Generalized Circuit Model for Eddy Current Effects in Multi-Winding Transformers

Digvijay Deswal, Francisco De León

Research output: Contribution to journalArticlepeer-review


This paper presents a novel circuit model for eddy-current effects for multi-winding transformers. It presents the theoretical framework to model eddy currents applicable to layer or disk windings with n-layers for two-dimensional (2-D) transformer arrangements. The new white-box model is physical, dual, and leakage reversible. Additionally, it does not have mutually coupled elements or negative inductors. The paper presents a complete circuit for transformer windings (including capacitances) and core. The model accurately predicts the variation of resistance (dc component, skin, and proximity effects) and leakage inductance of windings from dc to hundreds of kilohertz. Being derived from the principle of duality, the circuit elements can be physically related one-to-one to the distribution of flux and current in the winding geometry. A practical winding discretization, based on field penetration depth for the given frequency, allows estimating the parameters using very simple formulae requiring only geometrical information and properties of materials. Model verification is done using finite element simulations. It is shown that the circuit model matches very well with 2-D FEM simulations. The circuit can be easily implemented in any circuit simulation software like EMTP-RV, PSCAD, ATP, etc., by simply dragging and dropping elements.

Original languageEnglish (US)
Article number8630040
Pages (from-to)638-650
Number of pages13
JournalIEEE Transactions on Power Delivery
Issue number2
StatePublished - Apr 2019


  • Capacitive behavior
  • EMTP
  • core modeling
  • duality
  • eddy currents
  • leakage inductance
  • physical model
  • proximity losses
  • reversible model
  • transformer modeling

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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