Applications of Homotopy for solving AC Power Flow and AC Optimal Power Flow
Bibliographic record
Abstract
This paper introduces a new paradigm for solving AC Power Flow (ACPF) and AC Optimal Power Flow (ACOPF) with improved convergence robustness. This approach exploits the globally convergent properties of continuation methods. Continuation methods achieve robustness by generating a sequence of nonlinear problems and repeatedly and consistently providing good initial guesses for locally convergent nonlinear solvers such as Newton-Raphson. The Homotopy implemented in this paper, (referred to as Power Flow Homotopy, PFH), is formulated in a way that gradually transforms the “easy” DC into the “difficult” AC Power Flow. Successive changes of the homotopy parameter modify the system of equations from fully linear and convex DC into non-linear and non-convex AC (optimal) power flow. As a result, the AC solution is obtained with increased robustness and multiple AC power flow solutions can also be detected. Similarly, Optimal Power Flow Homotopy (OPFH) is defined for solving AC Optimal Power Flow, by gradually transforming the convex DC OPF problem. Simulation results provide a comparison between the simple Newton-Raphson method and PFH in terms of performance and quality of detected solution. Comparisons are also performed between the Interior-Point method and OPFH.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".