Abstract—We propose a fast real-time state estimator based
on the belief propagation algorithm for the power system state
estimation. The proposed estimator is easy to distribute and
parallelize, thus alleviating computational limitations and
allowing for processing measurements in real time. The
presented algorithm may run as a continuous process, with
each new measurement being seamlessly processed by the
distributed state estimator. In contrast to the matrix-based state
estimation methods, the belief propagation approach is robust
to ill-conditioned scenarios caused by significant differences
between measurement variances, thus resulting in a solution
that eliminates observability analysis. Using the DC model, we
numerically demonstrate the performance of the state estimator
in a realistic real-time system model with asynchronous
measurements. We note that the extension to the AC state
estimation is possible within the same framework.
Index Terms—Real-Time State Estimation, Electric Power
System, Factor Graphs, Gaussian Belief Propagation
I. INTRODUCTION
The state estimation (SE) function is a part of the energy
management system that allows for monitoring of electric
power systems. Input data for the SE arrive from supervisory
control and data acquisition (SCADA) technology. SCADA
provides communication infrastructure to collect legacy
measurements (voltage and line current magnitude, power
flow and injection measurements) from measurement devices
and transfer them to a central computational unit for
processing and storage. In the last decades, phasor
measurement units (PMUs) were developed that measure
voltage and line current phasors and provide highly accurate
measurements with high sampling rates. PMUs were
instrumental to the development of the wide area
measurement systems (WAMSs) that should provide
real-time monitoring and control of electric power systems
[1], [2]. The WAMS requires significant investments in
deployment of a large number of PMUs across the system,
which is why SCADA systems will remain important
technology, particularly at medium and low voltage levels.
Monitoring and control capability of the system strongly
depends on the SE accuracy as well as the periodicity of
evaluation of state estimates. Ideally, in the presence of both
legacy and PMU measurements, SE should run at the
M. Cosovic is with Schneider Electric DMS NS, Novi Sad, Serbia
(e-mail: ). D. Vukobratovic is
with Department of Power, Electronic and Communications Engineering,
University of Novi Sad, Novi Sad, Serbia (e-mail: ). Demo
source code available online at https://github.com/mcosovic.
This paper has received funding from the EU 7th Framework Programme
for research, technological development and demonstration under grant
agreement no. 607774.
scanning rate (seconds), but due to the computational
limitations, practical SE algorithms run every few minutes or
when a significant change occurs [3]. In this work, we
propose a fast real-time state estimator based on the belief
propagation (BP) algorithm. Using the BP, it is possible to
estimate state variables in a distributed fashion. In other
words, unlike the usual scenario where measurements are
transmitted directly to the control center, in the BP
framework, measurements are locally collected and
processed by local modules (at substations, generators or
load units) that exchange BP messages with neighboring
local modules. Furthermore, even in the scenario where
measurements are transmitted to the centralized control
entity, the BP solution is advantageous over the classical
centralized solutions in that it can be easily distributed and
parallelized for high performance.
Compared to our recent work on BP-based SE [4], [5] that
addresses classical (static) SE problem, this paper is an
extension to the real-time model that operates continuously
and accepts asynchronous measurements from different
measurement subsystems. More precisely, we assume
presence of both SCADA and WAMS infrastructure, and
without loss of generality, we observe active power flow and
injection measurements (from SCADA), and voltage phase
angle measurements (from WAMS). We present appropriate
models for measurement arrival processes and for the process
of measurement deterioration (or “aging”) over time. Such
measurements are continuously integrated into the running
instances of distributed BP-based modules. For simplicity,
we present the real-time BP-based SE applied on the DC SE
model, while extension to the AC SE model follows similar
lines as in the static SE scenario [4]. Our extensive
numerical experiments on the example IEEE 14 system show
that the BP algorithm is able to provide real-time SE
performance. Furthermore, the BP-based SE is robust to
ill-conditioned systems in which significant difference arise
between measurement variances, thus allowing state
estimator that runs without observability analysis. Note that
in this paper, we do not address the convergence guarantees
for the BP-based solution [6], and we leave the detailed
treatment of convergence for our future work.
The structure of this paper is as follows: In Section II, we
providebackgroundon conventionaland BP-based SE. Section
III described the proposed fast real-time BP-based SE, while
Section IV considers the performanceand numericalresults for
the IEEE 14 bus test case. Concluding remarks are provided
in Section V.