Probabilistic Load Flow Modeling Comparing Maximum Entropy and Gram-Charlier Probability Density Function Reconstructions
Bibliographic record
Abstract
Probabilistic load flow (PLF) modeling is gaining renewed popularity as power grid complexity increases due to growth in intermittent renewable energy generation and unpredictable probabilistic loads such as plug-in hybrid electric vehicles (PEVs). In PLF analysis of grid design, operation and optimization, mathematically correct and accurate predictions of probability tail regions are required. In this paper, probability theory is used to solve electrical grid power load flow. The method applies two Maximum Entropy (ME) methods and a Gram-Charlier (GC) expansion to generate voltage magnitude, voltage angle and power flow probability density functions (PDFs) based on cumulant arithmetic treatment of linearized power flow equations. Systematic ME and GC parameter tuning effects on solution accuracy and performance is reported relative to converged deterministic Monte Carlo (MC) results. Comparing ME and GC results versus MC techniques demonstrates that ME methods are superior to the GC methods used in historical literature, and tens of thousands of MC iterations are required to reconstitute statistically accurate PDF tail regions. Direct probabilistic solution methods with ME PDF reconstructions are therefore proposed as mathematically correct, statistically accurate and computationally efficient methods that could be applied in the load flow analysis of large-scale networks.
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".