  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.
