Abstract

Abstract. In this paper, we develop computationally efficient techniques to calculate statistics used in wind farm optimization with the goal of enabling the use of higher-fidelity models and larger wind farm optimization problems. We apply these techniques to maximize the annual energy production (AEP) of a wind farm by optimizing the position of the individual wind turbines. The AEP (a statistic) is the expected power produced by the wind farm over a period of 1 year subject to uncertainties in the wind conditions (wind direction and wind speed) that are described with empirically determined probability distributions. To compute the AEP of the wind farm, we use a wake model to simulate the power at different input conditions composed of wind direction and wind speed pairs. We use polynomial chaos (PC), an uncertainty quantification method, to construct a polynomial approximation of the power over the entire stochastic space and to efficiently (using as few simulations as possible) compute the expected power (AEP). We explore both regression and quadrature approaches to compute the PC coefficients. PC based on regression is significantly more efficient than the rectangle rule (the method most commonly used to compute the expected power). With PC based on regression, we have reduced on average by a factor of 5 the number of simulations required to accurately compute the AEP when compared to the rectangle rule for the different wind farm layouts considered. In the wind farm layout optimization problem, each optimization step requires an AEP computation. Thus, the ability to compute the AEP accurately with fewer simulations is beneficial as it reduces the cost to perform an optimization, which enables the use of more computationally expensive higher-fidelity models or the consideration of larger or multiple wind farm optimization problems. We perform a large suite of gradient-based optimizations to compare the optimal layouts obtained when computing the AEP with polynomial chaos based on regression and the rectangle rule. We consider three different starting layouts (Grid, Amalia, Random) and find that the optimization has many local optima and is sensitive to the starting layout of the turbines. We observe that starting from a good layout (Grid, Amalia) will, in general, find better optima than starting from a bad layout (Random) independent of the method used to compute the AEP. For both PC based on regression and the rectangle rule, we consider both a coarse (∼225) and a fine (∼625) number of simulations to compute the AEP. We find that for roughly one-third of the computational cost, the optimizations with the coarse PC based on regression result in optimized layouts that produce comparable AEP to the optimized layouts found with the fine rectangle rule. Furthermore, for the same computational cost, for the different cases considered, polynomial chaos finds optimal layouts with 0.4 % higher AEP on average than those found with the rectangle rule.

Highlights

  • In 2015, wind energy growth accounted for almost half of global electricity supply growth

  • In this paper, which is meant as a comprehensive introduction to uncertainty quantification methods applied to wind farm simulations, we describe in detail the polynomial chaos (PC) method and show that, for the efficient computation of the annual energy production (AEP), the PC method based on regression should be used

  • We focus on the convergence of the AEP (Sect. 6.2) and on the wind farm layout optimization problem to maximize the AEP (Sect. 6.3)

Read more

Summary

Introduction

In 2015, wind energy growth accounted for almost half of global electricity supply growth. A problem with putting turbines together in confined spaces is that they operate in the wakes of other turbines, i.e., in regions of reduced speed and increased turbulence This leads to an underproduction of power and decreased (10 %– 20 %) energy output for the farm (Barthelmie et al, 2007; Barthelmie et al, 2009; Briggs, 2013) when compared to ideal conditions. This loss in energy capture results in millions of dollars of loss for operators and investors and increased economic uncertainty for new installations. By optimizing the layout of the wind farm, the wake losses can be minimized, with a corresponding increase in energy production and revenue

Methods
Results
Conclusion
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call