Thermal analysis of cables in unfilled troughs: Investigation of the IEC standard and a methodical approach for cable rating

A robust algorithm, based on relaxation, is proposed for the implementation of the IEC Standard method for rating cables installed in unfilled troughs. Through hundreds of finite-element simulations, the validity range of the standardized equations is established. Studies are performed by varying the following parameters over a wide range: trough size, ambient air temperature, trough aspect ratio, position of cables, cable operating temperature, and intensity of solar radiation. A physically consistent analog thermal-electric equivalent circuit is proposed for the thermal rating of cables installed in unfilled troughs. In contrast with the standards, the equivalent circuit offers a methodological approach that considers all heat-transfer phenomena involved in cables in troughs, for example, the conduction of heat through the cable layers, the heat convection and radiation inside the trough, the conduction in the trough itself and soil, the convection to the surface air, and the solar radiation. Extensive finite-element verification in steady state and transients demonstrates the accuracy of the proposed equivalent circuit.