March 4, 2008

An RMS Coherence Measure: A basic for Unification of coherence and modal Analysis Model Aggregation Technique

R.A. Schlueter, H. Akhtar, H. Modir, Paper A 78 533-2, 1978 Summer meeting, Los Angeles. Ca, July 1978.
The principal objective of this research is to show that modal analysis and coherency based aggregation procedures can be considered completely parallel model aggregation procedures. Thus it will be shown that modal analysis equivalents are coherency equivalents and that procedures for aggregating coherent group can be considered to be equivalent to the rules of mode elimination for the modal analysis procedure. These results depend upon first deriving a general probabilistic model of power system disturbance and an appropriate linearized model the power system. An rms measure of coherence is then defined that measures the expected value of a time average of differences in voltage angel deviations on generator buses for the probabilistically described disturbances. The modal analysis based equivalent is then shown to be a coherency based equivalent by showing that the rules of mode elimination for forming a modal analysis equivalent for the linearized system model considered can be derived by a modal analysis of this rms coherency measure evaluated over an infinite internal with the same linearized system model and a completely un certain disturbance model. The procedure for aggregating coherent groups of generator is shown to be equivalent to the rules of mode elimination for modal analysis procedures because it is shown that (1), Both methods of reducing model order can be based on an rms coherency measure and any particular form of the generalized model of disturbance desired and (2) both methods should produce equivalents as the unreduced system

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