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 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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 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) | 0.001 | 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 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".