Data-Driven Power System Linear Model Identification via Quadrature-Based Balanced Truncation

This paper introduces the novel formulation of the quadrature-based balanced truncation (QBBT) method to precisely identify large-scale power system linear models. The QBBT interpolates a directional frequency dataset that is extracted from a dynamic system, following a quadrature rule to be applied from weighted data to derive a linear system model based on approximations of Gramians, and providing an alternative approach to the classic balanced truncation (BT) formulation that makes use of the system model. In this investigation, an accurate theoretical framework is presented to achieve the application of QBBT considering power systems as black-box models. The Boyd/Clenshaw-Curtis (BCC) quadrature rule is implemented by using different adjustments to accurately identify linear models of different order. The attained results and their validation with analytical power system models confirm the method's potential to retail oscillatory dynamics. The QBBT's effectiveness is compared with the Loewner-based frequency interpolation (LBFI) approach and the BT method on the Klein-Rogers-Kundur (KRK) benchmark power system and the equivalent of the New England transmission system - New York power system (NETS-NYPS), achieving a small absolute error in the magnitude of the frequency response of the models of the order of 1x10-3 dB in comparison with other state-of-the-art methods.