arXiv:2608.30201cs.LG2026-08

通过提升空间构造稳定安全区,直接保障电力系统小信号稳定性。

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

论文配图:Certified Safety Radii in Forecast-Error Space for Wasserstein Distributionally Robust Small Signal Stability-Constrained AC Optimal Power Flow via Lifted Spectrahedral Containment
图 1 · 摘自论文原文
  • 在提升变量空间中将稳定性转为凸半正定约束,构建安全区域。
  • 给出样本到故障的最小距离下界,可直接用于鲁棒优化。
  • 适用于电力系统调度中需严格保证稳定性的高可靠性场景。

直接在交流最优潮流中保障小信号稳定性极具挑战,因稳定边界在原始不确定性空间中隐式、高度非凸且随运行决策变化。本文提出新几何视角:对特定模型的稳定判据,经合适物理提升后,小信号稳定性要求变为提升变量中的仿射半正定约束,从而定义出凸的认证安全区。不直接逼近非线性失稳边界,而是优化原始不确定空间中的样本级安全半径,并在提升空间中认证:对应不确定性球的所有潮流像均包含于该凸稳定区内。为此,分量式Perron判据保证目标交流潮流分支在整个球内存在唯一解且雅可比矩阵正则;伴随消元法提供稳定性相关量的精确仿射-二次表示,严格矩阵余项界将其非线性变化转化为有限鲁棒半正定约束。所得半径为实测样本至失效点的距离下界,可直接耦合至基于距离的Wasserstein分布鲁棒机会约束重构,无需近似失稳边界。数值实验验证了所提框架的有效性。

原文摘要 · Abstract (English)

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.

电力系统鲁棒优化稳定性分析

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