Reduced-order equivalent model to large power networks derived from its spectral dispersion

This paper describes a general methodology for identification of a reduced-order dynamic equivalent with modal frequency distribution to large power networks, derived from its frequency-varying response. The method is used to define a state space model with modal frequency dispersion established from both, the application of the empirical orthogonal functions (EOFs) analysis and vector fitting (VF) procedure for rational functions approximation from frequency-domain data sets. Initially, our approach uses orthogonal modes of major contributions of spectral dispersion derived from the EOFs analysis to construct a reduced-order approximation with applications to multiple-input, multiple-output (MIMO) linear-time invariant (LTI) systems. This approximation defines an optimal distributed solution to the frequency-varying data set, where their fundamental properties are based on the interpretation of pre-selected frequencies contained into the eigenvectors of a cross-spectrum matrix. Once the reduced-order empirical modal decomposition is derived, its coefficients are used in the VF procedure in order to generate a rational function approximation into a frequency band with particular level of kinetic energy with applications to MIMO systems. Additionally, the reduced-order equivalent network in a state space model is derived from a VF, which can be efficiently incorporated in a power network simulator to electromechanical studies of multimachine dynamics with modal frequency splitting. Finally, an example for large power networks is examined to both demonstrate the effectiveness for fitting reduced-order dynamic equivalents and to capture its modal coherence and frequency distribution.