Probabilistic Optimal Power Flow Applications to Electricity Markets
Bibliographic record
Abstract
This paper presents the comparison of two solution methods for probabilistic optimal power flow problems; namely, the two-point estimate method (2PEM) and the cumulant method (CM). The goal of the P-OPF problem is to determine the probability distributions for all random variables in the problem. In this paper, bus loading and generators' supply power bids are considered as uncertain or probabilistic parameters in a P-OPF problem. Due to their importance in the context of electricity markets, special attention is paid to the uncertainty in locational marginal prices (LMPs) that results from uncertain behavior of market players. The proposed methods are tested on a modified version of the Matpower 30-bus system to demonstrate the capabilities of both approaches. Solution methodologies are compared in terms of accuracy and computational burden. Results are compared against those obtained from 10,000 sample Monte Carlo simulations (MCS). The proposed methods show high accuracy levels and are computationally significantly faster than an MCS approach
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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".