Higher-Order Dynamic Mode Decomposition to Identify Harmonics in Power Systems

Aboubacar Abdou Dango, Innocent Kamwa (), Himanshu Grover, Alexia N’Dori and Alireza Masoom
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Aboubacar Abdou Dango: Department of Electrical and Computer Engineering, University Laval, Quebec, QC G1V 0A6, Canada
Innocent Kamwa: Department of Electrical and Computer Engineering, University Laval, Quebec, QC G1V 0A6, Canada
Himanshu Grover: Department of Electrical and Computer Engineering, University Laval, Quebec, QC G1V 0A6, Canada
Alexia N’Dori: Department of Electrical and Computer Engineering, University Laval, Quebec, QC G1V 0A6, Canada
Alireza Masoom: Hydro Quebec Research Institute, Varennes, QC J3X 1S1, Canada

Energies, 2025, vol. 18, issue 19, 1-22

Abstract: The proliferation of renewable energy sources and distributed generation systems interfaced to the grid by power electronics systems is forcing us to better understand the issues arising due to the quality of electrical signals generated through these devices. Understanding and monitoring these harmonics is crucial to ensure the smooth and seamless operation of these networks, as well as to protect and manage the renewable energy sources-based power system. In this paper, we propose an advanced method of dynamic modal decomposition, called Higher-Order Dynamic Mode Decomposition (HODMD), one of the recently proposed data-driven methods used to estimate the frequency/amplitude and phase with high resolution, to identify the harmonic spectrum in power systems dominated by renewable energy generation. In the proposed method, several time-shifted copies of the measured signals are integrated to create the initial data matrices. A hard thresholding technique based on singular value decomposition is applied to eliminate ambiguities in the measured signal. The proposed method is validated and compared to Synchrosqueezing Transform based on Short-Time Fourier Transform (SST-STFT) and the Concentration of Frequency and Time via Short-Time Fourier Transform (ConceFT-STFT) using synthetic signals and real measurements, demonstrating its practical effectiveness in identifying harmonics in emerging power networks. Finally, the effectiveness of the proposed methodology is analyzed on the energy storage-based laboratory-scale microgrid setup using an Opal-RT-based real-time simulator.

Keywords: Higher-Order Dynamic Mode Decomposition (HODMD); harmonics; SST-STFT; ConceFT-STFT; renewable energy sources; real-time simulator; data-driven methods (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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