Symmetrical and Clarke-Park transformations for four-phase systems
Purpose - To provide a unified analytical tool for the theoretical and practical analysis of four-phase systems under sinusoidal condition but also under dynamic condition and to understand the contribution of each sequence components on the energy and air gap field points of view. Design/methodology/approach - Starting from the general procedures of analysis for the n-phase symmetric systems, the analysis of four-phase system is first developed in the phasorial domain, then, with reference to the asymmetrical sinusoidal conditions in terms of symmetric components. As a complement to what is already present in the literature, finally a formalization of the four-phase systems in an instantaneous form based on the Lyon and Clarke-Park vectors is proposed. Furthermore, a particular emphasis will be given to the physical meaning of the involved quantities, to their link with the three-phase quantities and to the instantaneous energetic interpretation. Findings - Four phase system presents the existence of the pseudozero-sequence component which is an additional descriptive variable of the four-phase configuration, absent in the three-phase system. Pseudozero-sequence component results completely independent on the need for a neutral wire. Knowledge of the Park vector is as much as necessary to generate the field in the air gap. Practical implications - The four-phase systems methodological analysis presented in this paper is very helpful for the formalization of the theoretical and applicative methodologies necessary for the development of four-phase systems in a systematic and unified way. Originality/value - The four-phase systems analysis is presented in this paper both for the sinusoidal and the variable conditions. Furthermore, the role of the pseudozero-sequence component, not present in three-phase case, and its implications in circuital terms have been investigated with attention. Finally, the energetic side and the definition of the correspondent instantaneous and average powers have been investigated as well.
electric power systems magnetic fields switching systems