Statistical Effects of Frequency Instability on Continuous Monitoring of Active and Reactive Power

Abstract

This paper provides an approximate analytical approach leading to the statistical characterization of the electric active/reactive power related to the harmonics in the real-time monitoring of a power system affected by frequency instability. The effect of additive noise is also included in the analysis. Frequency instability of voltage and current waveforms is modeled as a random variable ranging within a given frequency interval. Propagation of both the uncertainty sources through the whole measurement process based on analogto- digital conversion and discrete Fourier transform is investigated. Power evaluation is performed by proper multiplication of waveforms spectra. In fact, the requirement of real-time monitoring prevents the use of sophisticated algorithms to cope with the frequency change before spectra multiplication. Analytical expressions taking into account the weighting function used against spectral leakage are derived for the bias and the standard deviation of the measured power.