Vectorized Gaussian Belief Propagation for Near Real-Time Fully-Distributed PMU-Based State Estimation

2026-04-13

AI Summary

This work addresses the pressing need for highly accurate, scalable, distributed, and near real-time state estimation in complex power systems by proposing a factor graph–based vectorized Gaussian Belief Propagation (GBP) framework tailored for PMU-driven applications. The core innovations include multivariate GBP, which jointly models electrically coupled state variables and measurement relationships, and fused GBP, which simplifies the graph structure by integrating multiple measurements associated with the same group of variables. The approach enables fully distributed computation at the bus level and demonstrates rapid convergence—typically within a single iteration—while maintaining high accuracy and strong scalability, as validated on IEEE 1354- and 13,659-bus test systems.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Security and Privacy: Large-scale security measurements

Abstract

Electric power systems require accurate, scalable, distributed, and near real-time state estimation (SE) to support reliable monitoring and control under increasingly complex operating conditions. Limited monitoring capabilities can lead to inefficient operation and, in extreme cases, large-scale disturbances such as blackouts. To address these challenges, this paper proposes a vectorized Gaussian belief propagation (GBP) framework for phasor measurement unit-based SE, formulated over factor graphs and specifically designed to support distributed and near real-time monitoring. The proposed framework includes multivariate and fusion-based GBP formulations. The multivariate formulation jointly models related state variables and their measurement relationships, while the fusion-based formulation reduces factor graph complexity by combining multiple measurements associated with the same set of variables, resulting in a structure that more closely reflects the underlying electrical coupling of the power system. The resulting algorithms operate in a fully distributed manner at the bus level and achieve fast convergence and high estimation accuracy, often within a single iteration, as demonstrated by numerical results on systems with 1354 and 13659 buses.

Problem

• state estimation
• distributed monitoring
• real-time operation
• power systems
• phasor measurement unit

Innovation

• vectorized Gaussian belief propagation
• distributed state estimation
• phasor measurement unit
• factor graph fusion
• multivariate GBP