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 tha t has received considerable attention by many researchers. In typical analyses, non-linear boundary conditions resulting from convection and radiation have been addressed. In general, these non-linear boundary conditions force an iterative solution; almost exclusively, Gauss-Seid el has been the solution method of choice, offering linear convergence . Such a choice requires a large number of iterations on an equally la rge system of equations. Herein, a finite-difference heat transfer mod el is employed, with non-linearities treated via the Newton-Raphson te chnique with symbolic reduction. This reduces the dimension of the sys tem of equations requiring iteration as well as the number of iteratio ns required by offering quadratic convergence. ?he procedure for imple mentation 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. Appropr iate considerations for the extension of the method for more complex s ystems are discussed in a general sense. The overall scope of this pap er is to illustrate the procedure for application of the algorithm to non-linear thermal analyses. The finite-difference thermal model is ob tained from power balance equations at each node of a solution grid im posed on the cable cross-section. All calculations are based on a per- unit length section with constant rms conductor currents. Conductor re sistance variations with temperature are considered, and no conductors are assumed isothermal. The convergence of the presented algorithm ha s proven to provide substantial speed-up over standard and accelerated Gauss-Seidel methods, as illustrated by comparison.