LOSS OF STABILITY IN COMPLEX ELECTROMECHANICAL SYSTEMS (STATIC BIFURCATIONS, ENERGY-LIKE, LYAPUNOV FUNCTIONS).

摘要

This thesis concerns the stability analysis of a class of dynamical systems modeled by a second order vector non-linear equation. There are two aspects of the stability problem for such systems. One, the system must be stable at a nominal set of design parameters, for which the linearized equations are studied. Secondly, it is important to understand the qualitative dynamics of the system as the parameters vary with time and circumstances.;In this thesis we give a complete local stability analysis of dynamical systems with circulatory forces, modeled by a second order linear equations, using energy-like Lyapunov functions. The results are tailored for the electric power system model in which the circulatory forces arise if the transmission line resistance is included in the model, the so-called "model with transfer conductances". Further, based on the theory of generic bifurcations, a complete local characterization of the qualitative behaviour of the dynamical system, near an equilibrium point is presented. The theory is applied to classify the ways in which an electric power system can be expected to lose steady-state stability. It is also shown that both steady state stability and voltage collapse can be viewed in terms of a common mathematical structure which predicts a much richer set of mechanisms of power system static instability than previously recognized.