An alternative procedure to decrease the dimension of the frequency dependent modal transformation matrices: Application in three-phase transmission lines with a vertical symmetry plane

The objective of this paper is to show an alternative representation in time domain of a non-transposed three-phase transmission line decomposed in its exact modes by using two transformation matrices. The first matrix is Clarke's matrix that is real, frequency independent, easily represented in computational transient programs (EMTP) and separates the line into Quasi-modes α, β and zero. After that, Quasi-modes α and zero are decomposed into their exact modes by using a modal transformation matrix whose elements can be synthesized in time domain through standard curve-fitting techniques. The main advantage of this alternative representation is to reduce the processing time because a frequency dependent modal transformation matrix of a three-phase line has nine elements to be represented in time domain while a modal transformation matrix of a two-phase line has only four elements. This paper shows modal decomposition process and eigenvectors of a non-transposed three-phase line with a vertical symmetry plane whose nominal voltage is 440 kV and line length is 500 km. © 2006 IEEE.

Keywords

Electromagnetic transients analysis, frequency domain analysis, time domain analysis, transmission line matrix methods, Alternative procedures, Clarke's matrix, Electro-magnetic transient, Frequency dependent, Frequency domains, Frequency independent, matrix, Modal decomposition, Modal transformation, Nominal voltage, Processing Time, Symmetry planes, Three-phase lines, Time domain, Transformation matrices, Transmission line, Curve fitting, Electric lines, Frequency domain analysis, Linear transformations, Modal analysis, Transient analysis, Transmission line theory, Time domain analysis