Adjoint Optimisation for Wind Farm Flow Control with a Free-Vortex Wake Model

TL;DR

This paper introduces an adjoint-based optimization approach using a free-vortex wake model to enhance wind farm flow control, demonstrating improved power output and wake management in simulations.

Contribution

It presents a novel adjoint derivation for a free-vortex wake model enabling efficient gradient-based control optimization for wind turbines.

Findings

Effective mean power maximization in a two-turbine case study

Demonstration of wake steering and transition to greedy control under changing wind directions

Model captures curled wake dynamics under yaw misalignment

Abstract

Wind farm flow control aims to improve wind turbine performance by reducing aerodynamic wake interaction between turbines. Dynamic, physics-based models of wind farm flows have been essential for exploring control strategies such as wake redirection and dynamic induction control. Free vortex methods can provide a computationally efficient way to model wind turbine wake dynamics for control optimisation. We present a control-oriented free-vortex wake model of a 2D and 3D actuator disc to represent wind turbine wakes. The novel derivation of the discrete adjoint equations allows efficient gradient evaluation for gradient-based optimisation in an economic model-predictive control algorithm. Initial results are presented for mean power maximisation in a two-turbine case study. An induction control signal is found using the 2D model that is roughly periodic and supports previous results on dynamic induction control to stimulate wake mixing. The 3D model formulation effectively models a curled wake under yaw misalignment. Under time-varying wind direction, the optimisation finds solutions demonstrating both wake steering and a smooth transition to greedy control. The free-vortex wake model with gradient information shows potential for efficient optimisation and provides a promising way to further explore dynamic wind farm flow control.