Band Depth Clustering for Nonstationary Time Series and Wind Speed Behavior

We explore the behavior of wind speed over time, using the Eastern Wind Dataset published by the National Renewable Energy Laboratory. This dataset gives wind speeds over three years at hundreds of potential wind farm sites. Wind speed analysis is necessary to the integration of wind energy into the power grid; short-term variability in wind speed affects decisions about usage of other power sources, so that the shape of the wind speed curve becomes as important as the overall level. To assess differences in intra-day time series, we propose a functional distance measure, the band distance, which extends the band depth of Lopez-Pintado and Romo (2009). This measure emphasizes the shape of time series or functional observations relative to other members of a dataset, and allows clustering of observations without reliance on pointwise Euclidean distance. To emphasize short-term variability, we examine the short-time Fourier transform of the nonstationary speed time series; we can also adjust for seasonal effects, and use these standardizations as input for the band distance. We show that these approaches to characterizing the data go beyond mean-dependent standard clustering methods, such as k-means, to provide more shape-influenced cluster representatives useful for power grid decisions.