Finite-Element Time-Domain Method for Multiconductor Transmission Lines Based on the Second-Order Wave Equation

Based on the second-order wave equation of voltage, discrete equations for multiconductor transmission lines (MTLs) are derived by using finite-element time-domain (FETD) method and Newmark-Beta formulation. And then, the time-domain method to process lumped elements is also given based on the node admittance method of circuit analysis. Combining all the discrete equations and lumped elements, the global FETD equation is obtained based on the single iteration variable voltage. Finally, by means of the coupled equations between current and voltage, the iteration formulas of current along MTLs are derived. Compared with EMTP program by numerical examples, the proposed method in this paper is proved to be correct and effective. Furthermore, the simulation result demonstrates that the proposed method is better than the existing FETD methods in computation efficiency and convenience for the treatment of complex lumped networks.

[1]  H. L. Cox,et al.  Transient Analysis of Forced Vibrations of Complex Structural-Mechanical Systems , 1962, The Journal of the Royal Aeronautical Society.

[2]  Rino Lucić,et al.  Simulation of electromagnetic transients on single transmission lines via the finite element metod , 1999 .

[3]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[4]  F. Maradei,et al.  An explicit-implicit solution scheme to analyze fast transients by finite elements , 1997 .

[5]  T. Sarkar,et al.  Analysis of Time Response of Lossy Multiconductor Transmission Line Networks , 1987 .

[6]  John C. Houbolt,et al.  A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft , 1950 .

[7]  Jin-Fa Lee,et al.  WETD /spl minus/ a finite element time-domain approach for solving Maxwell's equations , 1994 .

[8]  Jun Zou,et al.  A Hermite Interpolation Model to Accelerate the Calculation of the Horizontal Electric Field of a Lightning Channel Along a Transmission Line , 2013, IEEE Transactions on Electromagnetic Compatibility.

[9]  Lionel Pichon,et al.  A 3D finite element method for the modelling of bounded and unbounded electromagnetic problems in the time domain , 2000 .

[10]  E. Meijering.  A chronology of interpolation: from ancient astronomy to modern signal and image processing , 2002, Proc. IEEE.

[11]  Thierry Blu,et al.  Linear interpolation revitalized , 2004, IEEE Transactions on Image Processing.

[12]  G.E. Bridges,et al.  Finite-difference analysis of dispersive transmission lines within a circuit simulator , 2006, IEEE Transactions on Power Delivery.

[13]  T.K. Sarkar,et al.  Time-domain response of multiconductor transmission lines , 1987, Proceedings of the IEEE.

[14]  Lei Liu,et al.  Simulation of Electromagnetic Transients of the Bus Bar in Substation by the Time-Domain Finite-Element Method , 2009, IEEE Transactions on Electromagnetic Compatibility.

[15]  C. Paul,et al.  Finite-difference, time-domain analysis of lossy transmission lines , 1996 .

[16]  A. Abdipour,et al.  Efficient Method for Time-Domain Analysis of Lossy Nonuniform Multiconductor Transmission Line Driven by a Modulated Signal Using FDTD Technique , 2012, IEEE Transactions on Electromagnetic Compatibility.

[17]  A. Piantini,et al.  Lightning-Induced Voltages on Overhead Lines—Application of the Extended Rusck Model , 2009, IEEE Transactions on Electromagnetic Compatibility.

[18]  A. Konrad,et al.  Lossy transmission line transient analysis by the finite element method , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[19]  U. Navsariwala,et al.  An unconditionally stable finite element time-domain solution of the vector wave equation , 1995 .

[20]  Min Tang,et al.  Finite-Difference Analysis of Interconnects With Frequency-Dependent Parameters Based on Equivalent Circuit Models , 2010, IEEE Transactions on Advanced Packaging.

[21]  C.R. Paul,et al.  A Brief History of Work in Transmission Lines for EMC Applications , 2007, IEEE Transactions on Electromagnetic Compatibility.

[22]  Song-Yop Hahn,et al.  Time domain finite element analysis of high power microwave aperture antennas , 1995 .

[23]  Xiang Cui,et al.  Time-Domain Finite-Element Method for the Transient Response of Multiconductor Transmission Lines Excited by an Electromagnetic Field , 2011, IEEE Transactions on Electromagnetic Compatibility.

[24]  Thomas J. R. Hughes,et al.  Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .

[25]  F. Teixeira,et al.  Differential Forms, Galerkin Duality, and Sparse Inverse Approximations in Finite Element Solutions of Maxwell Equations , 2007, IEEE Transactions on Antennas and Propagation.

[26]  Hendrik Speleers,et al.  Numerical solution of partial differential equations with Powell-Sabin splines , 2006 .