Composite Adaptive Higher-Order Control Barrier Functions for Joint Frequency-RoCoF Safety in Low-Inertia SIDS Microgrids

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 ($\pm 0.8$,Hz) and ENTSO-E RoCoF ($\pm 1$,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.