Calculation of the ampacity of high voltage cables laid in free air

Abstract

due to step function loads for cables laid in uniform environment [7]. A finite element mesh generator for thermal analysis of underground cables has been suggested [8], considering only the heat transfer by conduction. Such a model has also been elaborated for the evaluation of the ampacity of cables laid inside retaining ducts [9]. The finite element model for the evaluation of the ampacity of underground cables, elaborated in reference [10], has taken into account the drying out of soil and the heat transfer by convection from the soil surface. An enhanced version of this model, elaborated in reference [11], incorporating the radiation and solar heating effects. The latter model, for determining the current rating of the bunch of self-supporting insulated 10 kV cables, adequately adapted in reference [12], has been applied in this paper for comparison with analytical approaches. FINITE-ELEMENT MODEL Mathematical modelThe general form of the transient temperature equation for the subspace of cables under consideration, partitioned into a network of finite elements with N nodes, isCALCULATION OF THE AMPACITY OF HIGH VOLTAGE CABLES... 90TEHNIKA -ELEKTROTEHNIKA 67 (2018) 1 [C] is N by N heat capacitance matrix, [K] is N by N heat conductance, natural and forced convection and radiation matrix and [R(t)] is N dimensional heat load vector stemming from the internal heat generation, surface convection, and solar heating. Parameter matrices in (1) are In (1), [J(t)] is N dimensional column vector of temperatures of nodes,Indices c, h, r and s in (2) and (3) refer to conduction, convection, radiation and solar heating, respectively [11]. Index Q refers to the internal heat generation. The Joule losses in phase conductors and metallic sheaths have been taken into account as well as the dielectric losses in the insulating materials. Triangular finite elements have been used in this analysis.The matrices figuring in (1) -(3) have been obtained by transferring the corresponding relationships for elements written for their nodes in local coordinates [11] to entire network numbering scheme. Expressions (2) and (3) The coefficient matrices in equations (1) -(3) for a triangular element, in its local coordinates, are as given in [7, 10, 11, and 13]. They are complemented by relationships for heat load vector from specified surface heating, radiation and solar heating (Appendix A).After discretization for a minor step Dt, (1) converts into a simple recurrent relationship for determining temperature variation in time [13] )] (with g as the integration stability factor. In this analysis g=1 and Dt=2 min have been adopted, assuring a good accuracy for modest calculation time.The expressions for determination of characteristic parameters figuring in (1) Linear approximation of the heat transfer by radiationThe heat flux emitted by the radiation from a body at temperature ϑ equals

Improving surface temperature measurement of the power cable and insulated busbar using the heat insulated layer

“…where T ∞ and T are the ambient temperature and surface temperature, respectively. h is the convection heat transfer coefficient and ε is the emissivity of the surface, usually set to 0.95 for the oversheath (Tanaskovic, 2018). σ=5.67×10 -8 W/m 2 •K 4 is the Stefan-Boltzman constant.…”