Observability in the state estimation of power systems

Power system static state estimators usually employ more measurements than the minimum number necessary to completely define the state of the system. This paper solves the problem of determining the best measurement to add to a given set. This is done by showing that the poorest observability is in the direction of the eigenvector associated with the smallest eigenvalue of an observability matrix. Added new measurements in this direction are shown to improve observability and the best possible observability is shown to be where all the eigenvalues of the observability matrix are equal. The addition of measurements for determining the static state of a power system should improve observability. The technique for applying this concept to a power system is illustrated by a numerical example. The observability matrix and the smallest eigenvalues are found and the measurement to be added is determined by examining the components of the associated eigenvector. The improvement of this measurement over any other is verified by use of the Kalman filter.