Sensitivity analysis of wake steering optimisation for wind farm power maximisation

Abstract. Modern large-scale wind farms consist of multiple turbines clustered together, usually in well-structured formations. Clustering has a number of drawbacks during a wind farm's operation, as some of the downstream turbines will inevitably operate in the wake of those upstream, with a significant reduction in power output and an increase in fatigue loads. Wake steering, a control strategy in which upstream wind turbines are misaligned with the wind to redirect their wakes away from downstream turbines, is a promising strategy to mitigate power losses. The purpose of this work is to investigate the sensitivity of open-loop wake steering optimisation in which an internal predictive wake model is used to determine the farm power output as a function of the turbine yaw angles. Three different layouts are investigated with increasing levels of complexity. A simple 2×1 farm layout under aligned conditions is first considered, allowing for a careful investigation of the sensitivity to wake models and operating conditions. A medium-complexity case of a generic 5×5 farm layout under aligned conditions is examined to enable the study of a more complex design space. The final layout investigated is the Horns Rev wind farm (80 turbines), for which there have been very few studies of the performance or sensitivity of wake steering optimisation. Overall, the results indicate a strong sensitivity of wake steering strategies to both the analytical wake model choice and the particular implementation of algorithms used for optimisation. Significant variability can be observed in both farm power improvement and optimal yaw settings, depending on the optimisation setup. Through a statistical analysis of the impact of optimiser initialisation and a study of the multi-modal and discontinuous nature of the underlying farm power objective functions, this study shows that the uncovered sensitivities represent a fundamental challenge to robustly identifying globally optimal solutions for the high-dimensional optimisation problems arising from realistic wind farm layouts. This paper proposes a simple strategy for sensitivity mitigation by introducing additional optimisation constraints, leading to higher farm power improvements and more consistent, coherent, and practicable optimal yaw angle settings.