Methodology for determining angular displacement in three-phase transformers

Nicolás Muñoz Galeano, Jesús M. López Lezama, Fernando Villada Duque


This paper presents methodology for determining angular displacement (connections or vector group (colloquial)) in three-phase transformers. The proposed methodology is useful to determine the angular displacement if connections are known or the connections if angular displacement is known. Even though connection of three-phase transformers requires knowledge of angular displacement; the technical literature does not report a rigorous methodology or procedure for their explicit step by step determination. However, there are numerous applications in the areas of engineering and research that use time group connections. This paper presents the methodology for determining the Yy, Yd, Dy, Dd, Zy and Zd connections; including the use of time groups in some relevant engineering applications. The proposed methodology can be applied for commercial and noncommercial transformers, and also for power and distribution transformers.


Angular displacement; connections; three-phase transformers; voltage and current phasors; graphic method.

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