Analysis of the multi-phased system based on the concept of analytic signals

This paper presents a new analysis method of a multi-phased electric system, based upon the concept of analytic signals. Analytic signals are complex values, formed by pairs of real signals connected through the Hilbert Transform. Analytic signals are associated to the voltage and current signals that characterize the multi-phased electric system. Fortescue transformations, formally similar to those applied to the phasor values, are applied to these analytic signals. These transformations lead to analytic output signal sets, which will be called here symmetrical components sequences of the analytic signals. Each sequence is formed of the same number of analytic signals, which have the same module and are shifted one to the other with the same angle. Symmetrical components of analytic signals allow the simple calculus of powers of the multi-phased system, for each sequence. The analysis presented in the paper is suited for creating practical working algorithms in discrete time.