Linear Power-Flow Formulation Based on a Voltage-Dependent Load Model
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Bibliographic record
Abstract
The power-flow (PF) solution is a fundamental tool in power system analysis. Standard PF formulations are based on the solution of a system of nonlinear equations which are computationally expensive due to the iterations needed. On the other hand, distribution-system (DS) automation algorithms should be fast enough to meet real-time performance. The conventional load representation, as constant <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$P$</tex></formula> – <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Q$</tex></formula> , becomes less accurate as we get closer to the actual load's level. In this paper, a new load model is proposed which represents the loads' voltage dependency. A simple curve-fitting technique is used to derive a voltage-dependent load model which splits the load as a combination of an impedance and a current source. With this representation and some numerical approximations on the imaginary part of the nodal voltages, it is possible to formulate the load-flow problem as a linear power-flow (LPF) solution which does not require iterations. The approximation has been tested in systems up to 3000 nodes with excellent results. The LPF formulation is particularly important in the context of optimization algorithms for automated smart distribution systems. The extension of the technique to unbalanced distribution systems will be presented in future work.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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 it