Numerical simulation and analysis of non-linear dynamic systems for electrical applications

Abstract

In engineering field, the solution of a problem involving non-linear systems is a difficult task both when simulation and identification of the model are needed. The simulation of a non-linear system consists in solving a Direct Problem, meaning the estimate of the measurement of a phenomenon given the knowledge of its model. On the other hand, an Inverse Problem starts from the knowledge of experimental data and tries to estimate the generating model through an identification process. The resolution of a Direct Problem is not trivial. In general, a non-linear model, describing a real phenomena, is defined by a set non-linear equations for which exact solutions can not be determined via algebraic methods. Several approaches have been developed in literature to provide an approximated solution for non-linear problems by representing a system through numerical models. These concepts are discussed in Part I of this thesis. On the other hand, an Inverse Problem has several solutions and the search for optimal one constitutes a very complex goal. In general, the identification process for non-linear problems represents a difficult task and the choice of a particular optimization algorithm to solve a problem or other is dependent on the nature of the problem itself. In general, when a physical model is not available, the black box models represent a valid alternative because they imitate the real system behaviour as nearly as possible by means of observed data, without the knowledge of the inner mechanisms that regulate the system. Several ANN structures and training algorithms have been proposed in literature for mathematical modelling of numerical data coming from observations of phenomena, some of them are deeply analysed in Part II of this thesis. Moreover the advantages and disadvantages of modelling a non-linear system with Optimization techniques and the ANN are illustrated in Part II. The concepts presented in Part I and Part II of this work are exploited to solve practical problems, regarding non-linear systems in electrical applications. Thus, part III is focused on novel strategies proposed to face the modelling of non-linear phenomena occurring in some electrical applications. The first application proposed is the simulation of non-linear hysteresis phenomenon characterizing the magnetic materials and further applications of Artificial Neural Networks. The second study deals with the issues relating to the identification of dynamic non-linear models for batteries. In particular, a novel identification method for hybrid model is presented first, and then, an improvement of equivalent circuit model is proposed for increasing its generalization capabilities. Finally, third application concerns the optimization in Photovoltaic (PV) systems, whose management is a very challenging issue. A deep overview of the environmental conditions related effects of the PV power generation is illustrated. Moreover, an ANN-based strategy, including weather predictions, to forecast the PV power is presented.