The power electronics market is valued at $23.25 billion in 2019 and is projected to reach $ 36.64 billion by 2027. Power electronic systems (PES) have been extensively used in a wide range of critical applications, including automotive, renewable energy, industrial variable-frequency drive, etc. Thus, the PESs' reliability and robustness are immensely important for the smooth operation of mission-critical applications. Power semiconductor switches are one of the most vulnerable components in the PES. The vulnerability of these switches impacts the reliability and robustness of the PES. Thus, switch-health monitoring and prognosis are critical for avoiding unexpected shutdowns and preventing catastrophic failures. The importance of the prognosis study increases dramatically with the growing popularity of the next-generation power semiconductor switches, wide bandgap switches. These switches show immense promise in the high-power high-frequency operations due to their higher breakdown voltage and lower switch loss. But their wide adaptation is limited by the inadequate reliability study. A thorough prognosis study comprising switch degradation modeling, remaining useful life (RUL) estimation, and degradation-aware controller development, is important to enhance the PESs' robustness, especially with wide bandgap switches. In this dissertation, three studies are conducted to achieve these objectives- 1) Insulated Gate Bipolar Transistor (IGBT) degradation modeling and RUL estimation, 2) cascode Gallium Nitride (GaN) Field-Effect Transistor (FET) degradation modeling and RUL estimation, and 3) Degradation-aware controller design for a PES, solid-state transformer (SST). The first two studies have addressed the significant variation in RUL estimation and proposed degradation identification methods for IGBT and cascode GaN FET. In the third study, a system-level integration of the switch degradation model is implemented in the SST. The insight into the switch's degradation pattern from the first two studies is integrated into developing a degradation-aware controller for the SST. State-of-the-art controllers do not consider the switch degradation that results in premature system failure. The proposed low-complexity degradation-aware and adaptive SST controller ensures optimal degradation-aware power transfer and robust operation over the lifetime.

Power electronics have a significant role in modern electrical devices, for instance, hybrid electric vehicles. Power electronics are the technology in between the source and the load circuits and can convert the power from dc to ac or from dc to ac. There are also many types of dc-dc converters, like such as boost and buck converters, which exhibit switching ripple behavior. A boost converter increases the output voltage (with respect to the input voltage) and reduces the output current. A buck converter decreases the output voltage and increases the output current. Many models are used to predict the behavior of the boost and buck converters. The detailed (DET), state-space averaged (SSA), and generalized averaging method (GAM) models are capable of predicting the average behavior of dc-dc converters. For DET and GAM models, the rippling behavior can also be predicted. These models differ in terms of required run time, existence of constant equilibrium points, and accuracy. The DET model has a long run time and does not have constant equilibrium, but it is very accurate. The SSA technique is a mathematical and time-invariant model that capable of describing the behavior of a dc-dc boost converters. It can derive the small signal ac equations of a switching converter and is used to illustrate the average behavior of any linear or nonlinear system in converters. The SSA does not take extensive runtime simulation and has constant equilibrium points, and can be applied to continuous, discrete and sample data systems. The GAM model can predict the average and ripple behavior in power electronic systems and has constant equilibrium and fast run time. However, it has a numerical stability issue. The integrator stabilized multifrequency averaging (ISMFA) model is employed to solve the stability issue in the GAM model, but it is a complicated dynamic method and has restrictions in its process. In the present study, a simplified but stable GAM model is introduced to predict the average and ripple behavior of boost dc-dc converters and to overcome the limitations of other methods. In this work, the stabilized GAM model has been used for a dc-dc boost converters. The stability of the proposed model is analyzed. The performance of the improved GAM model is compared with the DET, SSA, and GAM models. The results show that the stabilized GAM model is stable with the additional poles created by the GAM assignable by parameter choice. The new GAM model predicts the same results as the existing GAM method without the underlying stability concerns. The stabilized GAM model exhibits constant ii equilibrium point and requires significantly lower run times than the DET model, but it is also able to predict the ripple performance of the converter. The stabilized GAM model does not take a long run time, is less complicated, has fewer restrictions, has constant equilibrium and internal stability, and has more straightforward implementation than other models, like the ISMFA model. It represents a suitable alternative to DET models when high accuracy simulations are desired without long simulation run times.

This thesis is concerned with the modeling and numerical study of nonsmooth dynamical systems (NSDS). The first part of the thesis deals with the modeling of some DC-DC power converters using the complementarity formalism. This mathematical theoretical framework allows us to ensure existence and uniqueness of solutions in a "natural" and synthetic way. Specifically, it works pretty well in power electronic converters because it incorporates generalized discontinuous conduction modes (GDCM), characterized by a reduction of the dimension of the effective dynamics. For systems with a single diode, analytical state-space conditions for the presence of a GDCM are stated and simulation results, showing a variety of behaviours, such as persistent or re-entering GDCM, are also presented. Furthermore, the analysis and simulation of a parallel resonant converter (PRC), which has four diodes, illustrate the convenience of the complementarity formalism to simulate electrical systems with a large number of ideal diodes. We also present the simulation of a boost converter with a sliding mode control, even though a general control theory for complementarity systems is not still developed.In the second part of the thesis we focus on the bifurcation analysis in NSDS, and in particular, we have studied different mechanical systems which involve impacts and dry-friction. It is known that nonsmooth or discontinuous dynamical systems can exhibit the bifurcations also exhibited by smooth systems. In addition to these, there are also some novel transitions so-called discontinuity-induced bifurcations (DIBs) which are unique to these systems. We have investigated the complex behaviour occurring in an impacting mechanical system. DIBs such as corner impact bifurcations and transitions from complete to uncomplete chattering motions have been analysed in detail. Another type of DIBs recently classified are the so-called sliding bifurcations. Such bifurcations are a characteristic feature of so-called Filippov systems. We present detailed examples of all the different sliding bifurcation scenarios in a dry friction oscillator using a measured friction characteristic firstly introduced by Popp. Furthermore, a codimension-two degenerate switching-sliding bifurcation is displayed. In this case of degenerate switching-sliding bifurcation two curves of codimension-one sliding bifurcations, crossing-sliding and adding-sliding, branch out from the codimension-two point. Also, a cusp smooth codimension-two bifurcation is shown and coexistence of periodic orbits in the region between both fold codimension-one curves is studied.We have also investigated the dynamic behaviour of the two-block Burridge model for earthquake simulations. Previous numerical studies investigated by Ruina verified that, with a friction force of Coulomb type, the system presents only periodic behaviour. We show that chaotic regions can be observed in a symmetric configuration even if a Coulomb friction is considered with the relaxation of one of the assumptions assumed in the seismological literature. Furthermore, we have studied the behaviour of the system with asymmetric configuration. Different periodic solutions and regions of chaos can be observed varying the asymmetry of the system. With respect to the bifurcation point of view, we have analysed several smooth bifurcations (smooth and DIBs) observed in this system.Chapter 6 of this thesis presents the SICONOS software platform dedicated to simulation of NSDS. We give an overview of the SICONOS software and the way NSDS are modeled and simulated within the platform. Routines for analysis (stability, bifurcations, invariant manifolds,.) of NSDS implemented in the platform are explained in detail. To conclude this part, several representative samples are shown in order to illustrate the SICONOS platform abilities.Conclusion and some open problems are presented in the last chapter.

Power electronic systems have been widely used in the electrical power processing for applications with power levels ranging from less than one watt in battery-operated portable devices to more than megawatts in the converters, inverters and rectifiers of the utility power systems. These systems typically involve the passive elements such as inductors, capacitors, and resistors, the switching electronic components such as IGBTs, MOSFETS, and diodes, and other electronic circuits. Multifrequency averaging is one of the widely used modeling and simulation techniques today for the analysis and design of power electronic systems. This technique is capable of providing the average behavior as well as the ripple behavior of power electronic systems. This work begins with the extension of multifrequency averaging to represent uniformly sampled PWM converters. A new multifrequency averaging method of solving an observed issue with model stability is proposed and validated. Multifrequency averaging can also be applied to study the instability phenomenon in power electronic systems. In particular, a reduced-order multifrequency averaging method, along with a genetic algorithm based procedure, is proposed in this work to estimate the regions of attraction of power electronic converters. The performance of this method is shown by comparing the accuracy and efficiency with the existing methods. Finally, a new continuous-time multifrequency averaging method of representing discrete-time systems is proposed. The proposed method is applied to model digitally controlled PWM converters. Simulation and hardware results show that the proposed method is capable of predicting the average behavior as well as the ripple behavior of the closed-loop systems. Future research in the area of multifrequency averaging is proposed.

During development of control systems for power electronic systems, it is desirable to test the controller in real-time, by interfacing it with an emulator device. In this context, this work comprises the development of an emulator that can model accurately the dynamics of high speed power electronic systems and provides interfaces that are compatible with the real hardware. The realtime state calculations, based on discrete models, were performed on custom logic, implemented on an FPGA. The realized system allows to emulate Linear Parameter Varying (LPV) systems, achieving sampling rates up to 12MHz using a low cost Xilinx FPGA. As a result, power electronic systems with very high switching frequencies can be modeled. In addition, the FPGA incorporates a soft-core processor that allows a designer to easily re-configure the system model through software. The emulator system has been validated for a multiphase DC-DC converter, by comparing its results with the real hardware setup.

Σκοπός της παρούσας εργασίας ήταν να γίνει μια εκτενής καταγραφή και παρουσίαση των ηλεκτρονικών μετατροπέων που χρησιμοποιούνται για τη διασύνδεση των Ανανεώσιμων Πηγών Ενέργειας (Α.Π.Ε) στο δίκτυο. Αφού γίνεται αρχικά μια αναφορά στις Α.Π.Ε και στα Ηλεκτρονικά Ισχύος, στη συνέχεια παρουσιάζονται οι διαφορετικές τοπολογίες των ηλεκτρονικών μετατροπέων που μπορούν να χρησιμοποιηθούν σε κάθε εφαρμογή. Για τους μετατροπείς, εξηγείται πρώτα η λειτουργία τους και στη συνέχεια αναφέρονται τα πλεονεκτήματα και μειονεκτήματα της κάθε τοπολογίας προκειμένου να παρέχεται στον αναγνώστη η δυνατότητα γρήγορης, εύκολης και άμεσης σύγκρισης. Επίσης, παρουσιάζονται κατάλληλα συστήματα για την αποθήκευση της ενέργειας προερχόμενη από Α.Π.Ε. Τέλος, προσομοιώνεται το ίδιο φωτοβολταϊκό σύστημα χρησιμοποιώντας τρεις διαφορετικούς μετατροπείς, διαφορετικής τοπολογίας ο κάθε ένας, προκειμένου να συγκριθούν και να αναλυθούν τα αποτελέσματα με βάση τη θεωρητική ανάλυση που έχει προηγηθεί. / The aim of this dissertation was to present the power-electronic systems for the grid integration of renewable energy sources. Once both the renewable energy sources and the power electronics are discussed, different topologies of power converters that can be used in such systems are presented. Converters’ operation is firstly explained, followed by a list of advantages and disadvantages of them so as the reader can make an easy, fast and direct comparison. Storage systems appropriate for renewable energy sources systems are also shown. At the end, a simulation of a photovoltaic system with three different kinds of inverter is performed in order to compare and analyze the results based on the theoretical analysis previously presented.