction. A graph-theoretic definition describes the wind farm as a collection of nodes (turbines) and time-varying weighted edges (inter-turbine wake propagation) that change as a function of incoming wind direction. The velocity at each turbine is determined through a discrete input-output model. Changes in wind direction serve as the input and the output is defined in terms of a time-varying weighted adjacency matrix that depends on the time-delay of information propagation between turbines. These delays, which are defined in terms of the advection speed of the wind and the distance between the turbines, capture the delayed effect of wind direction changes on the inter-connectivity of the graph as the wind conditions at the farm inlet propagate through the turbine array. An event-based update framework is employed to capture time-dependent topology changes due to shifts in wind direction. Simulation results for dynamically changing wind inlet directions to a circular wind farm are compared to predictions from both the static and dynamic versions of the FLOw Redirection and Induction in Steady State (FLORIS) model. The approach is shown to enable real-time tracking of dynamic changes to wind farm power output within a framework that can be easily integrated into real-time, horizon-based, control strategies that typically do not account for wind direction changes.