Abstract
Mathematical modeling of non-sinusoidal modes in power transmission lines is key to understanding and evaluating their operation in real conditions. This paper addresses the need to develop a model that takes into account nonlinearities and higher harmonics, which are widely present in modern power transmission networks. Operational data and energy audit results indicate the presence of non-sinusoidal modes, which requires the development of adequate mathematical models for accurate analysis. The study of multi-conductor transmission lines involves the use of mathematical models including telegraphic equations. However, the full adequacy of such a model requires additional consideration of several aspects, including two chain lines, surface effect, presence of lightning protection cables and ground effects on power transmission processes. This paper presents a mathematical model that takes into account the above aspects for multi-conductor transmission lines. The features of two circuit lines, the surface effect in the wires, the presence of lightning protection cables and the influence of the earth on power transmission are taken into account. This model is the result of improving and extending the existing mathematical framework for analyzing multi-conductor power transmission systems, which significantly improves the accuracy and reliability of predictions and calculations in the field of electrical engineering and electric power engineering. Keywords: telegraphic equations, power supply system, power losses, loss reduction, non-sinusoidal modes, Cayley-Hamilton theorem.