Reduced order modelling of electric components

Model order reduction (MOR) techniques allow to shorten the simulation time required to obtain the response of a system, by reducing the number of states used to represent it. MOR algorithms take a full order model (FOM) and produce a reduced order model (ROM). In this thesis the problem considered is the application of MOR to electric components. The problem was studied by using a combination of algorithms found in the literature and ready-made software toolboxes. Further analysis has been done on parametric model order reduction (PMOR) and its applications to solving nonlinear systems. PMOR is a type of MOR that allows to conserve the parametric dependence of the FOM (like the temperature dependence of electrical resistivity) to produce a ROM that well represents the FOM for various parameter values. The study starts from simple but effective (for small models) Balanced Truncation algorithms and transitions to Moment matching methods working for higher order ones. Several types of algorithms have been tested, some of them find the ROM automatically, while other need more data from the user. The results show that depending on the problem considered, both are valid options. Some interesting results were obtained by considering a nonlinear system as a parametric one and simulating it by changing the parameter at each time-step. The following chapters of this thesis are dedicated to a general review of snapshot-based and data driven methods for MOR, including system identification and machine learning.