Unified diagnostics for quantifying AC operating-point robustness under injection and topological uncertainties with regime changes

In the presence of uncertainty in load, generation, and network topology, power system operations and planning require consistent assessments of operating-point robustness under realistic conditions. Existing methods for incorporating uncertainty in power flow and optimal power flow provide partial and often incomparable views due to differing physical representations. This paper formulates operating-point robustness as a post-solution physical response problem around a solved AC optimal power flow equilibrium and develops a common primal response mapping that propagates injection and topology perturbations through an AC network, considering connectivity changes, generator saturation, and loss of voltage regulation. This enables a unified assessment prior to re-optimization. Quasi-duals are introduced to approximate cost sensitivities for off-optimal equilibria. Deterministic screening procedures are developed that generalize contingency analysis to include both physical and economic robustness under discrete and infinitesimal perturbations. The framework is extended to probabilistic screening under moment-based and distribution-based uncertainties, with order-reduction methods to manage combinatorial regime changes. These screening tools are demonstrated on a model of the Puerto Rican bulk power system, showing how consistent and interpretable robustness diagnostics can be visualized to support both operational and planning contexts.