Observability Analysis
Introduction
State estimation can not be carried out unless the network is fully observable by the existing measurement set. The power system network observability analysis is to determine whether a set of measurements is sufficient in number and location to make state estimation possible. If so, the network is observable; otherwise it is unobservable. If the network is unobservable, observability analysis includes identification of observable islands and measurement placement to make the network observable.
Two approaches for observability analysis have been proposed: graph-theory based approaches [1][2] and triangular factorization-based numerical methods [3-5]. The former approach makes use of the graph theory and determines network observability strictly based on the type and location of the measurements. The latter method is based on the gain matrix and done by using triangular factorization.
In this report, a numerical observability analysis method based on measurement Jacobian H matrix is proposed. Not only the existing measurements but also the non-existing line flow measurements are taken into the H matrix. If the system is originally observable, the column rank of H within existing measurement rows should be full, i.e. equal to n. Otherwise, the triangular factorization result of the H matrix can identify the unobservable branches so that all the observable islands can be determined. Furthermore, by the triangular factorization result, the additional candidate measurements, which can make the system observable, can be conveniently and effectively chosen. Existing state estimation programs can be modified with minimal effort to implement the proposed method as the observability analysis function. Details of the procedure are presented using numerical examples.
Proposed method
One indicator of observability is the column rank of the existing measurement Jacobian H, whose column rank is not affected by the... [continues]
Introduction
State estimation can not be carried out unless the network is fully observable by the existing measurement set. The power system network observability analysis is to determine whether a set of measurements is sufficient in number and location to make state estimation possible. If so, the network is observable; otherwise it is unobservable. If the network is unobservable, observability analysis includes identification of observable islands and measurement placement to make the network observable.
Two approaches for observability analysis have been proposed: graph-theory based approaches [1][2] and triangular factorization-based numerical methods [3-5]. The former approach makes use of the graph theory and determines network observability strictly based on the type and location of the measurements. The latter method is based on the gain matrix and done by using triangular factorization.
In this report, a numerical observability analysis method based on measurement Jacobian H matrix is proposed. Not only the existing measurements but also the non-existing line flow measurements are taken into the H matrix. If the system is originally observable, the column rank of H within existing measurement rows should be full, i.e. equal to n. Otherwise, the triangular factorization result of the H matrix can identify the unobservable branches so that all the observable islands can be determined. Furthermore, by the triangular factorization result, the additional candidate measurements, which can make the system observable, can be conveniently and effectively chosen. Existing state estimation programs can be modified with minimal effort to implement the proposed method as the observability analysis function. Details of the procedure are presented using numerical examples.
Proposed method
One indicator of observability is the column rank of the existing measurement Jacobian H, whose column rank is not affected by the... [continues]
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