A Study on improvement of single phase PLL algorithm stability and accuracy
Bibliographic record
Abstract
A distinguishing characteristics of distribution systems is their inherent imbalance. While the assumption of three-phase balance is fundamental to most transmission-level analyses and theoretical studies-and is generally valid in practical applications-distribution systems seldom operate under such ideal conditions. In many instances, a single feeder line extends from the distribution substation. Even when a feeder is designed as a three-phase system, the connected loads often draw power from only one or two phases rather than all three. Consequently, the measured system voltages and currents do not form a balanced three-phase set. When a power electronic device interfaces with an AC power system, it must accurately track the system’s frequency and phase angle. A widely adopted approach for this purpose is the Phase-Locked Loop (PLL). Among various PLL implementations, those based on orthogonal transformations, such as the DQ transformation, are particularly prevalent. This paper presents a single-phase PLL, a variant of the DQ transformation-based PLL, which utilizes a pseudo-quadrature-axis signal generated through a simple phase delay. Additionally, an interpolation technique is incorporated to enhance tracking accuracy. The theoretical foundation of this method is outlined, followed by a comparative evaluation demonstrating the proposed PLL’s effectiveness relative to existing techniques.
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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 | 0.002 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".