The growing threats of uncertainties, anomalies, and cyberattacks on power grids are driving a critical need to advance situational awareness which allows system operators to form a complete and accurate picture of the present and future state. Simulation and estimation are foundational tools in this process. However, existing tools lack the robustness and efficiency required to achieve the level of situational awareness needed for the ever-evolving threat landscape. Industry-standard (steady-state) simulators are not robust to blackouts, often leading to non-converging or non-actionable results. Estimation tools lack robustness to anomalous data, returning erroneous system states. Efficiency is the other major concern as nonlinearities and scalability issues make large systems slow to converge. This thesis addresses robustness and efficiency gaps through a dual-fold contribution. We first address the inherent limitations in the existing physics-based and data-driven worlds; and then transcend the boundaries of conventional algorithmic design in the direction of a new paradigm -- Physics-ML Synergy -- which integrates the strengths of the two worlds. Our approaches are built on circuit formulation which provides a unified framework that applies to both transmission and distribution. Sparse optimization acts as the key enabler to make these tools intrinsically robust and immune to random threats, pinpointing dominant sources of (random) blackouts and data errors. Further, we explore sparsity-exploiting optimizations to develop lightweight ML models whose prediction and detection capabilities are a complement to physics-based tools; and whose lightweight designs advance generalization and scalability. Finally, Physics-ML Synergy brings robustness and efficiency further against targeted cyberthreats, by interconnecting our physics-based tools with lightweight ML.

翻译：电网面临的不确定性、异常事件及网络攻击威胁日益增长，亟需提升态势感知能力，使系统运营商能够全面准确地掌握当前与未来状态。仿真与估计是实现该目标的基础工具。然而，现有工具在应对不断演变的威胁态势时，其鲁棒性与效率均无法满足高水平态势感知的需求。行业标准（稳态）仿真器对停电事件缺乏鲁棒性，常导致计算结果不收敛或不可操作；状态估计工具对异常数据敏感，易返回错误的系统状态。效率是另一核心挑战——非线性特性与可扩展性问题导致大规模系统收敛缓慢。本论文通过双重贡献弥补鲁棒性与效率的不足：首先剖析现有基于物理模型与数据驱动方法的内在局限，进而突破传统算法设计边界，提出融合两者优势的新范式——物理-机器学习协同框架。我们的方法基于电路模型构建，为输配电系统提供了统一框架。稀疏优化作为关键使能技术，使工具具备本质鲁棒性，可抵御随机威胁，精准定位（随机）停电与数据误差的主导根源。进一步，我们开发基于稀疏结构优化的轻量化机器学习模型，其预测与检测能力与物理模型形成互补，轻量化设计同时提升了泛化能力与可扩展性。最终，通过将物理工具与轻量化机器学习模型互联，物理-机器学习协同框架显著增强了对定向网络攻击的防御能力与运算效率。