State Estimation in Electric Power Systems Using Belief Propagation: An Extended DC Model

TL;DR

This paper models extended DC state estimation in power systems as a factor graph and applies belief propagation, providing analytical solutions and demonstrating effectiveness on a standard test case, with insights for future AC model applications.

Contribution

It introduces a belief propagation approach to extended DC state estimation, deriving closed-form message expressions and demonstrating its application on IEEE test cases.

Findings

BP algorithm performs well on IEEE 14 bus test case.

Closed-form expressions for BP messages are derived.

Provides insights into applying BP to complex power system models.

Abstract

In this paper, we model an extended DC state estimation (SE) in an electric power system as a factor graph (FG) and solve it using belief propagation (BP) algorithm. The DC model comprises bus voltage angles as state variables, while the extended DC model includes bus voltage angles and bus voltage magnitudes as state variables. By applying BP to solve the SE problem in the extended DC model, we obtain a Gaussian BP scenario for which we derive closed-form expressions for BP messages exchanged along the FG. The performance of the BP algorithm is demonstrated for the IEEE 14 bus test case. Finally, the application of BP algorithm on the extended DC scenario provides significant insights into a fundamental structure of BP equations in more complex models such as the AC model - the topic we will investigate in our follow up work. As a side-goal of this paper, we aim at thorough and detailed presentation on applying BP on the SE problem in order to make the powerful BP algorithm more accessible and applicable within the power-engineering community.