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

Tatiana De Almeida Prado,Giovanni Alfredo Guarneri,Andrea Macario Barros

doi:10.1109/access.2019.2952188

Tatiana De Almeida Prado, Giovanni Alfredo Guarneri + Show 1 more

Open Access

https://doi.org/10.1109/access.2019.2952188

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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.

Highlights

Harmonics and interharmonics disturbances in electrical systems increase as new electronic power devices are connected to the power system [1]
This section presents the evaluation of the performance of the HIESSD algorithm in estimating harmonics and interharmonics components of power systems signals
The Mean Absolute Error (MAE) is used for comparing methods under the following conditions: (I) signals not contaminated with noise; (II) signals in the presence of Gaussian white additive noise with signal-to-noise (SNR) ratios of 10, 20 and 40 dB; (III) different frequency grids using the l-fold method; and (IV) reduced signals sampling window

Summary

Introduction

Harmonics and interharmonics disturbances in electrical systems increase as new electronic power devices are connected to the power system [1]. IEC 61000-4-7 defines the methodology for estimating harmonics and interharmonics in power systems [6]. This standard establishes that the voltage and current of an electric system must be sampled using 200 ms windows (12 full cycles at 60 Hz or 10 at 50 Hz). These sampled signals are processed by the Discrete Fourier Transform (DFT), which calculates the energy of the signal’s frequency components and makes the estimation of harmonics and

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