Solution of Wave Equations on Transmission Lines where Leakage to Ground on the Line is Negligible
American Journal of Applied Mathematics
Volume 3, Issue 3, June 2015, Pages: 124-128
Received: May 3, 2015;
Accepted: May 15, 2015;
Published: May 26, 2015
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Michael Olufemi OKE, Department of Mathematical Sciences, Ekiti State University, Ado, Ekiti, Nigeria
This paper presents the solution of wave equations on transmission lines where leakage to ground on the line is very small. As a result of the leakages to ground on the transmission lines which are negligible, the conductance and the inductance, which are responsible for leakages on the line, are set to zero in the model of the general wave equation of the transmission line. The Laplace transform method was now applied to transform the resulting partial differential equation into ordinary differential equation and the method of variation of parameters was used to get the particular solution to the problem.
Michael Olufemi OKE,
Solution of Wave Equations on Transmission Lines where Leakage to Ground on the Line is Negligible, American Journal of Applied Mathematics.
Vol. 3, No. 3,
2015, pp. 124-128.
Mehta, V.K. and Mehta, R. (2008). Principles of Power Systems, S. Chand and Company Limited, New Delhi.
Wadhwa, C.L. (2009). Electrical Power Systems, New Age International Limited, New Delhi.
Gupta, B. D. (2009). Mathematical Physics, Vikas Publishing House PVT Limited.
Ajayi, E.O. (2009). Fourier and Hankel Transforms for Solving Boundary Value Problems, Deoban International Journal of Mathematical Sciences 11(3): 160 – 174.
Ezekiel, F.D. and Ojo, S.O. (2008). An Integral Transform Method for Solving Boundary Value Problems, Deoma International of Sciences 13(2): 106 – 120.
Dass, H. K. and Verma, R. (2011). Mathematical Physics, S. Chand and Company Limited, New Delhi.
Hayt, W.H. and Buck, J.A. (2006). Engineering Electromagnetics, McGraw-Hill Company Inc.
Oke, M. O. (2012). Mathematical Model for the Determination of Voltage and Current on Lossy Power Transmission Line, IOSR Journal of Mathematics 1( 4): 16 – 18.
Gupta, J.B. (2008). A Course in Power Systems, S.K. Kataria & Sons, New Delhi.
Stroud, K. A. and Dexter, J.B. (2003). Advanced Engineering Mathematics, Palgrave Macmillan Limited, New York.
Bhattacharyya, B. (2009). Mathematical Physics, New Central Book Agency Limited, New Delhi.
Zill, D.G. and Cullen, R. M. (2005). Differential Equations with Boundary-Value Problems, Brooks/Cole, Thomson Learning Inc., Canada.
Riley, K. F., Hobson, M. P. and Bence, S.J. (2002). Mathematical Methods for Physics and Engineering, Cambridge University Press, New York.