Multidimensional Extensions to Generalized Averaged Models for Multi-Frequency-Excited Dynamic Systems

In this paper, a novel Harmonic Axis Decoupling (HAD) method is proposed for extending the capabilities of the Generalized Averaged Modeling (GAM) technique. The conventional GAM technique is first revisited, and the problems encountered in the multiplication of two Double Fourier Series (DFS) signals in the time domain are investigated. The method of translating Fourier vectors to Discrete Fourier Images (DFI) in the frequency plane is proposed, and the ramifications of this conversion on DFS product terms in the time domain are investigated. The two-dimensional DFI convolution technique resulting from HAD is used for the dynamic modeling of power converters excited by two distinct frequencies. The novel technique efficiently incorporates a large number of harmonics present in a power converter. The proposed technique is then converted into an algorithm suitable for implementing in numerical Ordinary Differential Equation (ODE) solvers. Observations on the effects of harmonic truncation are made to validate the proposed algorithm. Finally, the efficacy of the proposed technique is assessed through a case study, wherein a single-phase inverter possesses LC filters on both the dc-link and the ac-side. The results obtained with the proposed method show an excellent congruence with a detailed simulation model.