Theoretical model to calculate steady-state and transient ampacity and temperature in buried cables

The temperature distribution and ampacity in a multilayered soil surrounding a system of three cables are calculated in the steady state and in emergency situations. In this paper, we present the mathematical model, which solves the heat diffusion equation in cylindrical coordinates inside the cables and in Cartesian coordinates in the surrounding soil. The finite difference method is used to solve the equations. In order to reduce the number of points studied that are of no interest to the results, a variable step discretization is used. Here, we present the development of the model and the effect of some of the parameters which influence the convergence and accuracy of the method. The application of the model in different configurations and situations is given in the second part of this work, sent for publication at the same time. The model is applicable to the study of buried cables in both the steady state and transient states for short-circuit and overload situations.