Millman’s Theorem revisited

Authors

  • G. Aguirre Zamalloa Department of Electrical Engineering Faculty of Engineering University of the Basque Country Author
  • F. Uriondo Department of Electrical Engineering Faculty of Engineering University of the Basque Country Author
  • J.R. Hernández Department of Electrical Engineering Faculty of Engineering University of the Basque Country Author

DOI:

https://doi.org/10.24084/repqj07.322

Keywords:

Millman’s Theorem, Single-phase Equivalent Circuit, Matrix methods, Voltage Unbalance, Octave/Matlab

Abstract

In this work we present some results bearing on Millman’s Network Theorem (MNT for short) with a specific focus towards its application to three phase power systems. First we present an original, insightful proof of the Theorem that simultaneously provides the foundation for the Universal Single Phase Equivalent Circuit (USPEC) framework. Next we introduce two modifications that generalise the standard MNT and render it better adapted to the analysis of three-phase power circuits. The first result is a vectorised version based on the USPEC method which allows a very concise calculation of load voltages and the second is aimed at the calculation of neutral point voltage unbalances in more general power circuits. We illustrate the practical application of these results with the help of several commented examples and besides we provide the Matlab/Octave scripts used to perform the analyses

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Published

2024-01-24

Issue

Vol. 7 No. 1 (2009)

Section

Articles