Methodology for determining angular displacement in three-phase transformers

  • Nicolás Muñoz-Galeano Universidad de Antioquia
  • Jesús M. López-Lezama Universidad de Antioquia
  • Fernando Villada-Duque Universidad de Antioquia
Keywords: Angular displacement, connections, three-phase transformers, voltage and current phasors, graphic method.


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.

Author Biographies

Nicolás Muñoz-Galeano, Universidad de Antioquia
Doctor en Ingeniería Electrónica, Departamento Ing. Eléctrica, Grupo de Manejo Eficiente de la Energía – GIMEL, Facultad de Ingeniería, Universidad de Antioquia, Medellín
Jesús M. López-Lezama, Universidad de Antioquia
Doctor en Ingeniería Eléctrica, Departamento Ing.  Eléctrica, Grupo de Manejo Eficiente de la Energía–GIMEL, Universidad de Antioquia, Medellín
Fernando Villada-Duque, Universidad de Antioquia
Doctor en Ingeniería Eléctrica, Departamento Ing. Eléctrica, Grupo de Manejo Eficiente de la Energía–GIMEL, Universidad de Antioquia, Medellín


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How to Cite
Muñoz-Galeano, N., López-Lezama, J. M., & Villada-Duque, F. (2017). Methodology for determining angular displacement in three-phase transformers. TecnoLógicas, 20(38), 41-53.


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