A Bi-Level Polyhedral-Based MILP Model for Expansion Planning of Active Distribution Networks Incorporating Distributed Generation
Bibliographic record
Abstract
This paper proposes a novel mixed-integer linear programming (MILP) model for the expansion planning of active distribution networks, which not only is able to accurately reflect the fundamental characteristics of the problem, but also provides the opportunity to find its optimal solution in a computationally efficient manner. This model is able to jointly expand both the network assets (feeders and substations) and distributed generators (DGs) while minimizing the investment and operation costs and taking all the necessary physical and technical constraints into account. A highly accurate linearization method based on polyhedral approximation is utilized to eliminate the nonlinearities of AC power flow equations and obtain the proposed MILP model. Furthermore, a bi-level approach is also proposed to accelerate the solution process and reduce the computation time. This solution approach is comprised of a pre-solution level in which a simplified MILP model is solved to find a near-optimal initial solution for the expansion planning problem, and a main solution level in which the proposed accurate MILP model is solved considering the already found initial solution. Finally, a 24-node distribution system is used to verify the effectiveness of the proposed planning methodology.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".