Dealing with front-end white noise on differentiated measurements such as frequency and ROCOF in power systems

This paper describes the way that white noise (including quantised input section sampling) imparts errors onto frequency and rate-of-change-of-frequency (ROCOF) measurements. The main paper focus concerns the use of filtered heterodyned (i.e. Fourier) analyses for single-phase and 3-phase systems, and the filtered Clarke transform for 3-phase systems. The rules and equations governing the effect of white noise on frequency and ROCOF are formulated for these techniques, explaining the subtle effects of aliasing, splitting signals and noise into their positive and negative frequency components, and the correlation or de-correlation of noise. It is shown that - as expected - for 3-phase AC measurements, averaging 3 single-phase Fourier measurements produces the same performance against noise as using a method based on Clarke’s transform, if identical filtering is used. Furthermore, by understanding the theory behind the frequency and ROCOF measurement processes, it is shown that to achieve the lowest RMS errors, in the presence of front-end white noise (alone, ignoring other dynamic signal and power quality aspects), a filter which provides ~40 dB/decade attenuation (i.e. a 2-boxcar cascade) is recommended for a frequency measurement, but a filter which rolls off at ~60 dB/decade (i.e. a 3-boxcar cascade) is recommended for a ROCOF measurement.