Higher-Order Dynamic Mode Decomposition to Identify Harmonics in Power Systems
Bibliographic record
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".