Optimal Differentiator Filter Banks for PMUs and Their Feasibility Limits

In this paper, we present a very general design approach for optimal linear-phase differentiator filter banks for phasor measurement units based on convex semi-infinite optimization. A detailed presentation of the formulation of both the cost functions and constraints is included for the positive-sequence phasor estimation problem. The design method is extremely powerful and flexible as it allows to control precisely the behavior of the system in terms of the total vector error (TVE), frequency error (FE), and rate of change of frequency error (RFE) metrics for several different scenarios. This feature is extremely useful for tailored designs of these filters for different applications. We also determine numerically the uniform feasibility limits of the system as a function of the filter lengths and, in particular, study the required filter lengths for compliance with the IEEE Standards C37.118.1-2011 and C37.118.1a-2014. It is found that all requirements can be achieved with a significant margin with the exception of the M class FE constraint for interharmonic components, an issue which is also reported in other works and briefly discussed here. Finally, an interesting comparison with the Taylor–Fourier filters is made to illustrate the advantages of our approach.