Optimal Modal Coherent Aggregation for Power System Dynamic Equivalents

A new aggregation method is developed that is similar to singular perturbation but can be used for systems that do not have a two time scale property and experience fault disturbances. The optimal modal coherent aggregation method is derived by formulating a parameter optimization problem that attempts to estimate the parameters of a reduced order model of fixed form. The performance index measures the squared error in all internal generator angle differences in the reduced and unreduced model for the study system where disturbances occur. The optimal modal coherent aggregation method is shown to have an identical form for both step and impulse disturbances which is similar to that for the singular perturbation aggregation method. Computational results and associated analysis show the global equivalent produced for a step probabilistic disturbance is a singular perturbation equivalent because it exploits the two time scale property. The global equivalent produced for a probabilistic impulse disturbance does not exploit the two time scale property and is not a singular perturbation equivalent. Local and parochial equivalents for a probabilistic disturbance over a subset of the generators and a deterministic disturbance respectively are also produced and discussed.