Energy Research, Vol. 2, Issue 1, Mar  2018, Pages 13-23; DOI: 10.31058/ 10.31058/

Investigation of The Small Oscillations of Electrical Systems

Energy Research, Vol. 2, Issue 1, Mar  2018, Pages 13-23.

DOI: 10.31058/

Allaev K.R. 1* , Makhmudov T.F. 1

1 Electrical Plants, Networks and Systems, Tashkent State Technical University, Tashkent, Uzbekistan

Received: 2 January 2018; Accepted: 2 February 2018; Published: 5 March 2018

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The article shows the efficiency of the joint application of the equations of nodal voltage and the Lyapunov`s function in quadratic form for the analysis of small oscillations of electrical system. The jointly solution of the equations of nodal voltage and the Lyapunov`s matrix equation makes it possible to determine the conditions for the stability of the electrical system and to reveal a generator that first approaches the stability limit. As will be shown below, studies of small oscillations of complex electrical systems can be carried out in full on the basis of matrix methods, successfully developed in recent decades. This is facilitated by the removal of memory limits and a sharp increase in the speed of computing modern computers.


Electric Power System, Nodal Voltage Equations, Lyapunov`s Function, Small Oscillations, Sylvesters Criterion


© 2017 by the authors. Licensee International Technology and Science Press Limited. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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