An investigation of the significance of singular value decomposition in power system dynamics

A theoretical explanation of the basics of singular value decomposition (SVD) is given to justify their use in applications in power system dynamics and control. The minimum singular value of a matrix not only specifies the rank of the matrix, it also gives a measure of distance of the matrix from the set of matrices having a rank less than its rank. This distance is used as a measure to compare the ability of inputs to control a mode. It is also used to compare the observability of a mode in a signal and to synthesize the optimum signal to maximize the minimum singular value of the observability matrix. The ideas are applied to a single-machine infinite busbar system with a static var controller (SVC). The system has two inputs and the SVD is used to compare the effectiveness of the outputs in controlling a mode. It is also used to determine the best output (signal) to have maximum observability of a mode in it. (C) 1999 Elsevier Science Ltd. All rights reserved.