23-08-2012, 03:23 PM
A Direct Numerical Method for Observability Analysis
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Abstract
This paper presents an algebraic method that uses the
triangular factors of singular, symmetric gain matrix to determine
the observable islands of a measured power system. This is accomplished
in a noniterative manner via the use of selected rows of the
inverse factors. Implementation of the proposed method presents
little additional effort, since sparse triangular factorization and
forward/back substitution procedures common to existing state estimators,
are the only required functions. The method is further
extended for the choice of pseudo-measurements in order to merge
the observable islands into a single observable system. Numerical
examples are given to illustrate the details of the proposed methods.
INTRODUCTION
THE static state estimation is a mathematical procedure to
compute the best estimate of the node voltage magnitude
and angle for each node from a given set of redundant measurements.
Network observability must be checked prior to state estimation,
to determine the observable islands. If there are two
or more islands, then a meter placement procedure will be followed,
in order to make the entire system observable again.
Observability analysis has so far been accomplished by the
help of either topological or numerical approaches. The topological
approach makes use of the graph theory and determines
network observability strictly based on the type and location of
the measurements. It does not use any floating point arithmetic
and needs to be implemented independent of the state estimation
solution itself [3]. The numerical approach is based on the
decoupled measurement Jacobian and the associated gain matrix.
It uses an iterative scheme to determine all the observable
islands if the system is found to be unobservable [1]. A similar
iterative procedure is employed for placement of pseudo-measurements
[2].
TEST RESULTS
The new observability analysis and measurement placement
algorithms have been tested on IEEE 14 and IEEE 118 bus systems.
A variety of measurement systems, including both observable
and unobservable cases, have been studied. In this section,
we will only show the results for the measurement systems used
in Ref. [2] for illustration.
CONCLUSION
This paper presents a direct numerical procedure to determine
observable islands of a measured network. The information
about the observable islands, is shown to exist within the inverse
triangular factors of the singular gain matrix. This constitutes
the main contribution of the paper. This result is then used
to develop a formal algorithm to determine observable islands
and for meter placement. Numerical examples are included to
illustrate the proposed algorithm. Implementation of the algorithm
is easy due to its use of existing sparse factorization and
substitution operations.