A Bayesian Method to Infer Parameters in Power Flow Models Using Linear Sensitivities
Bibliographic record
Abstract
This paper presents a Bayesian method to infer parameters in distribution system power flow models from noisy measurements of voltage magnitudes and phase angles along with active- and reactive-power injections collected from a subset of buses with synchronized phasor measurement capability. The proposed method bypasses the large number of repeated nonlinear power flow solutions that would typically be required in sampling-based Bayesian inference. Instead, the proposed method iteratively and analytically linearizes the nonlinear power flow model, converging to the linearized model with the maximum probability of being (closest to) the actual nonlinear model that gave rise to the measurement data. The combination of the linear system, Gaussian parameter prior, and Gaussian measurement noise enables closed-form evaluation of the parameter posterior, model evidence, and their gradients. This can help to improve computational scalability for large-scale networks with potentially many unknown parameters to be inferred. We illustrate the effectiveness and key features of the proposed method with numerical case studies involving the IEEE 33-bus test system.
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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 | 0.004 | 0.017 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".