Reactive power planning using convex line‐wise power balance equations for radial distribution systems
Bibliographic record
Abstract
Optimal capacitor placement for radial distribution systems (RDSs) considers minimising the total cost of new fixed capacitors, switchable capacitors, and losses, while satisfying power balance equations, limits on bus voltages and capacitor limits. It is a non‐convex mixed‐integer non‐linear programming (MINLP) challenge. In this study, the authors propose a solution method using a line‐wise model (LWM) of power balance equations. First, equations for LWM are presented with their Jacobian for solving the power flow problem using Newton–Raphson method. Then, an optimal non‐convex MINLP capacitor placement formulation with LWM power balance equations is presented. Thereafter, it is transformed into a convex mixed‐integer conic programming formulation using second‐order conic relaxation. Both the non‐convex and convex optimal capacitor placement formulations are used to study 69‐bus and 136‐bus RDS. The results are compared with a formulation that uses the branch flow model (BFM) for power balance equations. Results show that the non‐convex LWM‐based formulation is twice as fast when compared with the BFM‐based formulation. The convex LWM‐based formulation is from 4 to 30 times as fast when compared with the BFM‐based formulation, demonstrating the benefits of the use of the LWM‐based formulation for enhancing the solution space of the optimisation problem.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".