A Step Forward in Application of Dynamic Harmonic Domain: Phase Shifting Property of Harmonics

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In this paper, a novel analytical approach is put forward which leads to phase shifting property of harmonics in a periodic system. Based on the illustrations, it is shown that if all the input sources of the periodic system are shifted by α, the entire outputs will be shifted by α as well in both transient and steady states. There is no limitation for such system as it can be either single or three phase, linear or nonlinear, or supplied by periodic balanced or unbalanced sinusoidal/nonsinusoidal sources. According to this concept, the source angle affects only the phase angle of harmonics linearly but not their magnitude. However, related time domain response may be greatly affected. These characteristics of the harmonics are observed using the dynamic harmonic domain analysis which calculates exact variations of harmonics. To such aim, a phase shifting matrix is defined which provides exact phase shift calculation considering each harmonic order. The introduced concept significantly reduces the required simulation time and represents the effects of the source phase angle on the harmonic content and time domain response without performing extra simulations. Finally, the novel concept is successfully applied to two test cases, followed by analysis and discussion.

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