FLOWERS Annual Energy Production Model
Motivation and Objectives
Wind farm designers require tools to predict the time-averaged power production of wind turbine arrays over long operational periods (e.g., years). The annual energy production (AEP) of a wind farm is an important quantitative metric for performance given the variability of the wind conditions that the farm is expected to experience, namely the ambient wind speed and wind direction at the hub-height of the turbines. This metric is often a part of the objective in the optimization of a wind farm's layout, as in the placement of each wind turbine within a given footprint. These wind farm layout optimization (WFLO) problems can be computationally-intensive. This project aims to develop a new analytical model for wind farm AEP, called the 'FLOWERS' model, that is specifically tailored for use in WFLO problems in order to reduce computation time and streamline the design process.
Methods and Results
Annual energy production models are based on two fundamental concepts: (1) an analytical model for wind farm power production, which is essentially the power losses due to the wake interactions between turbines subtracted from the ideal power production assuming no turbine interactions, and (2) an integration method to account for the variability of the ambient wind speed and wind direction in the expected power production. "Conventional" AEP models use an analytical wake model (e.g., Jensen, Gaussian, etc.) to independently simulate a large set of wind conditions, and then sum the resulting power production from these simulations weighted by their expected frequency of occurrence. On the other hand, the FLOWERS AEP model takes the Jensen wake model, weighted by the probability density function for the wind conditions, and analytically integrates over the wind condition domain to obtain expected power production in a single closed-form expression. The main advantage of this approach is a 10-50x reduction in the computation time required to compute AEP.
The other major advantage of the FLOWERS model is rooted in the analytical formulation of AEP. The gradient of AEP with respect to the position of each turbine in the wind farm is obtained through analytic differentiation and is well-suited for layout optimization with a gradient-based algorithm. Across three wind farm layout optimization case studies, the FLOWERS-based layout optimization approach found equivalent or better optimal layouts in 100-1000x less computation time compared to the reference method.
Related Publications
Acknowledgements
This work was conducted in collaboration with colleagues at the National Wind Technology Center, a research facility of the National Renewable Energy Laboratory. Funding and computational resources were provided in part by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Wind Energy Technologies Office. Additional computational resources were provided by the Stanford Research Computing Center.