Fractional Order Control Design for Bus Voltage Control of a Microgrid Feeding CPLs
Bibliographic record
Abstract
This paper addresses bus-voltage regulation in a multi-converter DC microgrid feeding constant power loads (CPLs), where the negative incremental impedance of CPLs and the right-half-plane zero of boost converters reduce damping and may destabilize the system. The test system consists of four second-order boost converters supplying a 48 V DC bus and two CPLs regulated at 35 V and 40 V. A fractional-order PID (FOPID) controller is designed for the bus-voltage loop, and its five parameters are tuned via the Grey Wolf Optimization (GWO) algorithm using bounded search ranges and time-domain performance indices. The fractional differ-integral operators are realized through a band-limited Oustaloup approximation, enabling digital implementation. Simulation results show that, compared with a GWO-tuned integer-order PID, the proposed FOPID–GWO scheme reduces bus-voltage overshoot from about 18.7% to below 3%, shortens the 2% settling time from 0.24 s to 0.08 s, and decreases the ITAE index by nearly 80% under nominal conditions. Under 50% load-step uncertainties and injected sensor noise, the FOPID controller maintains accurate tracking of the bus and CPL reference voltages and preserves high overall efficiency 93.4%. A numerical eigenvalue and sensitivity analysis confirms left-half-plane closed-loop poles and acceptable robustness margins, indicating a stable and robust solution for DC microgrids with CPLs.
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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 | 0.000 | 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 | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".