Three-Phase Second-Order Analytic Probabilistic Load Flow With Voltage-Dependent Load
Bibliographic record
Abstract
This paper proposes a fully analytic second-order probabilistic load flow (PLF) method to realize an accurate and fast three-phase load flow analysis considering unbalanced uncertainties from voltage-sensitive loads and photovoltaic (PV) generation in distribution systems. The load flow equations are modelled by an accurate quadratic expression based on the bus injection model (BIM). To work at the distribution level, the voltage dependence of the load is considered based on the constant impedance, constant current, and constant power (ZIP) model, with the ZIP parameters acting as more realistic random variables. The PV generation is also considered as a constant power model. The uncertainties are modelled in time series as conditional probabilities, reducing the complexity of their probability distribution functions (PDFs). The PLF is modelled in a fully analytic second-order stochastic formulation, which can accurately and easily handle the PDFs of voltage and current by computing the first two moments. The computation is accelerated by an analytical calculation of the quadratic coefficients over the ZIP parameters. Case studies on a practical distribution network show the significance of considering the voltage-dependent load model and the high accuracy of the proposed method.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| 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".