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

Mirsad Cosovic; Armin Teskeredzic; Antonello Monti; Dejan Vukobratovic

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arXiv · 2604.12067

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

Mirsad Cosovic·Armin Teskeredzic·Antonello Monti·Dejan Vukobratovic

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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 few iterations, as demonstrated by numerical results on systems ranging from 60 to 13659 buses, where the fusion-based formulation achieves single-digit millisecond iteration times on the largest test case.

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Mirsad Cosovic, Armin Teskeredzic, Antonello Monti, Dejan Vukobratovic. 2026-04-13. Vectorized Gaussian Belief Propagation for Near Real-Time Fully-Distributed PMU-Based State Estimation. https://arxiv.org/abs/2604.12067

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