The Effect of GIBBS Factor on Transient Analysis in Underground Power Cables

Year 2019, Volume: 23 Issue: 5, 934 - 941, 01.10.2019

Yılmaz Uyaroglu , Selcuk Emiroglu

https://doi.org/10.16984/saufenbilder.529265

Abstract

In this
work, the transient over – voltage phenomena occurred at 34.5 kV AC underground
cable transmission systems during the closure of the underground cables is to
be studied and simulated by using MATLAB program. Then, the transient voltage
occurred at the underground cables is analyzed by using modified Fourier
transform. The studied systems of underground cables are firstly modeled in
frequency domain. Transient voltages induced at the sending-end and receiving-end
terminals of an underground cable of transmission system are calculated in
frequency domain and using inverse Fourier Transform, the sending end and receiving
end voltages are obtained by converting to time domain. The effects of cable
length and source impedance on transient over – voltage phenomena at
underground cables are investigated. Also, the effects of GIBBS factor in
transients are researched in order to eliminate GIBBS oscillations. Numerical
simulations are presented to demonstrate the transient voltages induced at the
terminals of sending-end and receiving-end of an underground cable at
transmission system and the effects of GIBBS factor.

Keywords

Transient analysis, underground cables, Fourier transforms, GIBBS oscillation

References

• Y. Uyaroğlu, Switching Transients Analysis in Underground Power Cables. M.Sc. Thesis, Sakarya University, 1997.(in Turkish)
• L. M. Wedepohl and C. S. Indulkar, “Switching Overvoltages in Long Crossbonded Cable Systems Using the Fourier Transform,” IEEE Transactions on Power Apparatus and Systems, pp. 1476- 1480, July/August 1979.
• Ana Isabel Brito, V. Maló Machado, M.E. Almeida, M. Guerreiro das Neves, “Skin and proximity effects in the series-impedance of three-phase underground cables,” Electric Power Systems Research,130,132-138, 2016.
• W. D. Humpage, K. P. Wong, T. T. Nguyen, and D. Sutanto, “Z-transform electromagnetic transient analysis in power systems,” Proc. Inst. Elec. Eng., C, Gen. Trans. Dist., vol. 127, pp. 370-378, Nov. 1980.
• W. D. Humpage, K. P. Wong, T. T. Nguyen, “Z-transform electromagnetic transient analysis in crossbonded cable transmission systems,” Proc. Inst Elec. Eng, C, Gen. Trans. Dist., vol. 128, pp. 55-62, 1981.
• T. Noda, A. Ramirez, “Z-transform based methods for electromagnetic transient simulations, ” IEEE Trans.on Delivery, vol. 22, no. 3, July 2007.
• I. Kocar, J. Mahseredjian, G. Olivier, “Weighting Method for Transient Analysis of Underground Cables,” IEEE Transactions on Power Delivery, vol. 23, no. 3, July 2008.
• B.A. Suleimanov, O.A. Dyshin, “Application of discrete wavelet transform to the solution of boundary value problems for quasi-linear parabolic equations,” Applied Mathematics and Computation 219 7036–7047, 2013.
• Heng-Xu Ha, Yu-Zhen Tan, Bo Chen, and Z. Q. Bo, “A Novel Electro-magnetic Transient Analysis Method Based on Orthogonal Projection Approach,” Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 18 -21, 2009.
• A. Semlyen and Mansour H. Abdel-Rahman, “A State Variable Approach for the Calculation of Switching Transients on a Power Transmission Line,” IEEE Trans. on Circuits and Systems, vol. cas. 29, no. 9, pp. 624-633, September 1982.
• L.M. Wedepohl , S.E.T. Mohamed, “Multiconductor Transmission Lines, Theory of Natural Modes and Fourier Integral Applied to Transient Analysis,” Proc.IEE ,Vol. 116., No 9., September 1969.
• L.M. Wedepohl , C.S. Indulkar, “Switching Overvoltages in Long Crossbonded Cable Systems Using the Fourier Transform,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-98, No 4 July/August, 1974.
• C. Lanczos, “Applied Analysis”, Prentice-Hall 539 pp., 1956.
• Ali Abdi, Seyed Mohammad Hosseini, “An investigation of resolution of 2-variate Gibbs phenomenon, ” Applied Mathematics and Computation 203, 714–732,2008.
• E. Berriochoa, A. Cachafeiro, J. Díaz, “Gibbs phenomenon in the Hermite interpolation on the circle,” Applied Mathematics and Computation, 253, 274-286, 2015.
• U. Ünver, “Transient Analysis of Cable Systems Including the effect of Nonlineer Protective Devices,” PhD. Thesis, University of Manchester Institute of Science and Technology, 1979.