Reduced-order realization of a nonlinear power network using companion-form state equations with periodic coefficients

This paper presents a methodology for the identification of a reduced-order dynamic equivalent of a nonlinear power network for the simulation of electromagnetic transients. The equivalent is deduced from the observer companion form of the state equations with periodic coefficients and includes the effects of the nonlinearity of the power network at its operating point. A previously proposed concept, the harmonic domain dynamic transfer function (HDDTF), is used to characterize the network's transient behavior, superimposed on the steady state. The HDDTF is obtained by linearization of the nonlinear state equations of the network corresponding to harmonic perturbations applied to the steady-state operating point. Then, reduced-order companion-form state equations with periodic coefficients are fitted to the HDDTF in the frequency domain using a least-squares procedure based on the SVD and QR algorithms. The fitting procedure includes sequential weighting, column scaling, and vertical partitioning to improve computational accuracy and efficiency. The SVD algorithm serves to determine an appropriate model order. A test network with nonlinear inductances is used to demonstrate the performance of the identification method as well as the time-domain simulation results.