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### Mathematical model of XLPE insulated cable power line with underground installation DOI:10.15199/48.2019.06.14

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Underground medium-voltage cable lines are used for distribution and transmission of electric energy. Single-core cables with cross-linked polyethylene insulation are widely used. Power consumption due to urban and industrial park development increases. Therefore, the issue of analyzing the capacity of cable lines becomes urgent. The capacity of electric power lines depends on the conductor temperature [1-4]. The temperature is significantly affected by the process of cable heat dissipation into the environment. Specific nature of thermal processes plays an important role in assessing the rational use of cable systems [5-7]. Various aspects in the research of power cables with allowance for thermal processes are presented in [8-17]. A popular approach is to determine the temperature of cable elements using the numerical method of the finite elements. However, significant computational resources that are required, the complexity of the initial data preparation, and analysis of the calculation results in some cases limit the application of this approach. Below it is proposed to determine the temperature of the cable based on the thermal equivalent circuit. The ambient temperature and losses in the cable elements, being taken into account, are considered to be the advantages of this model, as well as the ability to determine the effect of adjoining cables on the processes. Mathematical model of cable power line with crosslinked polyethylene insulation The mathematical model of the cable line with crosslinked polyethylene insulation is formed for the cable crosssection shown in Fig. 1, where r0 - rn are outer radii of cable layers, Θi is the temperature of the medial line of the i-th cable layer, that is the temperature of the i-th layer on the radius rmedi=ri+0.5·(ri+1 - ri), С. For a computational model of the single-core cable, each layer (Fig.2) of the cable cross-section (r1-rn) is represented as [...]

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