Physically symmetric components in electrical circuits do not exist. Symmetric components were introduced to significantly simplify the calculation of three-phase circuits due to the fact that the mathematically asymmetric system of three arbitrary vectors can always be replaced by two symmetric systems of vectors and one system of three co-directional vectors (Fig. 1).

Fig. 1. Transformation of an asymmetric system into a set of two symmetric and one system of co-directional vectors

Further, it is possible to carry out a calculation for each system of symmetric vectors, presenting a three-phase equivalent circuit with a single-line one, which is an order of magnitude easier than calculating the original circuit by the method of contour currents, according to the laws of Kirchhoff, etc.

Fig. 2. The calculation of a three-phase symmetric circuit is replaced by the calculation of a single-line circuit for phase A, the values in other phases are found by rotating the calculated phase A vector by an angle of 120 ° or 240 °