Hybrid modal-balanced truncation method based on power system transfer function energy concepts

Hybrid modal-balanced truncation method based on power system transfer function energy concepts

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The combined use of modal and balanced truncations methods is proposed for model order reductions. To efficiently combine these methods, a stopping criterion based on spectral energy concepts is also proposed. This criterion was implemented into the code of the widely known subspace accelerated dominant pole algorithm (SADPA), designed to compute a set of dominant poles and associated residues of transfer functions from large-scale, sparse, linear descriptor systems. The resulting enhanced SADPA code automatically stops once the computed set of dominant poles and associated residues is sufficient to build a modal reduced order model (ROM) whose energy content approaches that of the complete model within a specified tolerance and considering a frequency window of interest. The number of dominant poles in this set is much smaller than the number of poles of the full system model. Hence, their state-space realisation usually has a small enough dimension for the efficient application of the square root balanced truncation method. This new method, named hybrid modal-balanced truncation, produces ROMs whose order are much smaller than that of the modal ROMs and, most importantly, can also be applied to unstable models.


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