Holistic resilience analyses of power systems

Abstract

Power systems are undergoing a rapid transformation driven by the proliferation of distributed energy resources (DERs), increasing penetration of renewable energy, electrification of transportation, and integration of cyber infrastructure for sensing and control. With increasing frequency of weather hazards, significant challenges are emerging in planning, operation, and resilience assessment, particularly under conditions of limited observability, heterogeneous data, and strong interdependencies with other critical infrastructures. This dissertation develops a unified community-centric framework for the planning, operation, and resilience analysis of power distribution systems by integrating optimal transport theory, advanced statistical learning, and hetero-functional graph modeling. This dissertation proposes a novel optimal transport (OT)-based framework for planning distributed energy resources (DERs) to support resilient and community-aware power system operation. Strategic DER deployment enhances resilience by reducing reliance on centralized infrastructure and enabling localized service during outages. Conventional DER planning methods primarily optimize technical objectives while overlooking disparities in community-level energy outcomes. In this work, DER planning is mapped to distributional transformation of a community-centric metric using both unconstrained and constrained formulations to support socio-technical planning. The proposed approach enables balanced trade-offs between grid performance and community-level considerations, contributing to more resilient and inclusive energy system planning. The second part of this dissertation addresses robust operation and control of distribution systems under limited observability. Accurate distribution system state estimation (DSSE) and phase identification (PI) are critical for reliable grid operation but are hindered by sparse, noisy, and heterogeneous measurements. To overcome these challenges, this dissertation introduces a novel Fr´echet regression-based framework for DSSE and PI that operates on distributions rather than point estimates, improving robustness to measurement noise, missing data, and model uncertainties. A joint framework is further developed to simultaneously perform PI and state estimation, improving accuracy in low-observability regimes. In addition, community-centric operational strategies such as coordinated microgrid operation and transmission–distribution (TSO/DSO) interaction frameworks, are developed to incorporate community-level objectives into real-time grid control. These contributions enhance situational awareness and enable adaptive, resilient operation of modern distribution systems. The third part of the dissertation develops a hetero-functional graph (HFG) theory-based framework for resilience analysis of interdependent infrastructure systems. Conventional graph-based models primarily capture structural connectivity and fail to represent functional dependencies among system components, limiting their ability to model cascading failures. To address this gap, HFG theory is employed to represent multi-layered functional interactions among power systems and other critical infrastructures. The dissertation introduces analytical tools for modeling failure propagation across functionalities and develops sensitivity-based techniques to identify critical components influencing system resilience. The proposed framework enables a realistic and computationally efficient assessment of infrastructure robustness by capturing structural and functional interdependencies that govern disruption propagation and system degradation. Building upon this foundation, the final part of the dissertation investigates higher-order functional dependencies using topological data analysis (TDA). While conventional graph models capture only pairwise interactions, real-world infrastructure systems exhibit higherorder relationships among multiple entities. To model these interactions, persistent homology and Hodge Laplacian-based spectral analysis are integrated into the hetero-functional graph framework. A percolation-based robustness analysis is developed to quantify connectivity and higher-order cycles under random and targeted disruptions. The results show that higher-order topological metrics provide earlier indicators of system degradation than traditional graph measures, enabling proactive resilience enhancement.