Cell model of transient heat processes in underground electric cable and surrounding ground

Abstract

One of the most essential consequences of short circuits in underground cable networks of 6–10 kV is heating up the insulation with its possible inflammation and damage of adjacent objects of an electrical supply system that enlarge the concomitant damage many times as much. Various methods (including the methods, which are based on reference documents) to calculate the thermal state of underground cables are known. Despite the part of them are of extra complexity and require a lot of poorly identified parameters, the issue of the accuracy of forecasting calculations remains open. Hence, the issue of development of new approaches to model transient thermal processes in a cable, combining the simplicity, small computational time, and the reasonable accuracy of forecasting the process thermal parameters is an important one. The method of mathematical modeling is used to solve the problem. The model uses the mathematical tools of the Markov chains theory. It is adapted to the representation of ground as multilayer medium, and the non-stationary heat source may be placed in one of the layers. The heat transfer deep down into the ground is described by heat conduction, and the heat exchange with neighboring ground and environment is described by heat emission. The study of influence of the process parameters on the heat process behavior is carried out by numerical methods. The experimental validation of the model is not planned at the current stage of this investigation. The developed mathematical model allows predicting temperature in a cable and in surrounding ground depending on the heat capacity and depth of layout of the heat source, determined by the value of current in the cable. The results of numerical experiments come to agreement with the physical essence of the process. The obtained results have the scientific novelty as they are based on the universal algorithm of modeling and allow describing the transient processes in the object under consideration. The authors have proposed a mathematical tool to estimate the heat state of an underground electric cable depending on the heat capacity of the current, its depth of location in the ground and the thermo-physical properties of the ground. The model is simple to operate and takes exceedingly small computational time. It can be easily used in engineering practice.