Four-phase transmission lines have been recently proposed and studied as an alternative to the traditional threephase
lines. The identification of the best transformer typology to link the three-phase and four-phase system sections is
still an open problem, despite some specific solutions were proposed. However, these solutions were not included in a
general framework yet. Resorting to the classic Parton’s theory of phase transformation and to a rigorous
mathematical approach, this study provides a general framework for the specific problem in study. After having
recalled the underlying principles of the Parton’s theory of phase transformation, by formulating proper optimisation
problems and solving them using a rigorous mathematical procedure, this study derives several solutions for three-tofour
phase transformation, some of which were never proposed yet. This way, both traditional solutions (T-connection,
Leblanc connection, Scott connection) and more recent proposals are described together with the new solutions within
one common framework.
