Doctoral Thesis
DOI
10.11606/T.18.2017.tde-13062017-112014
Document
Author
Full name
Flávio Henrique Justiniano Ribeiro da Silva
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2004
Supervisor
Committee
Bretas, Newton Geraldo (President)
Costa, Vander Menengoy da
Milani, Basílio Ernesto de Almeida
Title in Portuguese
Funções de Lyapunov estendidas para análise de estabilidade transitória em sistemas elétricos de potência
Keywords in Portuguese
Condutâncias de transferência
Funções de Lyapunov
Método de Lyapunov
Abstract in Portuguese
Title in English
Extended Lyapunov function for analysis and control of electrical power systems transient stability
Keywords in English
Lyapunov functions
Lyapunov methods
Transfer conductances
Transient stability
Abstract in English
The method of Lyapunov, one of the direct method, is efficient for transient stability analysis of power systems. The direct methods are well-suited for stability analysis of power systems, since they do not require the solution of the set of differential equations of the system model. The great difficulty of the direct methods is to find an auxiliary function (V) which satisfies the conditions of Lyapunov's Theorem V > 0 and V '< or =' 0. For many years the inclusion of the transfer conductances in the power system model, with the reduced network, is a issue of interest for several researchers. In 1989, Chiang studied the existence of energy functions for power systems with losses and he proved the non existence of a Lyapunov Function for power systems when the transfer conductance is taken into account. The transfer conductances are responsible for generating regions in the state space where the derivative of V is positive. Therefore, the function V is nor a Lyapunov Function, because its derivative is not semi negative definite. Recently, an Extension of the LaSalle's Invariance Principle has been proposed by Rodrigues, Alberto and Bretas (2000). This extension relaxes some of the requirements on the auxiliary function which is commonly called Lyapunov Function. In this extension, the derivative of the auxiliary function can be positive in some bounded regions of the state space and, for distinction purposes, it is called, as Extended Lyapunov Function. Inthis work, the Extension of the LaSalle's Invariance Principle and the Extended Lyapunov Function are used for the transient stability analysis of power systems with the model taking transfer conductances in consideration. For at purpose in this research, Extended Lyapunov Functions for power system models which do not have Lyapunov Functions in the usual sense are proposed. Extended Lyapunov Functions are proposed for a single-machine-infinite- bus-system and multimachine systems. For obtaining good estimates of the critical clearing time in transient stability analysis, an iterative algorithm is proposed. This algorithm supplies a good local estimate of the attraction area for the post fault stable equilibrium point.