Numerical Simulation of the Heat Conduction in Electrical Cables

Abstract

The modelling of the heat conduction in electrical cables is a complex mathematical problem. To get a quantitative description of the thermo‐electrical characteristics in the electrical cables, one requires a mathematical model for it. It must involve the different physical phenomena occurring in the electrical cables, i.e. heat conduction, convection and radiation effects, description of heat sources due to current transitions. Since the space in mobile systems is limited and weight is always reduced, wire conductor sizes must be kept as small as possible. Thus the main aim is to determine optimal conductor cross‐sections for long standing loads. In this paper we develop and validate a set of mathematical models and numerical algorithms for the heat transfer simulation in cable bundles. The numerical algorithms are targeted to the two‐dimensional transient heat transfer mathematical models. Finally, a validation procedure for the coefficient validation of the differential equations is carried out. Results of numerical experiments are presented.

Parallel Numerical Algorithms for Optimization of Electrical Cables

“…A quantitative description of the thermo-electrical characteristics in the electrical cables can be obtained by using mathematical models based on parabolic partial differential equations. In our previous papers (see, [5,11]) we have proposed efficient parallel numerical algorithms for simulation of temperature distribution in electrical cables and have solved an inverse problem for fitting the diffusion coefficient of the air-isolation material mixture to the experimental data. In this paper we solve the optimization problem and minimize the total weight of cables.…”

Numerical Simulation of the Heat Conduction in Composite Materials

“…AGMG was used as a preconditioner for Krylov subspace methods, e.g. PCG, GMRES algorithms ( for similar simulations of electrical cables we have used also a preconditioned version of BiCGStab [5,6]). The matrix of a linear system obtained after the Picard linearization is an M-matrix.…”

“…Here we mention applications in engineering for detection the corrosion of containers, where direct and inverse heat transfer problems in composite materials are solved [2,9,18], and optimal design of electrical cables [5,6,11].…”

Custom integer optimization method for wire bundle dimensioning

“…There are simulators capable of predicting both the steady and transient temperature of wires and wire bundles ( [1], [2], [3], [4]), with the aim of either assessing the correct dimensions of wires or using them to find their optimum crosssections. It is possible to simulate all of the wires of a car if they are considered one by one, but, on the other hand, if one wants to study the temperature as a result of simultaneous current conduction in wire bundles, it is necessary to evaluate different combinations of modules in order to find the worst case.…”