Observability analysis and restoration for systems with conventional and phasor measurements

Abstract

SUMMARY This paper presents an efficient and fast method, using topological and numerical procedures, for observability analysis in state estimation with phasor measurement units as well as conventional (SCADA) measurements. Power and current flow measurements are used to build topologically flow islands that, in turn, are used to construct a reduced network and an associated gain matrix. To build this reduced order gain matrix, boundary power injections, and voltage phasors at flow islands are considered. Observability checking is carried out analyzing the pivots encountered during the triangular factorization of the gain matrix, and the observable islands are identified in a noniterative manner, by performing back substitutions with its triangular factors. Additional measurements that will render the system barely observable are directly provided, using the triangular factors of a reduced Gram matrix associated with existing and candidate power injections and candidate phasor measurements at boundary buses of observable islands. The dimension of the gain and Gram matrix is equal to the number of flow islands and boundary measurements, respectively, which is relatively low even for very large systems, and that makes the proposed algorithms fast and computationally efficient. The IEEE 14 and 30‐bus systems are used to illustrate the steps of the proposed algorithms. Copyright © 2012 John Wiley & Sons, Ltd.

A hybrid power system state estimator using synchronized and unsynchronized sensors

“…Consider a N − bus power system and a measurement set consisting of m S conventional measurements (bus voltage magnitudes, branch power flows, and bus power injections) provided by SCADA, m P phasorial measurements (bus voltage and branch current phasors) provided by PMUs, and m Z zero injections. Under the assumption that the available measurements are sufficient to make the entire system observable and compute the system‐wide state vector, the measurement model is described by an overdetermined system of linear and nonlinear equations relating measurements and unknowns (states) as follows: where z S is the m S × 1 vector of SCADA measurements; z P is the m P × 1 vector of PMU measurements; h S ( x ) is the m S × 1 nonlinear vector function relating conventional measurements to states; H P is the m P × n observation matrix relating the real and imaginary components of the phasor measurements to states; x is the state vector expressed in rectangular form (the i th element of x is associated with voltage phasor of bus i , with E i and F i standing for the real and imaginary part of voltage phasor at bus i , respectively); e S ( m S × 1) and e P ( m P × 1) are the vectors of random measurement errors, assumed to be normally distributed with zero mean and covariance matrix R S and R P , respectively; C is the m Z × n measurement matrix of zero current injection busses; and n = 2 N .…”

“…Since it has been assumed that the entire system is SCADA observable ( and, hence, ), the linear equations have nonsingular (full rank) coefficient matrix and can deliver a unique solution . The iterative procedure converges when max|Δ x k | < ε , where ε is a predetermined threshold.…”

PQ decoupled 3-phase numerical observability analysis and critical data identification for distribution systems

“…Observability analysis is also considered from the optimization perspective, such as nonlinear and linear integer programming. With the wide application of phasor measurement units (PMUs) in transmission systems, some authors studied power system observability analysis with PMUs and the optimal PMU placement while considering network observability.…”

Double contingency consideration in phasor measurement unit placement using MSFLA based on Pareto method

“…In recent years, PMU placement is considered in several papers [11][12][13][14][15][16][17][18][19] which have demonstrated state estimation problem. Accuracy of state estimation disrespecting and employed PMU number, are the disadvantages of these methodologies.…”

“…In [19], a method, using topological and numerical procedures is presented for observability analysis with phasor measurement units likewise conventional measurements.…”