Steady-state thermal analysis of power cable systems in ducts using streamline-upwind/petrov-galerkin finite element method

In this paper, numerical steady-state thermal analysis and ampacity evaluation of underground power cable systems placed in PVC ducts are presented. Between the outer surface of the cable and inner surface of the duct, there are three heat transfer modes, thermal conduction, thermal natural convection and thermal radiation. A Streamline-upwind/Petrov-Galerkin (SUPG) stabilized finite element method is proposed to solve the air governing formulas including the mass conservation equation, the momentum conservation equation and the energy conservation equation in the region between the cables and the containment ducts. During the numerical thermal field analysis, the Newton-Raphson iteration method is used to solve the weak electromagnetic-thermal coupling of underground power cable systems. The radiation heat exchange between the outer surface of the cable and inner surface of the duct is solved by the Newton-Raphson iteration method too. An experiment with several holes and three cables was conducted and the test results were compared with the results of analytical method and SUPG finite element method. The comparison reveals that the convection induced heat exchange is much stronger than the conduction induced heat exchange in the air between the outer cable surface and inner duct surface and calculation accuracy of SUPG finite element method is better than the analytical method. Finally, the Newton-Raphson iteration method is used to evaluate the ampacity of power cable systems placed in PVC ducts.