An algorithm for steady-state thermal analysis of electrical cables with radiation by reduced Newton-Raphson techniques

Thermal analysis of electrical cables and cable systems is a topic that has received considerable attention by many researchers. In typical analyses, nonlinear boundary conditions resulting from convection and radiation have been addressed. A finite-difference heat transfer model is employed, with nonlinearities treated via the Newton-Raphson technique with symbolic reduction. This reduces the dimension of the system of equations requiring iteration as well as the number of iterations required by offering quadratic convergence. The procedure for implementation of this reduced iterative algorithm is the major emphasis of this paper. In order to illustrate the procedure for implementation, only a single cable with radiation at the boundary is treated. Appropriate considerations for the extension of the method for more complex systems are discussed in a general sense. The overall scope of this paper is to illustrate the procedure for application of the algorithm to nonlinear thermal analyses. The finite-difference thermal model is obtained from power balance equations at each node of a solution grid imposed on the cable cross-section. All calculations are based on a per-unit length section with constant RMS conductor currents. Conductor resistance variations with temperature are considered, and no conductors are assumed isothermal. The convergence of the presented algorithm has proven to provide substantial speed-up over standard and accelerated Gauss-Seidel methods.>