On the frequency variation in load-flow calculations for islanded alternating current microgrids
Bibliographic record
Abstract
Load-flow analyses of islanded microgrids often assume constant line admittances evaluated at the grid’s nominal frequency. This paper investigates errors introduced by this assumption and leverages the versatile modified-augmented nodal-analysis (MANA) formulation to propose new algorithms to account for the frequency variation in line admittances in load-flow calculations. The proposed algorithms, namely MANA- Y ( ω ) , BD1-MANA- Y ( ω ) , BD2-MANA- Y ( ω ) , and their hybrid versions, are tested and compared to MANA on a 25-bus microgrid and a 906-bus grid. Simulations under varying loading conditions demonstrate the advantages of the proposed approach in terms of solution accuracy, particularly for loadability assessments. For the 25-bus case, the voltage magnitude accuracy improves by up to 5%, and the MANA- Y ( ω ) is particularly effective near the system’s maximum loadability point, enabling convergence up to 13% beyond the MANA-estimated limit. Under moderate loadability conditions, the block-dishonest Newton–Raphson method BD2-MANA- Y ( ω ) emerges as the most computationally efficient among the proposed methods. For the 906-bus grid under critical loading, its computation time is 25% faster than the full MANA- Y ( ω ) method, while maintaining comparable accuracy.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".