19
State Estimation
Danny Julian
ABB Power T&D Company
19.1
State Estimation Problem.
..............................................
19
1
Underly ing Assumptions
.
Measurement Representations
.
Solution Methods
19.2
State Estimation Operation.
...........................................
19
6
Network Topology Assessment
.
Error Identiﬁcation
.
Unobservability
19.3
Example State Estimation Problem .
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19
8
System Description
.
WLS State Estimation Process
19.4
Deﬁning Terms .
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19
11
An online AC power ﬂow is a valuable application when determining the critical elements affecting
power system operation and control such as overloaded lines, credible contingencies, and unsatisfactory
voltages. It is the basis for any realtime security assessment and enhancement applications.
AC power ﬂow algorithms calculate real and reactive line ﬂows based on a multitude of inputs with
generator bus voltages, real power bus injections, and reactive power bus injections being a partial list.
This implies that in order to calculate the line ﬂows using a power ﬂow algorithm, all of the input
information (voltages, real power injections, reactive power injections, etc.) must be known
a priori
to
the algorithm being executed.
An obvious way to implement an online AC power ﬂow is to telemeter the required input information
at every location in the power system. This would require not only a large number of
remote terminal
units
(RTUs), but also an extensive communication infrastructure to telemeter the data to the
SCADA
system, both of which are costly. Although the generator bus voltages are usually readily available, the
injection data is frequently what is lacking. This is because it is much easier and cheaper to monitor the
net injection at a bus than to measure separate injections directly.
Also, this approach presents weaknesses for the online AC power ﬂow that are due to meter accuracy
and communication failure. An online power ﬂow relying on a speciﬁc set of measurements could
become unusable or give erroneous results if any of the predeﬁned measurements became unavailable
due to communication failure or due to misoperation of measurement devices. This is not a desirable
outcome of an online application designed to alert system operators to unsecure conditions.
Given the above obstacles of utilizing an online AC power ﬂow, work was conducted in the late 1960s
and early 1970s (Schweppe and Wildes, Jan. 1970) into developing a process of performing an online
power ﬂow using not just the limited data needed for the classical AC power ﬂow algorithm, but using
all available measurements. This work led to the
state estimator
, which uses not only the aforemen
tioned voltages but other telemetered measurements such as real and reactive line ﬂows, circuit breaker
statuses, and transformer tap settings.
19.1 State Estimation Problem
State estimators perform a statistical analysis using a set of
m
imperfect redundant data telemetered
from the power system to determine the state of the system. The state of the system is a function of
n
ß
2006 by Taylor & Francis Group, LLC.
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: bus voltages and relative phase angles, and tap changing transformer positions.
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 Spring '10
 DR
 Normal Distribution, ........., Test method, Taylor & Francis Group, State Estimation

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