Effective Value Calculation in Wavelet Domain

This paper discusses the methods for calculating effective values of voltage and current in the wavelet domain. It is shown that when a voltage or current signal is decomposed and analyzed using discrete wavelets in a power-quality study, the effective values can be evaluated using the sets of coefficients at each decomposition level. Two formulas are mathematically proved in the paper. One is for orthogonal wavelet analysis; another one is for biorthogonal wavelet systems. Applications of these formulas are numerically illustrated based on two voltage waveforms, and the numerical issues related to using the formulas are also discussed. The formulas presented can be easily programmed and incorporated into power-quality analyzing devices.