Improving Linear OPF Model via Incorporating Bias Factor of Optimality Condition
Bibliographic record
Abstract
The linearization of the optimal power flow (OPF) model is widely-used to meet the computational demands of power system dispatch. To improve the accuracy of the OPF solution, existing studies are devoted to reducing the linearization error of nonlinear power flow constraints. However, the linearization accuracy of model fractions does not necessarily represent the linearization error of the OPF result. In this paper, an improved linear OPF formulation is derived from the optimality condition of the OPF solution. Based on the Karush–Kuhn–Tucker (KKT) condition, we transform the OPF optimization into solving a set of nonlinear equations, which consists of non-gradient and gradient terms. The traditional approach to linearize OPF constraints is regarded as deriving the first-order and zero-order Taylor expansions of non-gradient and gradient terms, respectively. The missing first-order component of gradient terms causes considerable linearization error. We formulate it as a bias factor in the OPF objective to improve the accuracy and maintain linearity of the OPF model. By considering the bias factor, the performance of linear OPF optimization is notably improved, which is illustrated in theory and verified in numerous IEEE and Polish test systems.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".