Frequency-response characteristics and error estimation in RMS measurement

Root-mean-square (rms) calculation is a popular method adopted in power system parameter classification. Typical examples are its application in voltage sag classification and relay protection. Starting from the viewpoint of frequency response, this paper seeks to study the characteristics of the rms method, for both the single-frequency and mixed-frequency signals. Analysis is made on its dependence on sampling rate, sampling window size, as well as point-on-wave through strict mathematical deductions. Interesting discoveries include the locations of the "pitfall" frequencies, the minimum sampling points for correct rms output as well as the fluctuation of rms magnitude. Estimation is made on the maximum rms output errors due to the presence of harmonics as well as frequency deviation. Reasonable approximation is adopted in such estimation. Such error estimations are useful in measurement of power system voltages, or any other parameters with relatively higher fundamental but lower harmonics levels.