Assessing the proximity of time evolutions through dynamic time warping

Comparing time-series is a frequent task in many scientific fields. In power systems, in particular, it may be of interest to compare the outputs of a simplified and a detailed model, or to validate the output of a model with respect to a measured time response. The classical Euclidean distance, involving pairs of points of the two data series aligned in time, is not suited to the practical time evolutions met in power systems, which often involve variable time delays and jumps at discrete times. In this study, an alternative measure of proximity, stemming from other scientific fields, is proposed for power system applications. It consists in warping the time axis to guarantee the best match between the two time-series, that is it maps points on two curves that are not aligned in time so as to minimise the sum of squared differences of their ordinates. Modifications and adaptations of the classical algorithm to better fit power system problems are discussed. The method is illustrated through three representative curve comparison problems. A multi-dimensional extension allowing system-wide measures of similarity is also proposed.