Modele integral axisymetrique pour le calcul des pertes AC dans les bobinages supraconducteurs.

摘要

The goal of this Master's thesis is to develop an accurate and a fast numerical model to solve current distribution and/or magnetic fields in superconductor windings, and especially to improve the conception of superconducting transformers. The model must be able to determine current distribution and alternative current losses (called AC losses) in the superconducting tapes of the simulated winding. Indeed, efficient and fast numerical models that compute AC losses of a superconducting winding with a large number of turns (10 to 1000 turns) do not exist yet. However, since the discovery of high temperature superconductors (HTS) in 1986, research in the superconductivity field never stopped evolving and the use of these materials in power devices becomes more and more realistic and even advantageous. Indeed, superconducting transformers have a greater efficiency than conventional transformers and are much more compact (about 30% smaller in terms of size and weight compared to conventional ones). Yet, new conception tools are required in order to reduce the cost of prototypes (by optimizing the use of superconductors) and thus, ensure the development of superconducting devices. The highly non-linear resistivity of superconductor materials and the large number of turns of real windings make the task challenging with the existing conception tools. In particular, commercial finite element software packages are not adapted to this task.;In this Master's thesis, in order to find the current distribution and the AC losses in superconducting tapes of a winding, we present a variation of a numerical method developed by my research supervisor Frederic Sirois and his team. The model was developped in Matlab environment and the main equation of the model, from which the solution of the current distribution is found consist of the integral form of the eddy current equation at low frequency (i.e. displacement current neglected). All the superconducting tapes are discretized in elements in which the current distribution is uniform. In the problem formulation, the Biot-Savart integral equation is used in order to establish a direct relationship between the current density and the vector potential.;Moreover, in order to compute the AC losses of a winding with a large number of turns within an acceptable time, we introduce in this Master's thesis a new approximation method called "far tape approximation". The idea behind it is to reduce the size of the problem by using different discretization for each tape of the winding. The fineness of the discretization is different whether we consider the studied tape (i.e. the tape for which the current density is being computed) or if it's one of its nearest neighbor, or a tape that is far enough from the studied one. These "far tapes" are regrouped in term of identical radius r, i.e. all the tapes that have the same radial coordinate are regrouped and considered as one single element with a uniform and known current density. This is possible as long as these tapes are far enough from the studied one, their contribution to the potential vector of the studied tape being about the same, whether we consider their detailed current distribution or an uniform version of it. This approximation reduces tremendously the number of unknowns for current density computation, and thus, the computing time is also much reduced.;At last, the project ends by the optimization of the numerical code in order to make the code as fast as possible. In order to do this, a part of the code has been written entirely in C.