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

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.