Layered Multi-Resource Restoration Control Under Nonsmooth Stability-Margin Constraints for Converter-Dominated Power Grids

Post-disturbance operation of a converter-dominated grid is often limited by a small-signal stability margin shared by several oscillation modes and frequency bands, while restoration resources can have conflicting side effects. This paper formulates margin restoration as maximization of the minimum of a wide-band margin family consisting of modal damping ratios, band-wise singular-value distances, and device limits at the nominal point and declared parameter-uncertainty vertices. The worst element is nonsmooth when the critical element switches; a trust-region bundle step using analytic eigenvalue and singular-value sensitivity formulas and risk-transfer floors is therefore used to avoid improving one element at the expense of another. The step is embedded in a layered receding-horizon scheme in which fast converter actions, rate-limited curtailment, and a topology alternative are engaged under a grid-resolved terminal target and an explicit escalation statement. A 90th-percentile calibrated screening margin, a validity period for parameter drift, and three-class action grading connect the simplified optimization model to a detailed linear verification model with control delays. On the constructed benchmark with a grid-following wind station, a grid-forming storage station, a STATCOM, and a VSC-HVDC link, the method restores the margin at the first simulated control instant in the recoverable designed scenarios, issues an escalation statement when no terminal-reaching candidate is found in the declared search domain, and withdraws candidates on verification conflict or timeout. On the fixed 150-case randomized benchmark set, observed recovery counts within 2 s are 149/150 for the proposed method and 146/150 for simplified-model check only; these descriptive outcomes are interpreted with risk-transfer results rather than as a population-level significance claim. Evidence is limited to the constructed benchmark and its generated family; simulated recovery times do not demonstrate end-to-end computation within the 0.2 s control period. Time-domain simulation of the detailed linear verification model cross-checks the frequency-domain margins.