Enhancement to Givens rotations for power system state estimation

Abstract

Orthogonalization has not been widely used in power system state estimation due to misgivings about its speed. Sparsity related issues and the various advances made in speeding up the orthogonalization are presented in this paper.The efficiency of the method is illustrated by tests on various networks. These tests indicate that the performance is comparable to the normal equations method.

State estimator condition number analysis

“…8 shows a plot of the condition number of and (13) for the IEEE 118 bus system versus the number of injection measurements and flow measurements, given voltage measurements for ordered placement of the measurements. The magnitudes of the condition number of matches the magnitudes described by the plane of the approximation (13). They are roughly at the same magnitude in most places.…”

“…Furthermore, as the number of buses in a system increases, the ill-conditioning of the state estimation problem becomes worse. Solution methods, such as orthogonal decomposition utilizing Givens rotations [1], [2], [9], [13], have been introduced to overcome this ill-conditioning without loss of sparsity.…”

Globally convergent state estimation based on givens rotations

“…Methods based on the application of Givens rotations [8], [9] have proved to be particularly successful in providing robust solutions, since they prevent further degradation of the problem's numerical conditioning.…”

“…Before the rotation, both rows are scaled by √ d and √ w, as shown in Eqs. (9). The result of the rotation is depicted in Eqs.…”

Weighted Least Absolute Value state estimation using interior point methods

“…A comparison of some of these approaches can be found in [17]. Specialized blocking methods were applied to the augmented formulation in [3, 251 and enhancements to orthogonal factorization using Givens rotations were introduced in [31]. The other area of focus in these methods has been in finding computationally viable and effective ways of detecting and eliminating bad data [24].…”