Abstract

Annual energy production (AEP) is often the objective function in wind plant layout optimization studies. The conventional method to compute AEP for a wind farm is to first evaluate power production for each wind direction and speed using either computational fluid dynamics simulations or engineering wake models. The AEP is then calculated by weighted-averaging (based on the wind rose at the wind farm site) the power produced across all wind directions. We propose a novel formulation for time-averaged wake velocity that incorporates an analytical integral of a wake deficit model across every wind direction. This approach computes the average flow field more efficiently, and layout optimization is an obvious application to exploit this benefit. The clear advantage of this new approach is that the layout optimization produces solutions with comparable AEP performance yet is completed about 700 times faster. The analytical integral and the use of a Fourier expansion to express the wind speed and wind direction frequency create a more smooth solution space for the gradient-based optimizer to excel compared with the discrete nature of the existing weighted-averaging power calculation.

Highlights

  • The layout of a wind plant is a primary design element that influences its performance

  • We propose a novel formulation for time-averaged wake velocity that incorporates an analytical integral of a wake deficit model across every wind direction

  • The primary benefits of FLOW Estimation and Rose Superposition (FLOWERS) lie in its suitability to drive layout optimization as a wake avoidance problem, despite the fact that simplifications made to develop FLOWERS might induce some errors in the predicted magnitude of Annual energy production (AEP)

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Summary

Introduction

The layout of a wind plant is a primary design element that influences its performance. 25 more of the flow physics is the added complexity, both in the calibration of additional parameters and in computational cost These steady-state wake models are well-suited to estimate wake velocity in simulations with a single wind direction. A strategy to reduce the number of 35 design variables is to restrict the layout to a grid (González et al, 2017; Perez-Moreno et al, 2018), or use a combination of placement along the farm boundary and a grid on the interior (Stanley and Ning, 2019) These approaches reduce the cost of the layout optimization study, especially for larger wind farms. We first derive the equations for the time-averaged wake velocity and a new formulation for AEP, 60 including its application in the wind plant layout optimization problem.

Mathematical Formulation
Annual Energy Production
Layout Optimization Problem
Aligned Case
Generalized Case
Optimization Comparison
FLOWERS and Gauss
Potential Model Improvements
Conclusions
Findings
370 Acknowledgements
Full Text
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