Uncertainty-Disentangled Probabilistic Stability Analysis in Wind Power Integrated Weak Grids

Conventional probabilistic small-signal stability analysis (PSSSA) propagates a single forecast distribution, conflating irreducible weather randomness (aleatoric) with reducible forecast-model uncertainty (epistemic). This letter propagates a second-order renewable forecast through the modal-stability map via an independent \emph{germ} variable, separating the two contributions exactly in closed form by a disentangled polynomial chaos expansion (d-PCE). The split underpins a forecast-aware $(\alpha ,\beta ,\gamma )$ stability certificate whose conservative branch converges to its irreducible aleatoric limit at $O(N^{-1\mathrm{/}2})$ – making a failed certificate diagnostic: epistemic-dominated risk recovers with better data; aleatoric-dominated risk needs improvements of the physical control system.