Voltage and Current Mode Vector Analyses of Correction Procedure Application to Clarke’s Matrix—Symmetrical Three-Phase Cases

DOI: 10.4236/jemaa.2010.21002   PDF   HTML   XML   5,394 Downloads   9,415 Views   Citations


Clarke’s matrix has been applied as a phase-mode transformation matrix to three-phase transmission lines substituting the eigenvector matrices. Considering symmetrical untransposed three-phase lines, an actual symmetrical three-phase line on untransposed conditions is associated with Clarke’s matrix for error and frequency scan analyses in this paper. Error analyses are calculated for the eigenvalue diagonal elements obtained from Clarke’s matrix. The eigenvalue off-diagonal elements from the Clarke’s matrix application are compared to the correspondent exact eigenvalues. Based on the characteristic impedance and propagation function values, the frequency scan analyses show that there are great differences between the Clarke’s matrix results and the exact ones, considering frequency values from 10 kHz to 1 MHz. A correction procedure is applied obtaining two new transformation matrices. These matrices lead to good approximated results when compared to the exact ones. With the correction procedure applied to Clarke’s matrix, the relative values of the eigenvalue matrix off-diagonal element obtained from Clarke’s matrix are decreased while the frequency scan results are improved. The steps of correction procedure application are detailed, investigating the influence of each step on the obtained two new phase-mode transformation matrices.

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A. PRADO, S. KUROKAWA, J. FILHO and L. BOVOLATO, "Voltage and Current Mode Vector Analyses of Correction Procedure Application to Clarke’s Matrix—Symmetrical Three-Phase Cases," Journal of Electromagnetic Analysis and Applications, Vol. 2 No. 1, 2010, pp. 7-17. doi: 10.4236/jemaa.2010.21002.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] H. W. Dommel, “Electromagnetic transients program— rule book,” Oregon, 1984.
[2] Microtran Power System Analysis Corporation, Transients Analysis Program Reference Manual, Vancouver, Canada, 1992.
[3] J. A. Brand?o Faria and J. Brice?o Mendez, “Modal analysis of untransposed bilateral three-phase lines—a perturbation approach,” IEEE Transactions on Power Delivery, Vol. 12, No. 1, January 1997.
[4] T. T. Nguyen and H. Y. Chan, “Evaluation of modal transformation matrices for overhead transmission lines and underground cables by optimization method,” IEEE Transactions on Power Delivery, Vol. 17, No. 1, January 2002.
[5] A. Morched, B. Gustavsen, and M. Tartibi, “A universal model for accurate calculation of electromagnetic transients on overhead lines and underground cables,” IEEE Transaction on Power Delivery, Vol. 14, No. 3, pp. 1032– 1038, July 1999.
[6] D. M. Nobre, 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 12th-16th, 2005.
[7] A. Budner, “Introduction of frequency dependent transmission line parameters into an electromagnetic transients program,” IEEE Transaction on Power Apparatus and Systems, Vol. PAS-89, pp. 88–97, January 1970.
[8] S. Carneiro Jr., J. R. Martí, H. W. Domme1, 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.
[9] T. F. R. D. Martins, A. C. S. Lima, and S. Carneiro Jr., “Effect of impedance approximate formulae on frequency dependence realization,” The 2005 IEEE Power Engineering Society General Meeting, CD ROM, San Francisco, USA, June 12th-16th, 2005.
[10] J. R. Marti, “Accurate modelling of frequency-dependent transmission lines in electromagnetic transients simulations,” IEEE Transaction on PAS, Vol. 101, pp. 147–155, January 1982.
[11] E. Clarke, “Circuit analysis of AC power systems,” Vol. I, Wiley, New York, 1950.
[12] L. M. Wedepohl, “Application of matrix methods to the solution of travelling-wave phenomena in polyphase systems”, Proceedings IEE, Vol. 110, pp. 2200–2212, December 1963.
[13] L. M. Wedepohl and D. J. Wilcox, “Transient analysis of underground power-transmission system—system model and wave propagation characteristics,” Proceedings of IEE, Vol. 120, No. 2, pp. 253–260, 1973.
[14] L. M. Wedepohl, H. V. Nguyen, and G. D. Irwin, “Frequency dependent transformation matrices for untransposed transmission lines using Newton-Raphson method”, IEEE Transaction on Power Systems, Vol. 11, No. 3, pp. 1538–1546, August 1996

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