Representation of Transmission Lines by State-Space Equations Obtained from the Propagation Function and Characteristic Impedance

The objective of this paper is to propose a generic state-space equation representation of transmission lines, based on the π circuit, for the study and analysis of electromagnetic transients in electrical power systems. In this proposal, the line is represented by an equivalent π circuit consisting of discrete circuit elements (resistors, inductors, and capacitors) whose values are obtained from the propagation function and the characteristic impedance of the line. Since it is a model based on discrete circuit elements, the currents and voltages at the terminals of the line can be expressed in the form of state equations, the solutions of which respond directly in the time domain. The model was applied to represent a single-phase transmission line during the energization process and incidence of lightning. The results were compared with the JMarti model, demonstrating that the proposed model was developed appropriately. The advantage of the proposed model is that it is developed directly in the time domain, considering the distributed nature of the line parameters and the frequency effect on these parameters. Another advantage of the model is that it can be easily implemented using any programming language and also in traditional software such as ATP and EMTP.