Some Considerations About A New Procedure To Derive Transmission Line Parameters Concerning Three-phase Lines

Abstract

The paper shows an alternative methodology to calculate transmission line parameters per unit length and to apply it in a three-phase line with a vertical symmetry plane. This procedure is derived from a general procedure where the modal transformation matrix of the line is required. In this paper, the unknown modal transformation matrix requested by general procedure is substituted by Clarke's matrix. With the substitution that is shown in the paper, the transmission line parameters can be obtained starting from impedances measured in one terminal of the line. First, the article shows the classical methodology to calculate frequency dependent transmission line parameters by using Carson and Pollaczeck's equations for representing the ground effect and Bessel's functions to represent the skin effect. After that, a new procedure is shown to calculate frequency dependent transmission line parameters directly from currents and voltages of an existing line. Then, this procedure is applied in a non-transposed three-phase transmission line whose parameters have been previously calculated by using the classical methodology. Finally, the results obtained by using the new procedure and by using the classical methodology are compared. The article shows simulation results for typical frequency spectra of switching transients (10 Hz to 10 kHz). Results have shown that procedure has © 2006 IEEE.Hofmann, L., Series expansions for line series impedances considering different specific resistances, magnetic permeabilities, and dielectric permittivities of conductors, air, and ground (2003) IEEE Trans. on Power Delivery, 18 (2), pp. 564-570. , AprPortela, C., Tavares, M.C., Modeling, simulation and optimization of transmission lines. Applicability and limitations of some used procedures (2002) IEEE PES Transmission and Distribution, , São Paulo, BrazilSemlyen, A., Some frequency domain aspects of wave propagation on nonuniform lines (2003) IEEE Trans, on Power Delivery, 18 (1), pp. 315-322. , JanS. Kurokawa, J. Pissolato, M. C. Tavares, C. M. Portela and A. J. Prado, A New procedure to derive transmission line parameters: Applications and restrictions, IEEE Trans. on Power Delivery, TPWRD-00566-2004 (article accepted and waiting to be published)Akke, M., Biro, T., Measurements of the frequency-dependent impedance of a thin wire with ground return IEEE Trans, on Power Delivery (Digital object identifier 101109/TPWRD.2004.834320)Marti, J.R., Accurate modeling of frequency-dependent transmission line in electromagnetic transient simulations (1982) IEEE Trans. Power App. and Systems, PAS-101 (NO1), pp. 147-155. , JanDommel, H.W., (1986) EMTP theory book, , VancouverWedephol, L.M., Nguyen, H.V., Irwin, G.D., Frequency-dependent transformation matrices for untransposed transmission lines using Newton-Raphson method (1996) IEEE Trans. Power Systems, 11 (NO3), pp. 1538-1546. , AugBrandão Faria, J.A., Briceno Mendez, J.H., Modal analysis of untransposed bilateral three-phase lines - A perturbation approach (1997) IEEE Trans. Power Delivery, 12 (NO1), pp. 497-504. , JanBudner, A., Introduction of frequency-dependent line parameters into an electromagnetic transients programs (1970) IEEE Trans. Power App. and Systems, PAS-89 (NO1), pp. 88-97. , JanBrandão Faria, J.A., Briceno, J.H., On the modal analysis of asymmetrical three-phase lines using standard transformation matrices (1997) IEEE Trans. Power Delivery, 12 (4), pp. 1760-1765. , OctTavares, M.C., Pissolato, J., Portela, C.M., Quasi-modes multiphase transmission line model (1999) Electric Power Systems Research, (49), pp. 159-167Tavares, M.C., Pissolato, J., Portela, C.M., Mode domain multiphase transmission line model - Use in transient studies (1999) IEEE Trans. Power App. and Systems, 14 (4), pp. 1533-1544. , OctMarti, L., Low-order approximation of transmission line parameters for frequency-dependent models (1983) IEEE Trans. Power App. and Systems, PAS-102 (11), pp. 3582-3589. , No