Stability of Algorithms for Electro-MagneticTransient Simulation of Networks with Switches and Non-linear Inductors
Bibliographic record
Abstract
This paper extends the analysis of the stability of electromagnetic transient simulation algorithms to non-linear systems with switching elements and non-linear inductor branches. A theoretical analysis based on common quadratic Lyapunov function (CQLF) theory is used to investigate the stability of numerical algorithms for the simulation of lumped strictly passive switched circuits (LSPSC). It is proved that only when certain fundamental physical properties, i.e., passivity and invariance of Lyapunov energy function are satisfied, does the widely used trapezoidal method result in stable simulations of such networks for any time-step size. This is different from the simulation of linear time invariant (LTI) systems where any real world stable system has a stable simulation if an A-stable integration method (e.g., trapezoidal rule) is used. Subsequently, it is shown that the problem of simulating a piecewise linear inductor can be equivalent to simulating a LSPSC; and ergo its simulation with the trapezoidal rule is also stable.
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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 | 0.004 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".