Polynomial chaos to efficiently compute the annual energy production in wind farm layout optimization
Polynomial chaos to efficiently compute the annual energy production in wind farm layout optimization
复制标题
多项式混沌有效计算风电场布局优化中的年发电量
作者：
A. S. Padron;Jared J. Thomas;A. Stanley;J. Alonso;A. Ning
摘要。在本文中，我们开发了计算效率高的技术来计算风电场优化中使用的统计数据，目标是能够使用更高保真度的模型和更大的风电场优化问题。我们通过优化单个风力涡轮机的位置，将这些技术应用于风力发电场的年发电量（AEP）最大化。AEP（一项统计数据）是风电场在一年内受不确定性风况（风向和风速）影响的预期发电量，这些不确定性是用经验确定的概率分布描述的。为了计算风电场的AEP，我们使用尾流模型来模拟由风向和风速对组成的不同输入条件下的功率。我们使用多项式混沌（PC），一种不确定性量化方法，在整个随机空间上构造功率的多项式近似，并有效地（使用尽可能少的模拟）计算期望功率（AEP）。我们探索了回归和正交两种方法来计算PC系数。基于回归的PC比矩形规则（最常用于计算期望功率的方法）效率高得多。与考虑的不同风电场布局的矩形规则相比，使用基于回归的PC，我们平均将准确计算AEP所需的模拟次数减少了5倍。在风电场布局优化问题中，每个优化步骤都需要进行AEP计算。因此，通过更少的模拟准确计算AEP的能力是有益的，因为它降低了执行优化的成本，从而可以使用计算成本更高的高保真模型或考虑更大或多个风电场优化问题。我们执行了大量的基于梯度的优化，以比较基于回归和矩形规则的多项式混沌计算AEP时获得的最优布局。我们考虑了三种不同的起动布局（网格、Amalia、随机），发现该优化具有许多局部最优，并且对涡轮机的起动布局很敏感。我们观察到，从一个好的布局（Grid, Amalia）开始，通常会比从一个坏的布局（Random）开始找到更好的优化，这与计算AEP所用的方法无关。对于基于回归和矩形规则的PC，我们同时考虑粗（~ 225）和细（~ 625）次模拟来计算AEP。我们发现，在大约三分之一的计算成本下，基于回归的粗糙PC优化得到的优化布局产生的AEP与使用精细矩形规则找到的优化布局相当。此外，在计算成本相同的情况下，对于考虑的不同情况，多项式混沌找到的最优布局的AEP平均比矩形规则找到的AEP高0.4%。
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.