Analytical solution of conductor tensile force in asymmetrical spans used in overhead power lines and substations with influence of tension insulators

Introduction. Designing electrical substations involves analyzing the horizontal tensile force in flexible tension conductors under varying temperatures. These temperature changes affect the conductor’s length and forces. Problem. Existing methods for calculating horizontal tensile force in conductors often focus on symmetric spans or require complex finite element modeling (FEM), which is impractical for routine substation design. Asymmetric spans with tension insulators present a more complex challenge that current solutions do not adequately address. Purpose. Universal analytical solution and algorithm for calculating the horizontal tensile forces in conductors in asymmetric spans with tension insulators used in power substations or short overhead power line spans. The solution is designed to be easily implementable in software without requiring complex tools or extensive FEM. Methodology. The methodology involves deriving an analytical solution based on the catenary curve formed by the conductor between attachment points at different heights. The analysis includes calculating the conductor’s length for a given tensile force and using a state change equation to determine forces under new temperature conditions. Validation is performed using FEM calculations. Results. The proposed solution was validated against FEM models with varying height differences (5 m and 15 m) and conductor temperatures (–30 °C, –5 °C, +80 °C). The results showed a minimal error (less than 0.15 %) between the analytical solution and FEM results, demonstrating high accuracy. Originality. This paper presents a novel analytical solution to the problem of calculating tensile forces in asymmetric spans with tension insulators. Unlike existing methods, our solution is straightforward and easily implementable in any programming language. Practical value. The solution is practical for routine design tasks in electrical substations or short overhead power lines. Especially in power substations, accurate tensile forces are needed not only for mechanical design and sag calculations but also for calculating the dynamic effects of short-circuit currents. References 23, tables 4, figures 3.