Equivalent circuit for the leakage inductance of multiwinding transformers: Unification of terminal and duality models

Casimiro Álvarez-Mariño, Francisco De León, Xosé M. López-Fernández

Research output: Contribution to journalArticlepeer-review


In this paper, a new equivalent circuit for the leakage inductance of multiwinding (or multisection) transformers is presented. The methods proposed in this paper unify terminal models with models derived from the principle of duality between electric and magnetic equivalent circuits. The new model is identified as the terminal-duality model (TDM). The elements of the circuit in addition to properly representing the transformer behavior at the terminals are physically related to flux paths in the transformer window. The circuit of the TDM consists of a set of mutually coupled inductors available in any circuit simulation program and, in particular, available in all Electromagnetic Transients Program-type programs. The circuit elements of the TDM can be computed in two ways: 1) from the observation of the behavior of the magnetic field in the transformer window (applying the principle of duality) and 2) from measurements on short-circuit tests performed at the transformer terminals. Both methods yield identical results. The 2-D finite-element simulations are used to compute the terminal behavior of a wide variety of winding configurations. Several examples are presented for the illustration of the model capabilities and validation.

Original languageEnglish (US)
Article number6095353
Pages (from-to)353-361
Number of pages9
JournalIEEE Transactions on Power Delivery
Issue number1
StatePublished - Jan 2012


  • Duality model
  • leakage impedance
  • leakage inductance
  • terminal model
  • transformer equivalent circuit

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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