Communication Capacity Requirement for Reliable
and Secure State Estimation in Smart Grid
Husheng Li
†
, Lifeng Lai
‡
and Robert. C. Qiu
§
†
Department of Electrical Engineering and Computer Science, The University of Tennessee, Knoxville, TN
‡
Department of Systems Engineering, University of Arkansas, Little Rock, AR
§
Department of Electrical and Computer Engineering, Tennessee Technological University, Cookeville, TN
Abstract— Secure system state estimation is an important issue
in smart grid to assure the reliability and security. In this paper,
the case of a single observation station and Gaussian noise
communication channel with an eavesdropper is considered. The
channel capacity requirement is studied from the information the-
oretic perspective. The smart grid is modeled as a linear dynamic
system. Then, the channel capacity requirement is studied for
the state estimation of general linear dynamic systems and then
applied in the system state estimation in smart grid. Numerical
simulations are used to evaluate the capacity requirement in
typical configurations of smart grid.
I. INTRODUCTION
In recent years, the smart grid technology has attracted
much attention in the communities of power systems, com-
munications, networking and control systems [5] [9] [7]. In a
smart grid, modern information technologies are applied for
power systems to report the instantaneous power load to the
power market and feed back the time-varying power price to
power consumers such that the power consumptions can be
controlled using a price mechanism.
In smart grid, communications play a key role since the
information about load and price needs to be delivered over
the communication network. Two fundamental issues exist for
the communication in smart grid:
• Capacity: The communication link should be able to con-
vey the information of load and price to the destinations
(the power market and the power consumer, respectively)
with negligible error in a realtime manner.
• Security: It is important to preserve the privacy of the
system state in smart grid. If the information is leaked,
an eavesdropper could use this information to break the
stability of the power market or steal personal private
information.
The information leakage could occur during both the in-
formation transmission and information storage stages. In this
paper, we address the above two issues during the information
transmission stage. For simplicity, we consider the case of a
single observation station and a control center. As illustrated
in Fig. 1, the observation station encodes the observation
on the system state into a bit string and then sends to
the control center, which decodes the codeword and then
uses the system state for further actions. The transmitted
This work was supported by the National Science Foundation under grants
CCF-0830451, MRI-0821658 and ECCS-0901425.
Fig. 1: An illustration of the meter report subject to eavesdrop.
channel symbols are contaminated by Gaussian noise before
the decoder at the power market. Meanwhile, an eavesdropper
overhears the received signal at the control center and the
signal is further contaminated by an independent Gaussian
noise. Then, the goal of the communication in smart grid
is to convey the system state to the control center reliably
and without being intercepted by the eavesdropper. Note that
the model considered in this paper is far simpler than the
practical case, in which the system observations are collected
from many distributed observers, e.g., the load information
is obtained from the reports of smart meters and the power
generation information is obtained from the power generation
companies. However, the study on the simplified model can
provide insights and tools for the study on more complicated
systems. Moreover, it is the first study on the secured system
state estimation via a communication channel in a dynamic
system, to our best knowledge. In the near future, we will
extend the study to the case of multiple observers.
We focus on the fundamental limit, i.e., how much chan-
nel capacity is needed to guarantee the secure and reliable
system state estimation in smart grid, from the information
theory perspective. The study on secure communications in
the information theory community traces back to 1975 [10],
when A. D. Wyner proposed the information theoretic study
on wire-tap channels. Subsequently, the information theorists
have studied the capacity requirement with security for dif-
ferent channels, like additive white Gaussian noise (AWGN)
channel [2]. Recent years witnessed the resurrection of the
information theoretic study on security issues, like channel
capacity requirements for fading channels, multiple access
channels, broadcast channels and interference channels. A
survey on these studies can be found in [3].
However, the traditional information theoretic studies on
communications with security usually focus on stationary and
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