A Didactic Procedure to Solve the Equation of Steady-Static Response in Suspended Cables

José Agüero-Rubio, Javier López-Martínez, Marta Gómez-Galán and Ángel-Jesús Callejón-Ferre
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José Agüero-Rubio: Department of Electricity, IES Alhamilla of Almería, 04005 Almería, Spain
Javier López-Martínez: Department of Engineering, University of Almería, Research Center CIAIMBITAL (CeiA3), Ctra. Sacramento, s/n, La Cañada, 04120 Almería, Spain
Marta Gómez-Galán: Department of Engineering, University of Almería, Research Center CIAIMBITAL (CeiA3), Ctra. Sacramento, s/n, La Cañada, 04120 Almería, Spain
Ángel-Jesús Callejón-Ferre: Department of Engineering, University of Almería, Research Center CIAIMBITAL (CeiA3), Ctra. Sacramento, s/n, La Cañada, 04120 Almería, Spain

Mathematics, 2020, vol. 8, issue 9, 1-19

Abstract: Students in the electrical branch of the short-cycle tertiary education program acquire developmental and design skills for low voltage transmission power lines. Aerial power line design requires mathematical tools not covered well enough in the curricula. Designing suspension cables requires the use of a Taylor series and integral calculation to obtain the parabola’s arc length. Moreover, it requires iterative procedures, such as the Newton–Raphson method, to solve the third-order equation of the steady-static response. The aim of this work is to solve the steady-static response equation for suspended cables using simple calculation tools. For this purpose, the influence of the horizontal component of the cable tension on its curvature was decoupled from the cable’s self-weight, which was responsible for the tension’s vertical component. To this end, we analyzed the laying and operation of the suspended cables by defining three phases (i.e., stressing, lifting, and operation). The phenomena that occurred in each phase were analyzed, as was their manifestation in the cable model. Herein, we developed and validated the solution of the steady-static response equation in suspended cables using simple equations supported with intuitive graphics. The best results of the proposed calculation procedure were obtained in conditions of large temperature variations.

Keywords: power transmission lines; suspended cables; reduced-order models; problem-based learning; mathematical modeling; high-temperature and low-sag conductors (HTLS conductors) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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