Modeling and analysis of electro-thermal processes in installations for induction heat treatment of aluminum cores of power cables

Abstract

Introduction. The development of the electric power industry is directly related to the improvement of cable lines. Cable lines meet modern requirements for reliability, they are increasingly used. Problem. Currently, power cables with an aluminum multi-conductor core, which requires heat treatment - an annealing process at the stage of the technological manufacturing process, are widespread. This process makes it possible to desirably reduce the electrical resistance of the wire and increase its flexibility. For effective use of induction heating during annealing of an aluminum core, it is necessary to determine the optimal frequency of the power source of the inductor. Considering the long length of the inductor and the large number of its turns, the numerical calculation of the electromagnetic field, which is necessary for calculating the equivalent electrical parameters of the turns of the inductor and its efficiency, requires significant computer resources. The goal is to develop a computer model for calculating electro-thermal processes in an induction plant for heating (up to the annealing temperature) an aluminum core of a power cable moving in the magnetic field of a long multi-turn inductor, as well as obtaining frequency dependences of the equivalent R, L parameters of such an inductor and determining the optimal the value of the frequency of the power source, which corresponds to the maximum value of the electrical efficiency of the inductor. Methodology. The mathematical model was developed to analyze the coupled electromagnetic and thermal processes occurring in a core moving in a time-harmonic magnetic field of an inductor at a constant speed. The differential equations for the electromagnetic and temperature fields, taking into account the boundary conditions, represent a coupled electro-thermal problem that was solved numerically by the finite element method using the Comsol software package. For a detailed analysis of the electromagnetic processes in the inductor, an additional problem was considered at the level of the elementary cell, which includes one turn of the inductor and a fragment of the core located near this turn. Results. According to the results of the calculation of the electromagnetic field in the area of the elementary cell, the equivalent electrical parameters of one turn of the inductor and the entire multi-turn inductor were calculated depending on the frequency of the electric current. The frequency dependences of the electrical efficiency of the inductor were calculated. Originality. Taking into account the design features of the inductor (its long length and large number of turns), the method of multiscale modeling was used. Electro-thermal processes in the core were studied at the macro level, and the distribution of the electromagnetic field and electric current density in the cross-section of the massive copper turn of the inductor was calculated at the micro level – at the level of an elementary cell containing only one turn of the inductor. The frequency dependences of the equivalent R, L parameters of the inductor, taking into account the skin effect, the proximity effect, and the geometric effect, were obtained, and the quantitative influence of the electric current frequency on these effects was studied. Practical value. The dependence of the electrical efficiency of the inductor on the frequency of the power source was obtained and it was shown that for effective heating of an aluminum core with a diameter of 28 mm, the optimal value of the frequency is in the range of 1–2 kHz, and at the same time the electrical efficiency reaches values of ηind = 0.3–0.33, respectively.