Single-Phase Modeling Approach in Dynamic Harmonic Domain

In this paper, a frequency-based analytical approach is presented for dynamic analysis of three-phase balanced systems in the presence of harmonic distortion based on single-phase analysis. By providing mathematical foundation, this study proves that a three-phase balanced system (linear or non-linear, supplied by periodic balanced sinusoidal or non-sinusoidal sources) is completely balanced during both transient and steady-state conditions. This is done by utilizing Dynamic Harmonic Domain (DHD) and defining a phase-shift matrix in frequency domain. As the most noteworthy application of the proposed methodology, single-phase modeling approach is put forward. Therefore, during the transient period, one can analyze only one phase of a three-phase balanced system and calculate exact quantities of the other phases without performing extra simulations, which is not possible through time domain. The introduced concept has been applied to different test cases including three-phase transformer inrush current. In addition, the proposed approach has been utilized to obtain a single-phase model of VSC-based power electronic devices for dynamic harmonic analysis, followed by discussion on results.