Designing Model-Free Time Derivatives in the Frequency Domain for Ambient PMU Data Applications

Model-free derivatives are essential to several synchrophasor applications. The standard approach to estimate them is to combine a smoothing operation with an ideal derivative computation. However, because the derivative operation increases the signal's content in higher spectral frequencies which can undo the effect of smoothing. Ambient data also brings unique challenges, as mere visual inspection of the estimate in the time domain does not provide insight into the quality of the final estimate. In this regard, the underlying signal's frequency spectrum can provide valuable information for designing a good derivative estimate. This paper introduces a framework for designing a model-free derivative estimate in the frequency domain that accounts for the system's underlying dynamics. The approach is demonstrated on two classic synchrophasor analytics problems on measurements from the Dominion Energy system.