Spectral energy indices for model order reduction

This paper proposes three indices which should be best used in combination for the automatic determination of reduced order models (ROMs) for large dynamic linear systems. The first index determines the range in the frequency response of the complete model which contains most of the signal energy, say 95%, and which the ROM should attempt to reproduce. The second index selects the most important poles and associated residues needed to the ROM to reproduce this behavior. In this sense, the second index is a pole dominance index (PDI). The third one is a global measurement of the ROM error in the frequency range determined by the first index. All three indices are based on the spectral energy concept. The theoretical developments and the application of the three proposed indices to construct a ROM of a medium size electric power system are presented. In addition the performance of the proposed PDI (PPDI) is compared to the performance of a conventional one, showing the superiority of the PPDI.