Direct Stability Methods

Authored by: Vijay Vittal

Power System Stability and Control

Print publication date:  April  2012
Online publication date:  April  2016

Print ISBN: 9781439883204
eBook ISBN: 9781439883211
Adobe ISBN:

10.1201/b12113-15

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Abstract

Direct methods of stability analysis determine the transient stability (as defined in Chapter 7 and described in Chapter 8) of power systems without explicitly obtaining the solutions of the differential equations governing the dynamic behavior of the system. The basis for the method is Lyapunov's second method, also known as Lyapunov's direct method, to determine stability of systems governed by differential equations. The fundamental work of A.M. Lyapunov (1857–1918) on stability of motion was published in Russian in 1893, and was translated into French in 1907 (Lyapunov, 1907). This work received little attention and for a long time was forgotten. In the 1930s, Soviet mathematicians revived these investigations and showed that Lyapunov's method was applicable to several problems in physics and engineering. This revival of the subject matter has spawned several contributions that have led to the further development of the theory and application of the method to physical systems.

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