Performances evaluation of a class of original discrete wavelet transform based hybrid algorithms

Abstract

The p a p er is concerned with the analysis based on the Discrete Wavelet Transform (DWT) of (non)stationary regimes in power systems. Different techniques are employed to perform decompositions using trees with 10 levels for different signals in (non)stationary regimes. The abilities of different methods to detect faults and res p ectively to deal with severe asymmetries are discussed. Power indices are calculated with different methods. A class of original hybrid algorithms is described, analyzed and discussed, generalization being p rovided. These algorithms can be used in all regimes and provide the fast "perfect reconstruction" property. Considering the results and other im p ortant criteria (run time, memory consum p tions), p ractical recommendations are made with res p ect to the selection of a p ro p er reliable and fast DWT algorithm de p ending on the operating conditions.

Real-time analysis using discrete wavelet transform in power systems

“…Table III [6] presents in a synthetic manner the results generated by the MATLAB function dwt, considering all the values for the option "dwtmode" [7]. The function dwt was called with instructions like: [cA,cD]= dwt(y,h,g,'mode', dwtmode_string) where cA represents the approximations , cD represents the details, y represents the decomposed signal, h/g denote the filters and dwtmode_string sets the extension mode.…”

“…The results presented by Table II were obtained with our original functions for filters of length 4, 6 and 8 [6].…”

“…Our researches related to stationary regimes or to regimes with small/medium distortions [6] revealed that only two signal extension modes can be used to deal with the "edge phenomenon" when dwt is used.…”

“…In [6] we explained our original method to preserve the perfect reconstruction property, simultaneously providing both norm preservation and almost-perfect orthogonality properties (the last one might be acceptably affected only at the algorithms with interpolations for at most l-2 components near the right border of the signal).…”

“…This paper is concerned with the abilities of our original set of functions (extended such as to implement filters of length 6 and 8 respectively) to deal with nonstationary regimes where severe irregular asymmetries, magnitude changing and affected periodicity can be noticed. The "dwm" algorithms used for the determination of approximation/detail vectors when performing a dwt decomposition with a filter of length l can be described by [4], [6]:…”