发表机构
College of Automation Engineering, Nanjing University of Aeronautics and Astronautics（南京航空航天大学自动化学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对交流最优潮流中小信号稳定性鲁棒化的难题，通过提升谱面体包含性，在预测误差空间中优化可证安全半径，结合Perron证书等技术实现Wasserstein分布鲁棒机会约束的重构，数值验证了框架有效性。
AI 中文摘要
直接对交流最优潮流中的小信号稳定性进行鲁棒化具有挑战性，因为原始不确定性空间中的稳定性边界是隐式的、高度非凸的，且随运行决策而变化。本文利用一种替代几何结构：对于固定的、允许适当物理提升的特定模型稳定性证书，小信号稳定性要求在提升变量中成为仿射半正定约束，从而定义了一个凸的可证安全区域。我们不近似非线性不稳定边界本身，而是在原始不确定性空间中优化逐样本安全半径，并在提升空间中证明，相应不确定性球的整个潮流图像包含在凸稳定区域内。为此，逐分量Perron证书保证了目标交流潮流分支在每个球内的存在性、唯一性和雅可比正则性；伴随消除则提供了稳定性相关量的精确仿射-二次表示，而严格的矩阵余项界将其非线性变化转化为有限的鲁棒半正定约束。所得半径是经验样本到故障距离的可证下界，因此可直接与Wasserstein分布鲁棒机会约束的基于距离的重构耦合，无需直接近似不稳定边界。数值研究证明了所提框架的有效性。
英文摘要
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.
