This paper presents a physics-aware cyberphysical resilience framework for radial microgrids under coordinated cyberattacks. The proposed approach models the attacker through a hypergraph neural network (HGNN) enhanced with model agnostic metalearning (MAML) to rapidly adapt to evolving defense strategies and predict high-impact contingencies. The defender is modeled via a bi-level Stackelberg game, where the upper level selects optimal tie-line switching and distributed energy resource (DER) dispatch using an Alternating Direction Method of Multipliers (ADMM) coordinator embedded within the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The framework simultaneously optimizes load served, operational cost, and voltage stability, ensuring all post-defense states satisfy network physics constraints. The methodology is first validated on the IEEE 69-bus distribution test system with 12 DERs, 8 critical loads, and 5 tie-lines, and then extended to higher bus systems including the IEEE 123-bus feeder and a synthetic 300-bus distribution system. Results show that the proposed defense strategy restores nearly full service for 90% of top-ranked attacks, mitigates voltage violations, and identifies Feeder 2 as the principal vulnerability corridor. Actionable operating rules are derived, recommending pre-arming of specific tie-lines to enhance resilience, while higher bus system studies confirm scalability of the framework on the IEEE 123-bus and 300-bus systems.

Abstract--Accurate voltage estimation in distribution networks is critical for real-time monitoring and increasing the reliability of the grid. As DER penetration and distribution level voltage variability increase, robust distribution system state estimation (DSSE) has become more essential to maintain safe and efficient operations. This paper presents a hierarchical graph neural network for substation-level voltage estimation that exploits both electrical topology and physical features, while remaining robust to the low observability levels common to real-world distribution networks. Leveraging the public SMART -DS datasets, the model is trained and evaluated on thousands of buses across multiple substations and DER penetration scenarios. Comprehensive experiments demonstrate that the proposed method achieves up to 2 times lower RMSE than alternative data-driven models, and maintains high accuracy with as little as 1% measurement coverage. The results highlight the potential of GNNs to enable scalable, reproducible, and data-driven voltage monitoring for distribution systems. Distribution System State Estimation (DSSE) is the process of determining the state variables of a distribution network given a limited set of measurements [1], [2]. Historically, distribution networks were operated as a passive part of the grid, delivering electricity from transmission substations to customers in a unidirectional manner [3].

Fault detection in power distribution grids is critical for ensuring system reliability and preventing costly outages. Moreover, fault detection methodologies should remain robust to evolving grid topologies caused by factors such as reconfigurations, equipment failures, and Distributed Energy Resource (DER) integration. Current data-driven state-of-the-art methods use Recurrent Neural Networks (RNNs) for temporal modeling and Graph Neural Networks (GNNs) for spatial learning, in an RNN+GNN pipeline setting (RGNN in short). Specifically, for power system fault diagnosis, Graph Convolutional Networks (GCNs) have been adopted. Yet, various more advanced GNN architectures have been proposed and adopted in domains outside of power systems. In this paper, we set out to systematically and consistently benchmark various GNN architectures in an RNN+GNN pipeline model. Specifically, to the best of our knowledge, we are the first to (i) propose to use GraphSAGE and Graph Attention (GAT, GATv2) in an RGNN for fault diagnosis, and (ii) provide a comprehensive benchmark against earlier proposed RGNN solutions (RGCN) as well as pure RNN models (especially Gated Recurrent Unit (GRU)), particularly (iii) exploring their generalization potential for deployment in different settings than those used for training them. Our experimental results on the IEEE 123-node distribution network show that RGATv2 has superior generalization capabilities, maintaining high performance with an F1-score reduction of $\sim$12% across different topology settings. In contrast, pure RNN models largely fail, experiencing an F1-score reduction of up to $\sim$60%, while other RGNN variants also exhibit significant performance degradation, i.e., up to $\sim$25% lower F1-scores.

The increasing reliance on cyber physical infrastructure in modern power systems has amplified the risk of targeted cyber attacks, necessitating robust and adaptive resilience strategies. This paper presents a mathematically rigorous game theoretic framework to evaluate and enhance microgrid resilience using a combination of quantitative resilience metrics Load Served Ratio LSR, Critical Load Resilience CLR, Topological Survivability Score TSS, and DER Resilience Score DRS. These are integrated into a unified payoff matrix using the Analytic Hierarchy Process AHP to assess attack defense interactions. The framework is formalized as a finite horizon Markov Decision Process MDP with formal convergence guarantees and computational complexity bounds. Three case studies are developed 1. static attacks analyzed via Nash equilibrium, 2. severe attacks incorporating high impact strategies, and 3. adaptive attacks using Stackelberg games, regret matching, softmax heuristics, and Multi Agent Q Learning. Rigorous theoretical analysis provides convergence proofs with explicit rates , PAC learning sample complexity bounds, and computational complexity analysis. The framework is tested on an enhanced IEEE 33bus distribution system with DERs and control switches, demonstrating the effectiveness of adaptive and strategic defenses in improving cyber physical resilience with statistically significant improvements of 18.7% 2.1% over static approaches.

The increasing vulnerability of electrical distribution systems to extreme weather events and cyber threats necessitates the development of economically viable frameworks for resilience enhancement. While existing approaches focus primarily on technical resilience metrics and enhancement strategies, there remains a significant gap in establishing market-driven mechanisms that can effectively commercialize resilience features while optimizing their deployment through intelligent decision-making. Moreover, traditional optimization approaches for distribution network reconfiguration often fail to dynamically adapt to both normal and emergency conditions. This paper introduces a novel framework integrating dual-agent Proximal Policy Optimization (PPO) with market-based mechanisms, achieving an average resilience score of 0.85 0.08 over 10 test episodes. The proposed architecture leverages a dual-agent PPO scheme, where a strategic agent selects optimal DER-driven switching configurations, while a tactical agent fine-tunes individual switch states and grid preferences under budget and weather constraints. These agents interact within a custom-built dynamic simulation environment that models stochastic calamity events, budget limits, and resilience-cost trade-offs. A comprehensive reward function is designed that balances resilience enhancement objectives with market profitability (with up to 200x reward incentives, resulting in 85% of actions during calamity steps selecting configurations with 4 DERs), incorporating factors such as load recovery speed, system robustness, and customer satisfaction. Over 10 test episodes, the framework achieved a benefit-cost ratio of 0.12 0.01, demonstrating sustainable market incentives for resilience investment. This framework creates sustainable market incentives

Learning-based approaches are increasingly leveraged to manage and coordinate the operation of grid-edge resources in active power distribution networks. Among these, model-based techniques stand out for their superior data efficiency and robustness compared to model-free methods. However, effective model learning requires a learning-based approximator for the underlying power flow model. This study extends existing work by introducing a data-driven power flow method based on Gaussian Processes (GPs) to approximate the multiphase power flow model, by mapping net load injections to nodal voltages. Simulation results using the IEEE 123-bus and 8500-node distribution test feeders demonstrate that the trained GP model can reliably predict the nonlinear power flow solutions with minimal training data. We also conduct a comparative analysis of the training efficiency and testing performance of the proposed GP-based power flow approximator against a deep neural network-based approximator, highlighting the advantages of our data-efficient approach. Results over realistic operating conditions show that despite an 85% reduction in the training sample size (corresponding to a 92.8% improvement in training time), GP models produce a 99.9% relative reduction in mean absolute error compared to the baselines of deep neural networks.

--Independent microgrids are crucial for supplying electricity by combining distributed energy resources and loads in scenarios like isolated islands and field combat. Fast and accurate assessments of microgrid vulnerability against intentional attacks or natural disasters are essential for effective risk prevention and design optimization. However, conventional Monte Carlo simulation (MCS) methods are computationally expensive and time-consuming, while existing machine learning-based approaches often lack accuracy and explainability. T o address these challenges, this study proposes a fast and explainable vulnerability assessment framework that integrates MCS with a graph attention network enhanced by self-attention pooling (GA T -S). MCS generates training data, while the GA T - S model learns the structural and electrical characteristics of the microgrid and further assesses its vulnerability intelligently. The GA T -S improves explainability and computational efficiency by dynamically assigning attention weights to critical nodes. Comprehensive experimental evaluations across various micro-grid configurations demonstrate that the proposed framework provides accurate vulnerability assessments, achieving a mean squared error as low as 0.001, real-time responsiveness within 1 second, and delivering explainable results. An independent microgrid, like a battlefield or island mi-crogrid, operates separately from the main grid, supplying electricity to a localized area by integrating distributed energy resources and loads via interconnected buses, transformers, and lines. Assessing the vulnerability of independent micro-grids is essential to ensure its normal power supply capacity against disruptions, particularly in scenarios like deliberate attacks and natural disasters. Chenhui Lin is with the State Key Laboratory of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China.

This paper addresses the challenge of neural state estimation in power distribution systems. We identified a research gap in the current state of the art, which lies in the inability of models to adapt to changes in the power grid, such as loss of sensors and branch switching. Our experiments demonstrate that graph neural networks are the most promising models for this use case and that their performance can degrade with scale. We propose augmentations to remedy this issue and perform a comprehensive grid search of different model configurations for common zero-shot learning scenarios in neural state estimation.