COMPARATIVE ANALYSIS OF EQUIVALENT CIRCUIT MODELS FOR BOUNDARY CONDITION IDENTIFICATION IN THE WAVE EQUATION OF A LONG TRANSMISSION LINE
DOI:
https://doi.org/10.32718/agroengineering2025.29.94-104Keywords:
equivalent circuit, long transmission line, boundary conditions, Γ-equivalent circuit, T-equivalent circuit, π-equivalent circuit, identificationAbstract
This paper proposes a methodology for identifying boundary conditions for the wave equation of a long transmission line, based on the use of equivalent circuits for the terminal discrete sections of the line. The main focus is made to the comparative analysis of three types of substitution schemes – Γ-, T-, and π-equivalent circuits – in order to investigate how their topology and symmetry affect the accuracy of numerical modeling of transient electromagnetic processes in lines with distributed parameters. The mathematical model is built upon the wave (telegraph) equation with second-order partial derivatives, which describes the dynamics of voltage and current along the line. Neumann and Robin–Poincaré boundary conditions are shaped analytically by incorporating the parameters of the equivalent circuits. Particular attention is given to the asymmetry arising from the use of the Γ-scheme. It is demonstrated that this scheme disrupts wave superposition, resulting in outcomes that vary depending on the direction of line energization. In contrast, the T- and π-schemes ensure symmetric loading of the model, leading to stable computational outcomes. Numerical experiments carried out in Intel Visual Fortran Compiler confirm the presence of systematic errors in the Γ-scheme and the accuracy of the T- and π-schemes. The scientific novelty lies in the first-time proposal of a boundary condition identification approach for the wave equation based on equivalent curcuit with symmetry evaluation and accuracy analysis. The proposed methodology is universal and can be applied to the modelling of high-voltage transmission lines operating under both direct and alternating current, which enhances its scientific and engineering value. The presented approach makes it possible to improve the performance of existing electromagnetic simulation tools by ensuring higher computational stability and consistent boundary-condition formulation under complex operating regimes.
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