Wind farms can be regarded as complex systems that are, on the one hand, coupled to the nonlinear, stochastic characteristics of weather and, on the other hand, strongly influenced by supervisory control mechanisms. One crucial problem in this context today is the predictability of wind energy as an intermittent renewable resource with additional non-stationary nature. In this context, we analyze the power time series measured in an offshore wind farm for a total period of one year with a time resolution of 10 min. Applying detrended fluctuation analysis, we characterize the autocorrelation of power time series and find a Hurst exponent in the persistent regime with crossover behavior. To enrich the modeling perspective of complex large wind energy systems, we develop a stochastic reduced-form model of power time series. The observed transitions between two dominating power generation phases are reflected by a bistable deterministic component, while correlated stochastic fluctuations account for the identified persistence. The model succeeds to qualitatively reproduce several empirical characteristics such as the autocorrelation function and the bimodal probability density function.

中文翻译：

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单个风力涡轮机的相关功率时间序列：数据驱动的模型方法

风电场可以被视为一个复杂的系统，一方面与天气的非线性、随机特性耦合，另一方面又受到监督控制机制的强烈影响。今天在这方面的一个关键问题是风能作为一种具有额外非平稳性质的间歇性可再生资源的可预测性。在这种情况下，我们分析了在海上风电场中测量的电力时间序列，总时间为一年，时间分辨率为 10 分钟。应用去趋势波动分析，我们表征了功率时间序列的自相关性，并在具有交叉行为的持续状态中找到了 Hurst 指数。为了丰富复杂大型风能系统的建模视角，我们开发了功率时间序列的随机简化模型。观察到的两个主要发电阶段之间的转变由双稳态确定性分量反映，而相关的随机波动解释了已识别的持久性。该模型成功地定性地再现了几个经验特征，例如自相关函数和双峰概率密度函数。