Nonstationarity in correlation matrices for wind turbine SCADA‐data

Abstract

Modern utility-scale wind turbines are equipped with a Supervisory Control And Data Acquisition (SCADA) system gathering vast amounts of operational data that can be used for analysis to improve operation and maintenance of turbines. We analyze high-frequency SCADA-data from the Thanet offshore wind farm in the United Kindom and evaluate Pearson correlation matrices for a variety of observables with a moving time window. This renders possible a quantitative assessment of nonstationarity in mutual dependencies of different types of data. We show that a clustering algorithm applied to the correlation matrices reveals distinct correlation structures for different states. Looking first at only one and then at multiple turbines, the main dependence of these states is shown to be on wind speed. This is in accordance with known turbine control systems, which change the behavior of the turbine depending on the available wind speed. We model the boundary wind speeds separating the states based on the clustering solution. Our analysis shows that for highfrequency data, the control mechanisms of a turbine lead to detectable nonstationarity in the correlation matrix. The presented methodology allows accounting for this with an automated preprocessing by sorting new data based on wind speed and comparing it to the respective operational state, thereby taking the nonstationarity into account for an analysis.

Sensitivity of principal components to system changes in the presence of non-stationarity

“…A first step to include multiple operational conditions in PCA-based failure detection for heat pumps was already undertaken by Zhang et al [45]. We intend to test the proposed method on wind turbines, where multiple operational normal conditions based on correlation matrix clustering have already been found [33] and PCA is being used for fault detection [10].…”

“…First, a system can slowly evolve due to influences such as climate [27] or the economic situation [31]. On the other hand, external conditions can vary on shorter time-scales, causing non-stationarity without an evolutionary trend [29,32,33]. Some systems also exhibit periodic non-stationarity [28].…”

“…the eigenvectors of the correlation matrix change their structure, the projections into PCA space are substantially different. Such non-stationarity in the correlation matrix has been thoroughly investigated, for example, in financial markets [31,34], road traffic [32] and wind turbine data [33]. We assume that such a distinction into well-separated individual states is most likely to happen for a difference in correlation structure.…”

“…We average the variance instead of the standard deviation. The average over the correlation matrix is also meant element-wise and is according to the centroid calculation in real data clustering in, for example, [31][32][33][34]. Standardization with the mean value and standard deviation of this average state will be denoted with a tilde: μ0 = 0 and σ0 = 1.…”

“…In general, one has to tailor the identification of the non-stationarity to the problem at hand. We have found that correlation matrix clustering is useful in many systems [31][32][33].…”