Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)


Electrical Engineering


Over the past ten years, a vast outflow of research and publications has resulted from the use of Lyapunov's "second or direct method" of stability analysis. This research trend stems from the appearance of the original work of Lyapunov in 1892, more than three quarters of a century ago; but only recently has this concept been appreciated to the point where researchers in the area of stability of dynamic systems are aware of its potentialities. La Salle and Lefschetz wrote the first comprehensive book in English about Lyapunov stability theory. In most cases describing a physical system, the energy stored in the system appears to be a natural candidate. This is neither a necessary nor a sufficient criterion for choosing a function and many examples of stable systems are known where the energy is not a suitable Lyapunov function. The extension of this abstract theory to the analysis of real-world problems has posed yet another problem; the conflict between the theorist and the practitioner. This treatise envisages the study of large power system stability with the aid of Lyapunov functions. The primary purpose of the investigation is an extensive study of Willems' conjecture (discussed in Chapter III) for the derivation of Lyapunov functions for multimachine power systems. The study extends the Lyapunov method to analyze operations of practical significance such as automatic circuit reclosing. An investigation is made into the effects of parameter variation on the extent of stability. New methods of generating Lyapunov functions have also been attempted. Wall's energy metric algorithm is shown to yield a suitable function for the analysis of a second-order system. Two systems have been studied using Lyapunov stability analysis. The advantages and disadvantages of Lyapunov's method are discussed and some suggestions are offered for further research.

Library of Congress Subject Headings

Lyapunov stability
Power (Mechanics)



Number of Pages



South Dakota State University