  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.
