Simulations of electromagnetic transients in transmission lines can be carried out using simple circuit model. In the case of applications of simple circuit models based on π circuits, there are problems mainly caused by numeric oscillations. The lumped-parameter π equivalent model can be used with some advantages. The numeric integration method applied to the simulations of electromagnetic transients is the trapezoidal rule. If this numeric method is associated to the π equivalent model, results obtained from the simulations are distorted by Gibbs' oscillations or numeric ones. The introduction of damping resistance parallel to the series RL branch of the π equivalent model can mitigate Gibbs' oscillations in obtained results. Voltage peaks caused by these oscillations can also be decreased. So, in this paper, the combined influences of the introduction of damping resistance, the number of π circuits and the time step are investigated searching for minimizing Gibbs' oscillations and the voltage peaks in electromagnetic transient simulations. For this, transient simulations are exhaustively carried out for determining the highest voltage peaks, ranges of damping resistances and other parameters of the model, which minimize these voltage peaks caused by Gibbs' oscillations.
2. Macıas, J. A. R., A. G. Exposito, and A. B. Soler, "Correction to “A comparison of techniques for state-space transient analysis of transmission lines"," IEEE Trans. on Power Delivery, Vol. 20, No. 3, 2358, July 2005.
3. Nelms, R. M., G. B. Sheble, S. R. Newton, and L. L. Grigsby, "Using a personal computer to teach power system transients," IEEE Trans. on Power Systems, Vol. 4, No. 3, 1293-1294, August 1989.
4. Mamis, M. S., "Computation of electromagnetic transients on transmission lines with nonlinear components," IEE Proc. Generation, Transmission and DistributioN, Vol. 150, No. 2, 200-204, March 2003.
5. Mamis, M. S. and M. Koksal, "Solution of eigenproblems for state-space transient analysis of transmission lines," Electric Power Systems Research, Vol. 55, No. 1, 7-14, July 2000.
6. Dommel, H. W., Electromagnetic Transients Program — Rule Book, Oregon, 1984.
7. Prado, A. J., L. S. Lessa, R. C. Monzani, L. F. Bovolato, and J. Pissolato Filho, "Modified routine for decreasing numeric oscillations at associations of lumped elements," Electric Power Systems Research, Vol. 112, No. 1, 56-64, July 2014.
8. Brandao Faria, J. A. and J. Briceno Mendez, "Modal analysis of untransposed bilateral three-phase lines — A perturbation approach," IEEE Trans. on Power Delivery, Vol. 12, No. 1, January 1997.
9. Brandao Faria, J. A. and J. Briceno Mendez, "On the modal analysis of asymmetrical threephase transmission lines using standard transformation matrices," IEEE Trans. on Power Delivery, Vol. 12, No. 4, October 1997.
10. Morched, A., B. Gustavsen, and M. Tartibi, "A universal model for accurate calculation of electromagnetic transients on overhead lines and underground cables," IEEE Trans. on Power Delivery, Vol. 14, No. 3, 1032-1038, July 1999.
11. Gustavsen, B. and A. Semlyen, "Combined phase and modal domain calculation of transmission line transients based on vector fitting," IEEE Trans. on Power Delivery, Vol. 13, No. 2, April 1998.
12. Chrysochos, I., G. P.Tsolaridis, T. A. Papadopoulos, and G. K. Papagiannis, "Damping of oscillations related to lumped-parameter transmission line modeling," Conf. on Power Systems Transients (IPST 2015), 7, 2015.
13. Galvao, R. K. H., S. Hadjiloucas, K. H. Kienitz, H. M. Paiva, and R. J. M. Afonso, "Fractional order modeling of large three-dimensional RC networks," IEEE Trans. Circuits and Systems – I: Regular Papers, Vol. 60, No. 3, 624-637, March 2013.
14. Gustavsen, B., "Avoiding numerical instabilities in the universal line model by a two-segment interpolation scheme," IEEE Trans. Power Delivery, Vol. 28, No. 3, July 2013.
15. Moreno, P. and A. Ramirez, "Implementation of the numerical Laplace transform: A review," IEEE Trans. on Power Delivery, Vol. 23, No. 4, October 2008.
16., Microtran Power System Analysis Corporation, Transients Analysis Program Reference Manual, Vancouver, Canada, 1992.
17. Brandao Faria, J. A., "Overhead Three-phase Transmission Lines – Non-diagonalizable situations," IEEE Transactions on Power Delivery, Vol. 3, No. 4, October 1988.
18. Clarke, E., Circuit Analysis of AC Power Systems, Vol. I, Wiley, New York, 1950.
19. Wedepohl, L. M., H. V. Nguyen, and G. D. Irwin, "Frequency-dependent transformation matrices for untransposed transmission lines using Newton-Raphson method," IEEE Trans. on Power Systems, Vol. 11, No. 3, 1538-1546, August 1996.
20. Nguyen, T. T. and H. Y. Chan, "Evaluation of modal transformation matrices for overhead transmission lines and underground cables by optimization method," IEEE Trans. on Power Delivery, Vol. 17, No. 1, January 2002.
21. Nobre, M., W. C. Boaventura, and W. L. A. Neves, "Phase-domain network equivalents for electromagnetic transient studies," The 2005 IEEE Power Engineering Society General Meeting, CD-ROM, San Francisco, USA, June 12–16, 2005.
22. Budner, A., "Introduction of frequency dependent transmission line parameters into an electromagnetic transients program," IEEE Trans. on Power Apparatus and Systems, Vol. 89, 88-97, January 1970.
23. Carneiro, Jr., S., J. R. Martı, H. W. Domme, and H. M. Barros, "An efficient procedure for the implementation of corona models in electromagnetic transients programs," IEEE Transactions on Power Delivery, Vol. 9, No. 2, April 1994.
24. Martins, T. F. R. D., A. C. S. Lima, S. Carneiro, and Jr., "Effect of impedance approximate formulae on frequency dependence realization," The 2005 IEEE Power Engineering Society General Meeting, CD-ROM, San Francisco, USA, June 12–16, 2005.
25. Marti, J. R., "Accurate modelling of frequency-dependent transmission lines in electromagnetic transients simulations," IEEE Trans. on PAS, Vol. 101, 147-155, January 1982.
26. Wedepohl, L. M., "Application of matrix methods to the solution of travelling-wave phenomena in polyphase systems," Proceedings IEE, Vol. 110, 2200-2212, December 1963.
27. Wedepohl, L. M. and D. J. Wilcox, "Transient analysis of underground power-transmission system — system model and wave propagation characteristics," Proceedings of IEE, Vol. 120, No. 2, 253-260, 1973.
28. Mamis, M. S. and M. E. Meral, "State-space modeling and analysis of fault arcs," Electric Power Systems Research, Vol. 76, No. 1–3, 46-51, September 2005.
29. Prado, A. J., S. Kurokawa, J. Pissolato Filho, L. F. Bovolato, and E. C. M. Costa, Phase-mode Transformation Matrix Application for Transmission Line and Electromagnetic Transient Analyses, Nova Science Publisher, Inc., Hauppauge, NY, 2011.
30. Andrade, P. R., R. C. Monzani, L. S. Lessa, T. Ingelbinck, A. J. Prado, J. Pissolato Filho, and L. F. Bovolato, "Physical model for representing transmission lines by undergraduate students," The 10th Latin-American Congress on Electricity Generation and Transmission — CLAGTEE 2013, CD-ROM, 5, Vina del Mar, Chile, 6–9 de outubro de 2013.
31. Gustavsen, B. and A. Semlyen, "Rational approximation of frequency domain responses by vector fitting," IEEE Trans. on Power Delivery, Vol. 14, No. 3, July 1999.