An Alternative Three-phase Transmission Lines Model in Phase Domain

C. G. Carvalho, S. Kurokawa, J. Pissolato

Universidade Estadual de Campinas (Unicamp), Electrical Engineering Department, Campinas, Brazil.
Universidade Estadual Paulista (Unesp), Electrical Engineering Department, Ilha Solteira, Brazil.

DOI: 10.4236/epe.2013.54B282                

Abstract

The objective of this paper is to show an alternative model of a non-transposed three-phase transmission line with a vertical symmetry plane in phase domain. Due the line physical characteristics, it can be represented by a system consisting of a single?phase and a two-phase line. In this system, the equations describing the behavior of the values in single-phase line terminals are known, while the equations for two-phase line to be obtained. Using a transformation matrix written explicitly according to three-phase line parameters, it is possible to obtain the currents and voltages in phase domain of two-phase line. Then, modal values of three-phase line are converted into phase domain and thus obtain the analytical model for this line. To verify the performance of this model, it was used to simulate the energization of a 440 kV three-phase line and the results were compared to results obtained using a classical model.

Keywords

Transmission Lines; Frequency Dependence; Modal Representation; Transformation Matrix; Newton-Raphson; Phase Domain

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. B. Fernandes and W. L. A. Neves, “Phase-domain Transmission Line Models Considering Frequency Dependent Transformation Matrices,” IEEE Transactions on Power Delivery, Vol. 19, No. 2, 2004, pp. 708-714. doi:10.1109/TPWRD.2003.822536
[2]	L. M. Wedephol, H. V. Nguyen and G. D. Irwin, “Frequency-Dependent Transformation Matrices for Untransposed Transmission Lines Using Newton-Raphson Method,” IEEE Transactions on Power Systems, Vol. 11, No. 3, 1996, pp. 1538-1546. doi:10.1109/59.535695
[3]	A. Budner, “Introduction of Frequency-Dependent Line Parameters into an Electromagnetic Transients Program,” IEEE Transactions on Power Apparatus and Systems, Vol. 89, No. 1, 1970, pp. 88-97. doi:10.1109/TPAS.1970.292674
[4]	L. Marti, “Low-order Approximation of Transmission line Parameters for Frequency Dependent Models,” IEEE Trans. Power App. and Systems, Vol. PAS-102, No. 11, 1983, pp. 3582 - 3589. doi:10.1109/TPAS.1983.317705
[5]	Chipman and A. Robert, “Teoria e Problemas de Linhas de Transmissio,” Ed. McGraw-Hill from Brazil, S?o Paulo, 1972.
[6]	S. Kurokawa, R. S. Daltin, A. J. Prado and J. Pissolato, “An Alternative Modal Representation of a Symmetrical Non-transposed Three-Phase Transmission Line,” IEEE Transactions on Power Systems, Vol. 22, No. 1, 2007, pp. 500-501. doi:10.1109/TPWRS.2006.889117
[7]	M. C. Tavares, J. Pissolato and C. M. Portela, “Mode Domain Multiphase Transmission Line Model – Use in Transient Studies,” IEEE Transaction on Power Delivery, Vol. 14, No. 4, 1999, pp. 1533-1544. doi:10.1109/61.796251
[8]	B. Gustavsen and A. Senlyen, “Combined Phase and Modal Domain Calculation of Transmission Transients Based on Vector Fitting,” IEEE Transactions on Power Delivery, Vol. 13, No. 2, 1998. doi:10.1109/61.660936
[9]	IEC 60060–1: ‘High-voltage Test Techniques – part 1: General Definitions and Test Requirements,” Ed. 3, 2010.