Numerical harmonic modeling of long coupled transmission lines using matrix series theory and recursive approach


Correspondence to: Hua Weng, Department of Electrical Engineering, Zhejiang University, Hangzhou 310027, Zhejiang Province, China.



To improve the efficiency of the harmonic analysis, this paper presents a direct phase-domain harmonic model for long coupled transmission lines, which can take the parameter frequency dependence, the configuration asymmetry, and the untransposition of the line into consideration. The steps of the proposed modeling method are as follows. First, in the direct phase domain and on the basis of the travelling wave equation, the coupled transmission line model was derived in a nodal admittance matrix form. Then the matrix series theory was adopted to realize the numerical calculation of the nodal admittance matrix without relying on the eigenvalue and eigenvector calculations of the propagation matrix. Finally, a recursive approach was proposed to handle the nodal equation of the network containing long transmission lines. Both the accuracy and the efficiency of the proposed approach were verified by comparing with the exact method in which it is necessary to calculate the eigenvalues and eigenvectors of the propagation matrix. The computation time and memory consumption analysis indicates that the proposed approach excels the exact method in saving computation time and memory. It should be emphasized that, by utilizing the recursive approach, the proposed approach is always numerically stable and can also be applied to DC transmission lines. Copyright © 2012 John Wiley & Sons, Ltd.