Coupling measures between modes and state variables in power-system dynamics

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Abstract
A new method for model reduction called Selective Modal Analysis uses the eigenvectors and reciprocal eigenvectors of the system matrix A to calculate participation factors associating modes to certain state variables. This paper investigates the idea in depth. The novel aspect of this paper is the use of MacFarlane's concept that the system matrix A represents an energy transformation map to show that the participation factors are actually modal energies. This interpretation has some advantage because of its direct link to stability. It is shown that the participation factors, or modal energies, can be taken to be coupling measures between modes and state variables. An application to a single-machine infinite-busbar system with and without controllers is given. The properties and limitations of these coupling measures are investigated.

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