Observability and criticality analysis in state estimation using integer-preserving Gaussian elimination

Abstract

SUMMARY This paper presents an efficient numerical method for observability and criticality analysis in power system state estimation based on integer Gaussian elimination of integer coefficient matrices. Because all computations performed are exact, no round‐off error, numerical instability, or zero identification problems occur. The observable islands are identified in a noniterative manner by performing back substitutions on the integer triangular factors of the gain matrix. The additional measurements for placement are provided by a direct method, using the integer triangular factors of the Gram matrix associated with a reduced size Jacobian matrix. The critical measurements are identified by checking for diagonal entries of the integer residual sensitivity matrix. Implementation of the proposed method needs little additional effort, because it requires minor modifications of sparse triangular factorization and forward/backward substitution algorithms common to state estimators. The IEEE 14‐bus system is used to illustrate the steps of the proposed algorithms. Test results for a 10 343‐bus system are provided to demonstrate the features of the proposed algorithms. Copyright © 2012 John Wiley & Sons, Ltd.

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