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Data Driven Analytical Modeling of Power Transformers

Jyrki Sakari Penttonen(1*), Matti Lehtonen(2)

(1) Department of Electrical Engineering, Aalto University and Vensum Ltd., Finland
(2) Department of Electrical Engineering, Aalto University, Finland
(*) Corresponding author



In power systems there are complex transformer structures, whose accurate analysis is not possible using the techniques available today. This paper presents a systematic data driven analysis method for coupled inductors of arbitrary complexity. The method first establishes a winding matrix N mapping the windings to the limbs of the transformer. A permeance matrix P is created from the reluctance network of the magnetic core. A generalized inductance matrix L mapping currents in the transformer windings to the induced voltages is generated based on the winding (N) and permeance (P) matrices. The inductance matrix representation of a coupled inductor is then transformed to an admittance matrix, which can be integrated to the nodal analysis of the electrical circuit surrounding the coupled inductor. The method presented is validated by simulations with real transformer structures using electromagnetic transient program (EMTP/ATP).
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Power Transformer; Coupled Inductor; Electro-Magnetic Modeling

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S. Kulkarni, S. Khaparde,”Transformer Engineering”, CRC Press, 2012, Second Edition, ISBN: 978-1-4398-5377-1.

R. Del Vecchio, B. Poulin, P. Feghali, D. Shah, R. Ahuja, “Transformer Design Principles”, CRC Press, 2010, Second Edition, ISBN: 978-1-4398-0582-4.

Xusheng, “A Three-Phase Three Winding Core-type transformer Model for Low-Frequency Transient Studies”, IEEE Transactions on Power Delivery, Vol. 11, No. 3, July 1997.

E. TeNyienhuis, G. Mechler, R. Girgis, “Flux Distribution and Core Loss Calculation for Single Phase and Five Limb Three Phase Transformer Core Designs”, IEEE Transactions on Power Delivery, Vol. 15, No. 1, January 2000.

Dzafiq, R. Jabr, H. Neisius, ”Transformer Modeling for Three-Phase Distribution Network Analysis”, IEEE Transactions on Power Systems, Vol 30, No 5, September 2015.

M. Irving, A. Al-Othman, “Admittance Matrix Models of Three-Phase Transformers with Various Neutral Grounding Configurations”, IEEE Transactions on Power Systems, Vol 18, No 3, August 2003.

X. Chen, “A Three-Phase Multi-Legged Transformer Model in ATP Using the Directly Formed Inverse Inductance Matrix”, IEEE Transactions on Power Delivery, Vol 11, No. 3, July 1995.

F. Corcoles, L. Sainz, J. Pedra, J. Sancez-Navarro, M. Salichs, “Three-phase transformer modelling for unlanbaced conditions, Part I: core modeling and introductory examples”. IET Electric Power Applications, 2008, Vol. 2, No. 2, pp. 99-112.

J. Elovaara, L. Haarla, “Sähköverkot I”, Gaudeamus Helsinki University Press, Tallinna, 2011, ISBN: 978-951-672-360-3.

Baktash, A. Vahedi, “Modeling of tape wound cores using reluctance networks for distribution transformers”, International Power System Conference 27-29 October 2014, Tehran.

Gabriel Kron (1939), "Tensor Analysis of Networks", John Wiley & Sons, New York, 1939; Chapman & Hall, London, 1939, 635 pages. 2nd Edition with a new introduction: MacDonald, London, 1965.

K. Umetani, J. Imaoka, M. Yamamoto, S. Arimura, and T. Hirano, “Evaluation of the Lagrangian method for deriving equivalent circuits of integrated magnetic components: a case study using the integrated winding coupled inductor,” IEEE Trans. Ind. Appl., vol. 51, no. 1, pp. 547-555, Jan. 2015.

S. D. Mitchell and J. S. Welsh, "Modeling Power Transformers to Support the Interpretation of Frequency-Response Analysis," in IEEE Transactions on Power Delivery, vol. 26, no. 4, pp. 2705-2717, Oct. 2011.

S. Sarma, J. Glover, T. Overbye, “Power System Analysis and Design”, Cengage Learning, 2012,Fifth Edition, ISBN-10: 1111425779.

Micro_Cap 11, Electronic Circuit Analysis Program User’s Guide, Spectrum Software, Version 11, 2014 Spectrum Software.

ATPDRAW, version 5.6, for Windows 9x/NT/2000/XP/Vista, User’s manual, 2009.


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