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An improved formula for the assessment of the external thermal resistance of three buried single-core, metal-sheathed, touching cables, laid in a flat formation, is proposed. The formula arises from the analysis based on a coupled electric-thermal model, as well as on the stochastic optimization method based on differential evolution. The effect of the new formula on cable rating is illustrated in a numerical example. Index Terms--External thermal resistance, numerical modeling, optimization methods, underground cables.

An original nonlinear-coupled electric-thermal model of underground cables with the solid sheaths is proposed. The model deals with the numerical evaluation of losses, heating, and ampacity. The computation of the current dependent losses is undertaken by means of the filament method, where conductors and sheaths are represented by a number of smaller subconductors or filaments. Furthermore, heat-transfer phenomena through an 'infinite' domain beneath the soil surface are modeled combining the finite and the mapped infinite elements, respectively. The corresponding finite-element meshes are generated by the advancing front method. The numerical results presented throughout this work suggest that the International Electrotechnical Commission relation concerning the external thermal resistance for touching cables, placed in flat formation, having appreciable sheath losses, should be re-examined. Index Terms--Ampacity, numerical modeling, underground cables.