Title :
Robust Calculation of Frequency-Dependent Transmission-Line Transformation Matrices Using the Levenberg–Marquardt Method
Author :
Chrysochos, Andreas I. ; Papadopoulos, Theofilos A. ; Papagiannis, Grigoris K.
Author_Institution :
Dept. of Electr. & Comput. Eng., Aristotle Univ. of Thessaloniki, Thessaloniki, Greece
Abstract :
This paper presents a new method for the calculation of smooth frequency-dependent transmission-line (TL) transformation matrices. The proposed method, based on the Levenberg-Marquardt algorithm, solves an equivalent real-valued approach of the generalized complex eigenproblem. The implemented formulation incorporates a robust convergence criterion and is applicable to all TL configurations, due to the included numerically well-defined computational scheme. Smooth modal transformation matrices are calculated for overhead and underground TL configurations under different representations of the imperfect earth. Results are compared and validated with the corresponding results obtained from the Newton-Raphson and the sequential quadratic programming methods, revealing the accuracy, efficiency, and robustness of the proposed formulation, even in cases where the other methods fail.
Keywords :
Newton-Raphson method; convergence; eigenvalues and eigenfunctions; matrix algebra; modal analysis; power transmission lines; quadratic programming; underground transmission systems; Levenberg-Marquardt algorithm; Levenberg-Marquardt method; Newton-Raphson methods; TL transformation matrices; computational scheme; convergence criterion; eigenproblem; equivalent real-valued approach; frequency-dependent transmission-line transformation matrices; modal transformation matrices; overhead TL configurations; sequential quadratic programming methods; underground TL configurations; Earth; Eigenvalues and eigenfunctions; Equations; Frequency-domain analysis; Mathematical model; Matrix decomposition; Transmission line matrix methods; Eigenproblem; Levenberg–Marquardt; Newton–Raphson; matrix perturbation theory; modal transformation matrices; sequential quadratic programming;
Journal_Title :
Power Delivery, IEEE Transactions on
DOI :
10.1109/TPWRD.2013.2284504