A Phase Domain Transmission Line Model Taking into Account the Algebraic Representation of its Eigenvectors

Abstract

An alternative phase domain representation for transmission lines using ABCD matrices is presented. The proposed representation requests analytical calculation of the [Z][Y] product eigenvalues, where [Z] and[Y] are, respectively, the longitudinal impedance and the transversal admittance matrices of the line. The main idea is to apply the modal domain representation to obtain a direct phase domain model. For this, the analytical development of the conversion phase-mode-phase for the line currents and voltages are done. This way, the phase voltages and currents written as functions of the line longitudinal and transversal parameters are obtained, and these equations can be written as an ABCD matrix. To validate the proposed model, it was applied to represent a typical three-phase line over the entire frequency range during transient conditions. For this, the model was used to simulate the energization by a three-phase sinusoidal generator and lightning striking a phase of the line. The results obtained were compared with those obtained from a classic model developed in the modal domain, and both models are in agreement.

Keywords:

• transmission line model
• ABCD matrix
• phase domain
• modal domain

Additional information

Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001.

Notes on contributors

Newton Vieira de Souza

Newton Vieira de Souza Junior Degree in Mathematics (2007). Master in Electrical Engineering from the Universidade Estadual Paulista (UNESP). PhD in Electrical Engineering from the Universidade Estadual Paulista (UNESP), Ilha Solteira, Sâo Paulo, Brazil. His research focus in the área of electromagnetic transientes.

Carolina Goulart de Carvalho

Carolina Goulart de Carvalho Degree in Mathematics (2007). Master in Electrical Engineering from the Universidade Estadual Paulista (UNESP). PhD student in Electrical Engineering from the Universidade Estadual Paulista (UNESP), Ilha Solteira, Sâo Paulo, Brazil. His research focus in the area of electromagnetic transientes.

Sérgio Kurokawa

Sérgio Kurokawa Degree in Electrical Engineering (1990). Since 1994 serves as Teacher in the Faculty of Engineering of Ilha Solteira – Universidade Estadual Paulista (UNESP). PhD in Electrical Engineering at the Faculty of Electrical Engineering and Computer Science at University of Campinas (UNICAMP). His main areas of interest are transients electromagnetic in power systems and transmission lines models for electromagnetic transient simulations in power systems.