An Algorithm Based on Sparse Decomposition for Estimating Harmonic and Interharmonic Components of Stationary Signals in Power Systems

Abstract

Many methods for estimating frequency components of stationary signals in power systems are based on the Discrete Fourier Transform. These methods have a fixed frequency resolution which depends on the sampling frequency and the number of samples of the signal, making it difficult to estimate interharmonics. This paper presents an algorithm for estimating harmonics and interharmonics of power system signals using the signal sparse decomposition technique with an overcomplete dictionary. Discrete Trigonometric Transforms have been analyzed for building this dictionary. The l-fold method has also been applied to the dictionary, which has allowed the adjustment of the frequency grid of the output spectrum. The algorithm proposed is called Harmonics and Interharmonics components Estimation based on Signal Sparse Decomposition, and it was assembled using a dictionary formed by atoms of Discrete Cosine and Discrete Sine Transforms of type II. Three synthetic signals containing harmonic and interharmonics distortions with different noise conditions were used to test the algorithm. The proposed method presented better results in the estimation of harmonic and interharmonics than Discrete Fourier Transform, Matrix Pencil Method and Fast Matching Pursuit algorithms. The results demonstrated robustness to noise and adequate estimation of the interharmonics when the frequency grid is adjusted correctly. INDEX TERMS Discrete trigonometric transform, harmonics and interharmonics estimation, overcomplete dictionary, power quality signal analysis, signal sparse decomposition.