Duality-Based Transformer Model Including Eddy Current Effects in the Windings

Saeed Jazebi, Francisco De León

Research output: Contribution to journalArticlepeer-review


This paper presents a general method for building equivalent electric circuits of power transformers, including eddy current effects in windings and core. A high-frequency equivalent dual model for single- and three-phase transformers with two multilayer windings is derived from the application of the principle of duality. The model is built from elements available in circuit simulation programs, such as Electromagnetic Transients Program (EMTP)-Alternative Transients Program, EMTP-RV, PSCAD, and PSpice. The parameters of the frequency-dependent leakage inductance and winding resistance are computed with analytical formulae obtained from the solution of Maxwell's equations that are based on the geometrical dimensions and material information. Ideal transformers are utilized to isolate the electric components (winding resistors and capacitors) from the magnetic components (inductors). The physically correct connection points for electric and magnetic components are clearly identified. The proposed methodology is successfully validated versus finite- element simulations and laboratory measurements.

Original languageEnglish (US)
Article number7097070
Pages (from-to)2312-2320
Number of pages9
JournalIEEE Transactions on Power Delivery
Issue number5
StatePublished - Oct 1 2015


  • Eddy currents
  • electromagnetic transients
  • leakage inductance
  • principle of duality
  • transformer modeling

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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