Analisi di sistemi elettrici nel dominio del tempo tramite il metodo PEEC

The thesis is developed by addressing various fields of application of the PEEC method, partial element equivalent circuit, in the time domain. We start by talking about strictly theoretical aspects, addressing problems and critical issues, we will talk about techniques to improve and optimize the PEEC method, to then arrive at real applications and comparison with experimental data. In chapter 1 the PEEC method is summarized. Starting from the Maxwell Equations, the whole process of calculating 3D models and some tricks related to the simulation of the model is provided. Particular attention has been given in Chapter 2 to the phenomenon of physical delays related to the propagation of an electrical signal. In a discrete time system with fixed time intervals, the use of common basic functions, rectangular or Dirac delta, creates an approximation that often turns out to be unsatisfactory and in some cases leads to the problem known as late time instability. We started from a theoretical analysis of the problem, we obtained the equations and, through the use of a script, created ad hoc for the discretization of the geometries to be examined, we came to obtain a solver. Another topic, dealt with in chapter 3, concerns the formulation of integral equations for the solution of electromagnetic problems with the PEEC method with an approach to surfaces. The objective is to obtain a formulation based on the principle of surface equivalence that requires only the discretization of surfaces and not more than volumes as happens in the standard PEEC method. The use of the surface formulation is aimed at reducing the unknowns. The process leads to a reduction of the computational complexity and consequently to the reduction of the processing time necessary for the resolution of systems of differential equations obtained by the PEEC method. We started from a theoretical analysis of the problem, we obtained the equations and, through the use of a script, created ad hoc for the discretization of the geometries to be examined, we came to obtain a solver. Chapter 4 then describes another optimization strategy that uses automatic learning techniques to reduce the processing time of solvers based on the PEEC method. The use of these techniques is useful in the case where one can only use the numerical approach to solve a problem. As for the case study, we want to use neural networks to predict partial inductance values. In chapter 5, a contribution concerning magnetic materials is given. Starting from the PEEC formulation which incorporates magnetic materials, completely analytical formulas have been developed to populate the matrices that describe the density of flow in the case of orthogonal geometries. Conspicuous part of the thesis work, composed by the formulation of the PEEC method applied to moving objects, is presented in chapter 6. This implementation allows to widen considerably the field of use of the method, such as creating and simulating the behavior of geometries that have elements in rotation and or in revolution. Specifically, a solver was created for the simulation of an electric motor. In the formulation we take into account the magnetic field generated by the flows of current in the conductive elements present in the stator and the interaction of this field with the rotor elements.