Estimação de componentes harmônicos e inter-harmônicos utilizando a técnica de decomposição esparsa de sinais

Abstract

This work presents an algorithm based on Signal Sparse Decomposition for estimation of frequency components in signals with harmonics and interharmonics distortions acquired from the power system. The use of this technique needs an overcomplete dictionary and an atomic decomposition algorithm. The overcomplete dictionary design is made based on the basis-functions of the Discrete Trigonometric Transforms and 4-fold overcomplete system. This combination renders the frequency resolution adjustable. For this application, the Discrete Trigonometric Transforms of type II have the most suitable features for signal decomposition. Greedy pursuit and convex relaxation algorithms are evaluated for many iterations until convergence, the sparsity of results, approximation and measurement of frequency components errors. The performed tests demonstrate the applicability of the OMP algorithm. The estimation of frequency components in four synthetic signals under different noise conditions, frequency resolution, and sampling window size show that the proposed algorithm is suitable for this purpose. Unlike the methods based on the Discrete Fourier Transform, the proposed algorithm estimates inter-harmonic components with a frequency resolution of up to 0,5 Hz. When compared to the Matrix Pencil Method, the proposed algorithm does not present errors of frequency and smaller errors in the estimation of amplitude.