Certified Safety Radii in Forecast-Error Space for Wasserstein Distributionally Robust Small Signal Stability-Constrained AC Optimal Power Flow via Lifted Spectrahedral Containment

2026-08-30

AI Summary

本文通过提升谱拉赫尔包含，优化样本安全半径，并在提升空间中认证稳定性，解决了AC最优潮流中小信号稳定性鲁棒化的问题。

Abstract

Directly robustifying small-signal stability in AC optimal power flow is challenging since the stability boundary in the original uncertainty space is implicit, highly nonconvex, and changes with the operating decision. This paper exploits an alternative geometry. For a fixed model-specific stability certificate admitting suitable physical lifts, the small-signal stability requirement becomes an affine positive semidefinite constraint in the lifted variables, thereby defining a convex certified safe region. Instead of approximating the nonlinear instability boundary itself, we optimize a sample-wise safe radius in the original uncertainty space and certify, in the lifted space, that the entire power-flow image of the corresponding uncertainty ball is contained in the convex stability region. To this end, a componentwise Perron certificate guarantees existence, uniqueness, and Jacobian regularity of the target AC power-flow branch throughout each ball. An adjoint elimination then provides an exact affine-quadratic representation of the stability-relevant quantities, while rigorous matrix remainder bounds convert their nonlinear variation into finite robust PSD constraints. The resulting radii are certified lower bounds on the distances from empirical samples to failure and can therefore be coupled directly to the distance-based reformulation of a Wasserstein distributionally robust chance constraint, without directly approximating the instability boundary. Numerical studies demonstrate the effectiveness of the proposed framework.

Problem

• small-signal stability
• AC optimal power flow
• stability boundary
• uncertainty space
• nonconvex

Innovation

• Wasserstein distributionally robust
• lifted space
• certified safety radii
• Perron certificate
• adjoint elimination