Model Order Reduction Based on Space-Harmonic Separation for Nonlinear Periodic EQS Problems

In the case of periodic problems with large time constants, the time-domain approach to achieve the steady-state results is time-consuming. The harmonic balance method (HBM) is an efficient method for addressing this issue; however, its coefficient matrix is often of high dimension, posing a computational challenge. To overcome this, we develop a model order reduction (MOR) based on space-harmonic separation by combining the proper generalized decomposition (PGD) and the HBM and utilize the QR-factorization empirical interpolation method (QDEIM) to update the nonlinear terms. Additionally, we propose the separated space-harmonic penalty function method to treat the periodic Dirichlet boundary conditions in the PGD/HBM scheme. The developed method is applied to the insulation evaluation of a converter transformer when it is supplied by a composite ac–dc periodic voltage. Numerical results show the accuracy and efficiency of the separated space-harmonic reduced order model (ROM).