Based on multi-dimensional representation and vector calculus definitions, this paper proposes two novel and quite simple algorithms for utility applications and power quality analysis. The first one is a synchronizing procedure, based on a digital PLL (Phase Locked Loop). Its design and dynamic behavior are analyzed for single and three-phase systems. The second one is a positive sequence detector, which uses the proposed PLL to ensure that the positive sequence components can be calculated even under distorted waveform conditions or frequency variations. Since it is not based on Fortescue’s classical decomposition and no special input filtering are needed, its dynamic response may be as fast as one fundamental cycle. In order to validate the proposed models, simulations are shown and experimental results were obtained by means of a DSP-based system and a prototype of Power Quality Monitor. Furthermore, the PLL algorithm was implemented in a selective active filter to confirm the expectations in a closed-loop application.
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