Mathematical Modeling of Transient Heating Processes in the System of Three Single-Pole Cables

In this paper, we calculate a mathematical model of the transition process of forming the temperature field of a cable line with insulation from cross-linked polyethylene at various currents close to the maximum allowed. The model of underground cable laying with a triangle in standard climatic conditions is considered. When the current is applied, the temperature difference between the medium and the cable is a solution to the ordinary linear differential equation, which implies that the thermal balance of the system occurs 30 min after the start of operation. The model of formation of the thermal field of a cable using an equivalent screen shows proportionally close heating of the core and the screen. The temperature change of all cable elements describes a two-dimensional parabolic type equation with zero Neumann boundary conditions. The simulation is done in PDETool Matlab. Empirically, the heating time of the cable core to temperatures of 27, 40, 50 degrees was determined. Numerical modeling takes into account the change in the thermophysical parameters of the cable with increasing temperature. For this, the simulation time is divided into three iterations with updating of the initial conditions and parameters of the equation. The proposed model makes it possible to evaluate the limiting currents of the cable load, possible changes in the materials used, laying methods, and determine the interdependence of the model parameters. Thermal analysis is used to solve operational problems, such as determining the values of the cross-sectional area of the cable and screen, methods of connecting and grounding the shielding shells.