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.

The computation burden of solving nonlinear optimization Recent years have seen a rich literature of data-driven approaches problems in operation and planning has motivated the designed for power grid applications. However, development of data-driven alternatives to state estimation insufficient consideration of domain knowledge can impose (SE) [7] [19], power flow (PF) analysis [4][14], optimal power a high risk to the practicality of the methods. Specifically, flow (OPF) [2] [9][6], as well as data-driven warm starters ignoring the grid-specific spatiotemporal patterns (in load, to collaborate with physical solvers [12][20], etc. generation, and topology, etc.) can lead to outputting infeasible, Despite their popularity in recent years, people have long unrealizable, or completely meaningless predictions on been aware of the risks of machine learning (ML) tools regarding new inputs. To address this concern, this paper investigates their impracticality[11] under realistic power grid real-world operational data to provide insights into power conditions. The risks come from the "missing of physics" in grid behavioral patterns, including the time-varying topology, general ML methods. Specifically, the transient system dynamics, load, and generation, as well as the spatial differences changing topology, and varying supply and demand (in peak hours, diverse styles) between individual loads and are physical reasons behind the temporal grid evolution.