Abstract
This paper deals with a methodological approach for the analytical solution of three-phase transients. The proposed approach is based on the well-known Clarke transformation leading to the definition of space vectors representing three-phase currents and voltages. It is shown that the conventional state-equation approach can be used for space-vector variables, and the solution of space-vector state equations provides a concise and powerful representation of three-phase transients. In particular, it is shown that the geometrical shape of the trajectory of a space vector on the complex plane provides a complete and meaningful transient representation. Thus, the proposed analytical approach provides a deeper insight into the transient phenomenon with respect to the conventional numerical approach performed by means of commercial simulation tools.
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