Certified Hybrid Non-Convex Robust Dynamic Operating Envelopes for Unbalanced Distribution Networks

Robust dynamic operating envelopes (RDOEs) are increasingly used to allocate low-voltage flexibility while preserving voltage and thermal security under uncertain load and distributed energy resource behavior. Purely linear robust approximations scale well but can misestimate nonlinear boundary regions in unbalanced feeders, whereas full non-convex robust unbalanced three-phase optimal power flow (UTOPF) is often too expensive for high-cadence operation. We present a hybrid method that couples a certified linear screening stage with selective non-convex escalation and prove two properties: (i) accepted screened points are robust-feasible under explicit residual assumptions, and (ii) accepting all certifiable points is compute-optimal among admissible deterministic escalation rules. The method is evaluated on a reproducible four-experiment suite covering security-runtime tradeoffs, online uncertainty calibration, fairness-sensitive allocation, and cross-solver shadow-mode behavior. Across 600 configuration-seed samples per experiment family, nominal screening behavior remains consistent with the safety theorem, observed runtime reduction is substantial for boundary-aware operation, uncertainty calibration tracks target risk with bounded coverage error, and cross-solver discrepancy remains within predefined operational tolerances in synthetic stress regimes. The broader contribution is a deployable bridge between optimization guarantees and operational evidence: theorem-scoped safety and optimality are connected to experiment-level diagnostics, reproducibility artifacts, and policy-sensitive allocation analysis.