Linearized Optimization for Enhanced Aggregate Modeling of Invisible Hybrid Distributed Energy Resources
Bibliographic record
Abstract
ABSTRACT The increasing penetration of distributed energy resources (DERs)—including photovoltaics, wind turbines, and battery energy storage systems—poses challenges for modern power distribution systems, particularly in scenarios with high penetration of DERs outside the monitoring capabilities of distribution utilities. Addressing invisible DERs in operational planning studies requires innovative modeling methodologies, often involving aggregated models. This paper proposes a mixed‐integer linear programming (MILP) formulation to locate and size aggregate hybrid DER models in radial distribution systems by minimizing residuals in the estimates of existing field measurements. These equivalent models grasp the collective effect of many invisible DERs and enable the reconstruction of unobserved bus voltages and branch flows, enhancing system visibility. Case studies demonstrate average errors below 5% for the estimation of unobserved branch flows with limited voltage magnitude measurements. OpenDSS is employed to showcase the computational efficiency and accuracy of the proposed method, also under unbalanced system loading conditions.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 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".