Harmonic linear time invariant modeling of grid-connected parallel inverters-based microgrids

Modern power systems with high penetration of renewable energies, such as wind and photovoltaic (PV), commonly experiment harmonic issues and in some cases this power quality problem leads to instability. To understand and study this phenomenon, small-signal models have been proposed; however, most of these models neglect the harmonic cross-coupling and the harmonics themselves. Consequently, the harmonic interaction among controllers, network elements, loads, and power electronic converters is overlooked. This paper presents two approaches to obtain the small-signal model of a grid-connected AC microgrid constituted by multiple parallel three-phase inverters; one approach is analytical and the another is numerical. The extended harmonic domain (EHD) is used as frame of reference for the proposed small-signal models since it retains the harmonic cross-coupling among all the harmonic components, and transforms a linear periodic time-varying system into a linear time invariant (LTI) system allowing the straightforward use of LTI tools.