Features Of Boundary Condition Formation For The Long Transmission Line Equation Using Equivalent Circuit Approaches

Abstract

This paper presents a comparative analysis of the application of Γ- and Π-type equivalent circuits for modeling boundary conditions to the long transmis- sion line equation with distributed parameters. The main objective is to assess how the choice of substi- tution scheme for the first and last discrete segments of the line affects the accuracy of transient process sim- ulation and the symmetry of voltage and current dis- tribution along the line. Mathematical models of an intersystem overhead AC transmission line in a single- phase representation were developed, the wave equation was discretized using the method of lines, and the simu- lations were implemented in the Fortran programming environment. Two numerical experiments were con- ducted: the first using a direct Γ-type equivalent cir- cuit, and the second using a symmetric Π-type equiv- alent circuit. In each experiment, the line was ener- gized alternately from both ends, enabling the evalua- tion of model symmetry. The simulation results show that the Π-type scheme ensures complete symmetry of the electromagnetic quantities regardless of the direc- tion of power flow, in contrast to the Γ-type scheme, which introduces minor asymmetry. The obtained find- ings justify the choice of equivalent circuit depending on the required model accuracy and complexity, and may be useful in the development of modern methods for analyzing non-stationary regimes in high-voltage trans- mission networks.