Power systems are the backbone of a nation's infrastructure. As these systems undergo rapid transformation due to increasing integration of smart grid resources and technologies, they face unprecedented challenges in monitoring and control. This project aims to address these challenges by developing innovative solutions to enhance the safety, reliability, and efficiency of modern power distribution systems. Specifically, this project will develop advanced algorithms built on foundational mathematical and statistical principles to help utility operators make better use of the large volumes of data collected from the grid, leading to more informed decision-making and improved system performance. The ultimate goal is to advance national prosperity and welfare through reduced energy costs, minimum service disruptions, and transition to a smarter, more resilient energy future. This project tackles the complexity of modern power distribution systems by integrating and analyzing multi-time-scale, heterogenous data from advanced metering infrastructure, supervisory control and data acquisition systems, and micro-Phasor Measurement Units to enhance situational awareness and enable advanced control strategies. Existing data analysis methods, including statistical and machine learning approaches, often rely on overly simplified models that assume linearity, normality, and precisely known inputs. These limitations reduce their effectiveness in dealing with the stochastic, dynamic,