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.
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 failure analysis and prediction to improve operation and maintenance of turbines. We analyse high freqeuency SCADA-data from the Thanet offshore windpark in the UK and evaluate Pearson correlation matrices for a variety of observables with a moving time window. This renders possible an asessment of non-stationarity in mutual dependcies of different types of data. Drawing from our experience in other complex systems, such as financial markets and traffic, we show this by employing a hierarchichal k-means clustering algorithm on the correlation matrices. The different clusters exhibit distinct typical correlation structures to which we refer as states. Looking first at only one and later at multiple turbines, the main dependence of these states is shown to be on wind speed. In accordance, we identify them as operational states arising from different settings in the turbine control system based on the available wind speed. We model the boundary wind speeds seperating the states based on the clustering solution. This allows the usage of our methodology for failure analysis or prediction by sorting new data based on wind speed and comparing it to the respective operational state, thereby taking the non-stationarity into account.
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 failure analysis and prediction to improve operation and maintenance of turbines. We analyse high freqeuency SCADA-data from an offshore windpark and evaluate Pearson correlation matrices for a variety of observables with a moving time window. This renders possible an asessment of non-stationarity in mutual dependcies of different types of data. Drawing from our experience in other complex systems, such as financial markets and traffic, we show this by employing a hierarchichal k-means clustering algorithm on the correlation matrices. The different clusters exhibit distinct typical correlation structures to which we refer as states. Looking first at only one and later at multiple turbines, the main dependence of these states is shown to be on wind speed. In accordance, we identify them as operational states arising from different settings in the turbine control system based on the available wind speed. We model the boundary wind speeds seperating the states based on the clustering solution. This allows the usage of our methodology for failure analysis or prediction by sorting new data based on wind speed and comparing it to the respective operational state, thereby taking the non-stationarity into account.
The distribution of liquidity within the limit order book is essential for the impact of market orders on the stock price and the emergence of price shocks. Limit orders are characterized by stylized facts: the number of inserted limit orders declines with the price distance from the quotes following a power law and limit order lifetimes and volumes are power law distributed. Strong dependencies among these quantities add to the complexity of limit order books. Here, we analyze the limit order book in the dimensions of price, time, limit order lifetime and volume altogether. This allows us to identify regularities that are not visible in marginal distributions. Particularly, we find that the limit order book is divided into two regimes. Around the quotes, we find a densely filled regime with mostly short living limit orders closely adapting to the price. Far away from the quotes, we find a sparse filling with long living limit orders, mostly inserted at particular times of the day being prone to flash crashes. We determine the characteristics of those two regimes and point out the main differences. Based on our research, we propose a model for simulating the regime around the quotes.
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