Linear time complexity sorting algorithms for electromagnetic transient simulation of MMC‐HVdc system
Bibliographic record
Abstract
In the electromagnetic transient (EMT) simulation programs, the candidate integration methods backward Euler (BE) method and Trapezoidal rule (TR) are normally used to discretise the submodule capacitors in modular multilevel converter (MMCs). This study proposes linear time complexity sorting algorithms for nearest level control‐based BE and TR MMC models to further accelerate the EMT simulation of the equivalent MMC‐HVdc models. First, the capacitor voltage increments in the charging and discharging processes are investigated from an EMT point of view. Second, for both BE and TR methods, although the actual capacitor voltage increments are not identical at each time step, the voltage ranking of the capacitors from the same inserted/bypassed category at each control period are proved to be unchanged. Taking this advantage, when preparing the entire ranked voltage table for the next control period, the sorting can be significantly simplified since one only needs to compare the capacitor voltages from capacitor categories of ascending orders. Third, when implementing the sorting algorithms, at most ( N –1) comparisons for BE model and (2 N –3) comparisons for TR model are required, showing that the proposed sorting algorithms have linear time complexities. Finally, all the proposed approaches are validated by EMT simulations on MATLAB/Simulink.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".