# Observability Analysis for Large-Scale Power Systems Using Factor Graphs

## TL;DR

This paper introduces a novel observability analysis method for large-scale power systems using factor graphs and Gaussian belief propagation, enabling efficient and distributed determination of observable islands and measurement placement.

## Contribution

It pioneers the use of factor graphs and belief propagation for power system observability analysis, offering a scalable and distributed approach for large networks.

## Key findings

- Method scales linearly with system size due to sparsity.
- Effective identification of observable islands and measurement placement.
- Applicable to power systems with up to 70,000 buses.

## Abstract

The state estimation algorithm estimates the values of the state variables based on the measurement model described as the system of equations. Prior to applying the state estimation algorithm, the existence and uniqueness of the solution of the underlying system of equations is determined through the observability analysis. If a unique solution does not exist, the observability analysis defines observable islands and further defines an additional set of equations (measurements) needed to determine a unique solution. For the first time, we utilise factor graphs and Gaussian belief propagation algorithm to define a novel observability analysis approach. The observable islands and placement of measurements to restore observability are identified by following the evolution of variances across the iterations of the Gaussian belief propagation algorithm over the factor graph. Due to sparsity of the underlying power network, the resulting method has the linear computational complexity (assuming a constant number of iterations) making it particularly suitable for solving large-scale systems. The method can be flexibly matched to distributed computational resources, allowing for determination of observable islands and observability restoration in a distributed fashion. Finally, we discuss performances of the proposed observability analysis using power systems whose size ranges between 1354 and 70000 buses.