统一诊断用于在注入和拓扑不确定性下量化交流工作点鲁棒性
Unified Diagnostics for Quantifying AC Operating-Point Robustness Under Injection and Topological Uncertainties with Regime Changes
AI总结：
本文提出统一框架，通过构建物理响应映射和准对偶，评估在注入和拓扑不确定性下的工作点鲁棒性，引入确定性和概率性筛查方法，结合地理空间数据提升运营和规划意识。
摘要：
在负荷、发电和网络拓扑的不确定性存在下，电力系统规划必须反映运营条件，而运营需要对可信不确定性集有情境意识。现有方法对电力流和最优功率流设置进行筛选、分析、嵌入和传播不确定性，但仅提供部分关于物理约束、控制和经济互动如何塑造稳态工作点鲁棒性的见解。通过将工作点鲁棒性作为围绕解决的AC最优功率流（AC-OPF）均衡后的后解物理响应问题进行建模，本文提出一个统一框架，用于在不重新优化的情况下评估在注入和拓扑不确定性下的鲁棒性。我们构建了一个原物理响应映射，考虑了连接变化、有功功率再分配、发电机饱和包括$PV \rightarrow PQ$过渡，以及AC网络传播，并引入了准对偶，为非最优均衡的影子价格提供了几何解释。利用这些映射，我们开发了确定性筛查程序，将$N-k$ contingency分析推广到包含成本脆弱性$C-k$，并通过灵敏度归一化边际和风险容忍度定义了局部类比$N+δ(k)$和$C+δ(k)$。该框架扩展到概率性筛查，用于分布和矩基础的不确定性，通过顺序修剪混合建模和$α$-应力制度构造来管理组合分支。对波多黎加大电网的案例研究展示了与地理空间数据的整合，以增强运营和规划意识。
英文摘要：
In the presence of uncertainties in load, generation, and network topology, power system planning must reflect operational conditions, while operations require situational awareness over credible uncertainty sets. Existing methods screen, analyze, embed, and propagate uncertainty in power flow and optimal power flow settings, but provide only partial insight into how physical constraints, controls, and economic interactions shape steady-state operating-point robustness. By formulating operating-point robustness as a post-solution physical response problem around a solved AC optimal power flow (AC-OPF) equilibrium, this paper presents a unified framework for assessing robustness under injection and topological uncertainty without re-optimization. We construct a primal physical response mapping that accounts for connectivity changes, active power redistribution, generator saturation including $PV \rightarrow PQ$ transitions, and AC network propagation, and introduce quasi-duals that provide a geometric interpretation of shadow prices for off-optimal equilibria. Using these mappings, we develop deterministic screening procedures that generalize $N-k$ contingency analysis to include cost vulnerability $C-k$, and local analogs $N+δ(k)$ and $C+δ(k)$ defined through sensitivity-normalized margins and risk tolerances. The framework is extended to probabilistic screening for distribution- and moment-based uncertainties, with sequentially-pruned mixture modeling and $α$-stressed regime constructions to manage combinatorial branching. A case study on the Puerto Rican bulk power system demonstrates integration with geospatial data to enhance operational and planning awareness.
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