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Mathematical Problems in Engineering
Volume 2013, Article ID 215647, 10 pages
Research Article

Simulations of Transformer Inrush Current by Using BDF-Based Numerical Methods

1Faculty of Electrical Engineering, Tuzla University, 75000 Tuzla, Bosnia and Herzegovina
2Faculty of Electrical Engineering and Computing, Zagreb University, 11000 Zagreb, Croatia
3Faculty of Electrical Engineering and Computer Science, Maribor University, 2000 Maribor, Slovenia

Received 7 April 2013; Revised 8 July 2013; Accepted 9 July 2013

Academic Editor: Evangelos J. Sapountzakis

Copyright © 2013 Amir Tokić et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper describes three different ways of transformer modeling for inrush current simulations. The developed transformer models are not dependent on an integration step, thus they can be incorporated in a state-space form of stiff differential equation systems. The eigenvalue propagations during simulation time cause very stiff equation systems. The state-space equation systems are solved by using A- and L-stable numerical differentiation formulas (NDF2) method. This method suppresses spurious numerical oscillations in the transient simulations. The comparisons between measured and simulated inrush and steady-state transformer currents are done for all three of the proposed models. The realized nonlinear inductor, nonlinear resistor, and hysteresis model can be incorporated in the EMTP-type programs by using a combination of existing trapezoidal and proposed NDF2 methods.