{
  "abstract": "Small Island Developing States (SIDS) face simultaneous frequency nadir and rate-of-change-of-frequency (RoCoF) violations under high renewable penetration. This paper proposes a \\emph{Composite Adaptive Higher-Order Control Barrier Function} (CA-HOCBF) for BESS-coupled virtual synchronous generators that jointly enforces IEEE~1547 frequency ($\\pm0.8$\\,Hz) and ENTSO-E RoCoF ($\\pm1$\\,Hz/s) limits as hard safety constraints under parametric uncertainty. The method unifies three tools: (i)~a dual barrier architecture with a zeroing CBF for frequency and an algebraic RoCoF constraint with a robust inertia-floor fallback; (ii)~a composite energy function coupling logarithmic safety barriers with quadratic parameter and disturbance error terms, which drives safety-weighted adaptation; and (iii)~a disturbance observer integrated into the barrier dynamics. We prove that the closed-form QP is always feasible under a BESS capacity condition and, under explicitly stated assumptions, that the composite energy remains finite along trajectories, rendering the joint safe set forward invariant \\emph{without requiring parameter convergence}. Simulation on a 10\\,MW Caribbean microgrid ($H=2$\\,s, 70\\% renewables) shows the CA-HOCBF eliminates all frequency and RoCoF violations under a compound disturbance, achieving steady-state error of 0.001\\,Hz and RoCoF of 0.50\\,Hz/s, where fixed-gain VSGs suffer a 0.62\\,Hz offset with 2.25\\,Hz/s RoCoF violations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23123",
  "author_total": 3,
  "authors": [
    {
      "name": "Shankar Ramharack"
    },
    {
      "name": "Jonathan Nancoo"
    },
    {
      "name": "Rajiv Sahadeo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e4tpft8e288p2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23123",
  "fulltext_url": null,
  "id": "e4tpft8e288p2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23123",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Microgrid Control and Optimization"
    ]
  ],
  "openalex": "W7214035357",
  "pdf_url": "https://arxiv.org/pdf/2609.23123",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e4tpft8e288p2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23123",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23123"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Composite Adaptive Higher-Order Control Barrier Functions for Joint Frequency-RoCoF Safety in Low-Inertia SIDS Microgrids",
  "title_text": "Composite Adaptive Higher-Order Control Barrier Functions for Joint Frequency-RoCoF Safety in Low-Inertia SIDS Microgrids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/e4tpft8e288p2",
  "venue": "arXiv",
  "versions": []
}