Correlation between Load Current and Temperature for a Power Cable Installed in a Vertical PVC Pipe

The heating of an ethylene-propylene rubber (EPR) insulated cable installed in a vertical polyvinyl chloride (PVC) pipe is analysed in this paper. In particular, this paper considers the heating of an EPR cable used to energize a submersible water pump and analyses the upper part of the well where the space between the EPR cable and the inner surface of the PVC pipe is filled with air. The temperatures of the cable’s surface are determined analytically, and then such temperature values are validated numerically by using the finite element method (FEM) in COMSOL. In addition to these calculations, experiments are performed on a physical model representing the part of the well between the static water level and the solid concrete cover of the well. The percentage deviation of the calculated values for the cable’s surface temperature from the measured ones at different load currents ranges from 1.47% to 4.63%. After the experimental validation of the calculated values for the cable’s surface temperature, an analytic expression (i.e. correlation) that defines the dependence of that temperature on the load current and the pipe’s inner surface temperature is derived. Finally, an analytic expression for the cable load current as a function of the cable’s surface temperature and the pipe’s inner surface temperature is also derived, which can be further used to determine the ampacity of any power cable for known service conditions.