Bibliographic record
Abstract
Optimal power flow (OPF) refers to optimize power systems considering a chosen objective subject to a set of constraints. Existing OPF formulations used to settle electricity markets include a set of bus-wise power balance equations (PBE) that is comprised exclusively of high order terms which have sinusoidal components. Accordingly, such OPF formulations remain nonlinear and nonconvex optimization problems. Even though commercial OPF solvers are robust and efficient, they still cannot guarantee a global optimum. The US Federal Energy Regulatory Commission estimates that the best commercial OPF solvers are off by 10%, amounting to an annual loss of US $400 billion worldwide. For these motivating reasons, OPF remains a major research focus and forms the topic of this thesis. This thesis aims to: (1) develop new sets of PBE with lower order terms and lesser numbers of sinusoidal terms yielding better solution space, (2) build new OPF formulations using this new set of PBE, and (3) incorporate voltage stability constraints into the developed OPF formulations. The genesis of the new set of PBE stems from: (1) the fact that power of a constant impedance load is proportional to the square of voltage magnitude, and, (2) power flow in branches can be expressed in terms of square of voltage magnitude. Accordingly, a set of line-wise PBE is developed, both in polar and rectangular forms and are solved Newton-Raphson technique. Tests show that the proposed line-wise power flow (LWPF) algorithms are accurate, provide monotonic convergence, and scale well for large systems. The algorithms are faster comparing to classical bus-wise power flow methods. Further, the ability to directly identify the set of critical lines that are the most susceptible to Voltage collapse. A novel line-wise optimal power flow (LWOPF) formulation is developed based on polar LWPF and solved using successive linear programming technique. Tests show that LWOPF consistently yields a better solution than that computed using bus-wise OPF, namely in half the time. LWOPF is extended to include voltage stability constraints and implemented using both linear and nonlinear optimization techniques. It demonstrates improved performance in achieving lower cost optimal solutions with better voltage-stable states.
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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 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.024 | 0.006 |
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".