Algebraic Topology Approach to Stability Studies of Electrical Power Systems

Leon Luxemburg


In this paper we study geometric structure of stability regions of a fairly broad class of dynamical systems, including gradient systems. The lower bounds obtained via an algebraic topology approach can be used to estimate the structure of the boundary of this region and in many cases give the exact number of equilibria corresponding to the bounding surfaces. The results have numerous applications to electrical power systems and to electronic circuits. The methods we use in this study belong in the area of Morse Theory, Algebraic topology and geometric dynamical systems.


Differential manifolds, Homology groups, Stability of dynamical systems, Transversality, Electrical power systems, Regions of stability, Boundary of stability region, Morse theory.


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