A Mixed-Integer Nonlinear Model to Support the Operation of Distribution Systems With Hidden DERs
Bibliographic record
Abstract
With impending deep electrification powered by innumerable Distributed Energy Resources (DERs), modeling each DER individually is becoming a critical challenge to the Distribution System Operators (DSOs). Even though the DSOs know the total DER installed capacity at the feeder level, the exact individual type, location, and size of such generators may remain unknown. This paper proposes a mixed-integer nonlinear programming formulation to support the operation of distribution systems under massive DER integration. The proposal accurately estimates distribution system power flows, relying on a limited set of measurements. It aims to establish equivalent DER models representing hidden resources and improve the representation of limited-visibility networks. The only DER information required is the total solar and wind installed capacity at the feeder level. The performance is assessed by comparing estimated and measured values of bus voltage magnitudes and branch power flows. Results demonstrate the efficacy of the proposed formulation in accurately replicating measurements, achieving an accuracy of over 90% when estimating active power flows in unmetered branches.
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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 | 0.001 |
| 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 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".