Ladder-Type Soil Model for Dynamic Thermal Rating of Underground Power Cables

Abstract

This paper presents an optimal RC ladder-type equivalent circuit for the representation of the soil for dynamic thermal rating of underground cable installations. This is useful and necessary for their optimal and accurate real-time operation. The model stems from a nonuniform discretization of the soil into layers. The resistive and capacitive circuit elements are computed from the dimensions and physical parameters of the layers. The model is perfectly compatible with the International Electrotechnical Commission thermal-electric analog circuits for cables. The optimum model order is determined, for fast and slow thermal transients, from a comprehensive parametric study. It is shown that an exponential distribution of the soil layers leads to accurate results with differences of less than 0.5 • C with respect to transient finiteelement simulations. An optimal model with only five layers that delivers accurate results for all practical installations and for all time scenarios is presented. The model of this paper is a simple-to-use and accurate tool to design and analyze transient operation of underground cables. It represents a relevant improvement to the available operation and monitoring tools. For illustration purposes, a step-by-step model construction example is given. The model has been validated against numerous dynamic finite-element simulations.INDEX TERMS Ampacity, cable thermal rating, dynamic ratings, soil modeling, transient ratings, underground cable installations. NOMENCLATURE

Introducing Mutual Heating Effects in the Ladder-Type Soil Model for the Dynamic Thermal Rating of Underground Cables

“…A model that reproduces accurately (1) for one cable has been reported in [20], [21] and was optimized in [22]. Essentially, these models suggest that when only one cable is under analysis, the surrounding soil can be modeled with a RC electro-thermal equivalent ladder model; see Fig.…”

“…As it is explained in [21] and [22], the values of (thermal capacitances) are calculated also taking into account the geometry of each soil layer that is used to calculate (see Appendix for further details). The model can be enhanced if the same framework is used to consider the effects of mutual heating from the neighboring cables.…”

“…A similar rationale allows the reuse of the model defined in [22] (copied here in Fig. 1(a) for completeness), to include the mutual heating effects of all neighboring cables in a single RC ladder-type model for transient simulations of the cable under study (p).…”

“…The model extends the RC circuit model representing the soil proposed in [20], [21] and optimized in [22] to include mutual heating. Therefore, the proposed model is perfectly consistent with the modeling techniques for the cable used in the IEC standards themselves.…”

“…The new model is tested and validated against numerous finite elements simulations for realistic cable installations. The characteristics of this model have been presented in [22], but it is succinctly described in the Appendix of this paper for the sake of completeness.…”