The topic of this diploma thesis is mathematical model of electric vehicle. The traction drive consists of Li-Ion battery, free-phase DC/AC converter and permanent magnet synchronous machine. The main goal of the thesis is development of function model and making simulations in SIMULINK/SIMSCAPE program. Work is divided into three main parts. The first part is dedicated to the theoretical description of the main drive components. The second part describes partial subsystems of the model. In the last part is build a complete model of electric vehicle and simulated different driving mode.

Recently, due to the increasing adoption of distributed energy resource (DER) technologies including battery energy storage (BES) and electric vehicle (EV) systems, bidirectional power converters are becoming more popular. These converters are broadly utilized as interface devices and provide a bidirectional power flow in applications where the primary power supply can both supply and receive energy. A dc capacitor, called the dc-link, is an important component of such bidirectional converters. For a wide range of applications, the converter is required to control the dc-link voltage. Commonly, a proportional-integrating (PI) controller is used by the dc capacitor voltage controller to generate a set-point for the inner current controller. This approach tightly regulates the dc-link voltage to a given value. The research presented in this dissertation shows that such an approach compromises the stability margins of the converter for reverse power flow and weak grid conditions. It is shown that by allowing a small variation of dc capacitor voltage in proportion to the amount of power flowing through the converter, the stability and robustness margins are improved. This approach also simplifies the design process and can be applied to both dc/dc and dc/ac (single-phase and three-phase) converters. Moreover, it grants an inherent power sharing capability when multiple converters share the same dc-link terminals; removing the need to a communication link between parallel converters. The proposed controller is equipped with a current limiting mechanism to protect the converter during low-voltage/over-current transients. Detailed analyses, simulations, comparisons, and experimental results are included to illustrate the effectiveness of the proposed control approach. To mathematically establish the properties of the proposed method in a single-phase dc/ac application, this dissertation also derives a new and systematic modeling approach for a grid-connected bidirectional single-phase inverter controlled in stationary frame. Implementing the control system in the stationary frame has advantages over rotating frame. However, the combination of dc and ac state variables and nonlinearities make its stability analysis challenging. In the proposed model, an imaginary subsystem is properly generated and augmented to allow a full transformation to a synchronous rotating frame. The proposed modeling strategy is modular and has a closed form which facilitates further extensions. It is successfully used to demonstrate enhanced stability margins of the proposed controller.

Η παρούσα διδακτορική διατριβή αναφέρεται σε οικιακά Φ/Β συστήματα συνδεδεμένα στο δίκτυο χαμηλής τάσης, τα οποία αξιοποιούν την τεχνολογία των Φ/Β Πλαισίων Εναλλασσομένου Ρεύματος (Φ/Β Πλαίσια Ε.Ρ. – AC-PV Modules). Πρόκειται για Φ/Β διατάξεις μικρής ισχύος (έως 300W), οι οποίες δημιουργούνται από την ενσωμάτωση ενός μόνο Φ/Β πλαισίου και ενός μετατροπέα (ενός η πολλών σταδίων) συνεχούς τάσης σε μονοφασική εναλλασσόμενη τάση, σε μια αυτοτελή ηλεκτρονική διάταξη. Για το λόγο αυτό ονομάζονται και Φ/Β πλαίσια με ενσωματωμένο μετατροπέα (Module Integrated Converters, MIC). Στα συστήματα αυτά οι απαιτήσεις για επίτευξη υψηλού βαθμού απόδοσης, για την καλύτερη εκμετάλλευση της παρεχόμενης ηλιακής ενέργειας, καθώς και ρεύματος ημιτονοειδούς μορφής στην έξοδο είναι αδιαμφισβήτητες. Βασικός σκοπός της παρούσας διατριβής είναι η συμβολή της στον τομέα των Φ/Β μονάδων διεσπαρμένης παραγωγής και επικεντρώνεται στην ενδελεχή ανάλυση, στη βελτιστοποίηση της λειτουργικής συμπεριφοράς, στον υπολογισμό των απωλειών στα στοιχεία του μετατροπέα, στην παραμετροποίηση και τελικά στο βέλτιστο σχεδιασμό ενός αντιστροφέα ρεύματος τύπου Flybcak (Flyback Current Source Inverter – Flyback CSI). Οι κύριοι στόχοι που έπρεπε να εκπληρωθούν για την ολοκλήρωση της παρούσας διατριβής ήταν:  Η ενδελεχής ανάλυση της λειτουργίας του αντιστροφέα για δύο διαφορετικές στρατηγικές ελέγχου που εφαρμόζονται σε αυτόν.  Ο κατά το δυνατόν ακριβέστερος υπολογισμός των απωλειών στα στοιχεία του Flyback CSI, καθώς και η παραμετροποίηση των σχέσεων αυτών.  Ο βέλτιστος σχεδιασμός του Flyback CSI, ο οποίος βασίζεται στη διατύπωση της μεγιστοποίησης του σταθμισμένου βαθμού απόδοσης ως πρόβλημα βελτιστοποίησης.  Η υλοποίηση του ελέγχου της λειτουργίας του μετατροπέα μέσω ψηφιακού μικροελεγκτή, καταργώντας τον ήδη υφιστάμενο αναλογικό έλεγχο. Αρχικά η μελέτη επικεντρώνεται σε μία πρώτη τεχνική ελέγχου, η οποία ωθεί τον μετατροπέα να λειτουργεί στην περιοχή της ασυνεχούς αγωγής (Discontinuous Conduction Mode, DCM). Στη συνέχεια προτείνεται μία δεύτερη τεχνική ελέγχου η οποία, αφ' ενός μεν αναγκάζει το μετατροπέα να λειτουργεί στο όριο συνεχούς και ασυνεχούς αγωγής (Boundary between Continuous and Discontinuous Conduction Mode, BCM), αφ' ετέρου δε παρέχει καθαρά ημιτονοειδές ρεύμα στην έξοδο. Με την προτεινόμενη νέα τεχνική ελέγχου, που ονομάσθηκε i-BCM (improved BCM) και αποτελεί βελτίωση της υπάρχουσας στη βιβλιογραφία τεχνικής ελέγχου BCM, βελτιώνεται σημαντικά ο συντελεστής ισχύος στην έξοδο του αντιστροφέα, παρέχοντας στο δίκτυο καθαρά ημιτονοειδές ρεύμα. Οι δύο διαφορετικές στρατηγικές ελέγχου διαμορφώνουν διαφορετικές κυκλωματικές συνθήκες. Για τις δύο περιπτώσεις αναπτύσσονται αναλυτικές εκφράσεις τόσο για τη μέση, όσο και για την ενεργό τιμή των ρευμάτων που διαρρέουν όλα τα στοιχεία του μετατροπέα (ημιαγωγικά στοιχεία, Μ/Σ κλπ). Επιπρόσθετα, εξάγονται κριτήρια για τα ασφαλή όρια λειτουργίας του μετατροπέα με γνώμονα την καταπόνηση των ημιαγωγικών στοιχείων ισχύος από υψηλές τιμές τάσης και ρεύματος. Ιδιαίτερο βάρος δίνεται στον υπολογισμό της διακύμανσης της τάσης του πυκνωτή του φίλτρου εξόδου, η οποία αναπτύσσεται και πάνω στα ημιαγωγικά στοιχεία του μετατροπέα, επηρεάζοντας την επιλογή τους. Στην συνέχεια, προσδιορίζονται μέσω αναλυτικών μαθηματικών σχέσεων οι απώλειες αγωγής και οι διακοπτικές απώλειες των ημιαγωγικών στοιχείων και προσεγγίζονται, με ιδιαίτερη λεπτομέρεια, οι απώλειες του μετασχηματιστή (τυλιγμάτων και πυρήνα) και για τις δύο προαναφερθείσες στρατηγικές ελέγχου, δεδομένου ότι η διακοπτική συχνότητα λειτουργίας του μετατροπέα είναι υψηλή. Για το λόγο αυτό απαιτείται εις βάθος μελέτη της υπάρχουσας βιβλιογραφίας, επιλογή ή επινόηση των κατάλληλων μοντέλων απωλειών σε ένα Μ/Σ (πυρήνα και χαλκού) και προσήκουσα προσαρμογή αυτών στις κυκλωματικές συνθήκες του αντιστροφέα Flyback. Παράλληλα με την ανάλυση των απωλειών πραγματοποιείται και η παραμετροποίηση του συστήματος. Η διαδικασία αυτή στηρίζεται στη διαχείριση των εξισώσεων κατά τέτοιο τρόπο ώστε να προσδιορίζονται όλες οι μεταβλητές και οι σταθερές του μετατροπέα, καθώς και οι παράμετροι από τις οποίες εξαρτώνται οι απώλειες, με τον απλούστερο δυνατό τρόπο. Συνεπώς, έχει δοθεί ιδιαίτερη έμφαση στην διαχείριση των αναλυτικών σχέσεων ώστε οι απώλειες, χωρίς έκπτωση στην ακρίβεια, να εξαρτώνται από τον ελάχιστο δυνατό αριθμό παραμέτρων. Με αυτό τον τρόπο η μελέτη είναι πλήρης αλλά περιορίζεται η πολυπλοκότητα, με αποτέλεσμα να προκύπτουν μόνο τέσσερις ανεξάρτητες σχεδιαστικές μεταβλητές. Στο επόμενο στάδιο, πραγματοποιείται ο βέλτιστος σχεδιασμός του Flyback CSI, ο οποίος βασίζεται στη διατύπωση της μεγιστοποίησης του σταθμισμένου βαθμού απόδοσης ως πρόβλημα βελτιστοποίησης. Αυτό, πρακτικά, σημαίνει τον προσδιορισμό της αντικειμενικής συνάρτησης (objective ή cost function), των σχεδιαστικών μεταβλητών και σταθερών, των περιοριστικών συνθηκών και τον ορισμό του πεδίου τιμών αυτών. Ο σταθμισμένος βαθμός απόδοσης αποτελεί την αντικειμενική συνάρτηση, ενώ οι προδιαγραφές εισόδου και εξόδου του μετατροπέα αποτελούν τις σχεδιαστικές σταθερές.. Με τη χρήση μίας στοχαστικής μεθόδου βελτιστοποίησης, η οποία αναδείχτηκε ως η πιο κατάλληλη έπειτα από εκτεταμένη βιβλιογραφική αναζήτηση, προσδιορίζονται οι τιμές των τεσσάρων σχεδιαστικών μεταβλητών και επιτυγχάνεται ο μέγιστος δυνατός σταθμισμένος βαθμός απόδοσης. Η επίτευξη του στόχου ολοκληρώνεται με την ανάπτυξη ενός νέου επαναληπτικού αλγορίθμου, με τον οποίο, βάσει των εξισώσεων των απωλειών, επιτυγχάνεται ο βέλτιστος σχεδιασμός του Flyback CSI και για τις δύο διαφορετικές τεχνικές ελέγχου. Επιπροσθέτως, υλοποιείται ο έλεγχος της λειτουργίας του μετατροπέα μέσω ψηφιακού μικροελεγκτή, καταργώντας τον ήδη υφιστάμενο αναλογικό έλεγχο. Η αλλαγή της φιλοσοφίας υλοποίησης του ελέγχου προσφέρει μεγαλύτερη ευελιξία και ανεξάντλητες δυνατότητες στην κατάστρωση και υιοθέτηση διαφορετικών στρατηγικών ελέγχου. Ιδιαίτερα, κατά τη λειτουργία στο όριο μεταξύ συνεχούς και ασυνεχούς αγωγής (i-BCM), με κατάλληλο προγραμματισμό του μικροελεγκτή εξαλείφεται η ανάγκη για μέτρηση των ρευμάτων στα τυλίγματα του μετασχηματιστή. Ο μικροελεγκτής που χρησιμοποιείται είναι ο dspic30F4011 της εταιρείας Microchip ο οποίος διαθέτει μεγάλη υπολογιστική ικανότητα και μία πληθώρα περιφερειακών που επιτρέπουν αυτοματοποίηση κάποιων λειτουργιών, όπως η διαδικασία σύνδεσης και αποσύνδεσης με το δίκτυο και η δυνατότητα ενσωμάτωσης της μονάδας ανίχνευσης του μέγιστου σημείου ισχύος (M.P.P.T) της Φ/Β γεννήτριας στην ίδια ψηφιακή μονάδα. Τέλος, υλοποιήθηκαν εργαστηριακά πρωτότυπα με βάση τις βέλτιστες παραμέτρους που υπολογίσθηκαν σε κάθε περίπτωση σύμφωνα την προτεινόμενη μέθοδο βελτιστοποίησης και ακολούθησε πειραματική επιβεβαίωση με χρήση ενός αναλυτή ισχύος υψηλής ακρίβειας, για την επιβεβαίωση των θεωρητικών προσεγγίσεων. Επιπλέον, μελετήθηκε η ευεργετική επίδραση της συνδυαστικής χρήσης των δύο τεχνικών ελέγχου στην πυκνότητα ισχύος / This thesis pertains to domestic on-grid PV systems that utilize the AC-PV Modules technology. These low power PV topologies (up to 300W) are implemented by integrating one PV Module and a single phase inverter (one or multi stage), in one independent electronic apparatus. For this reason they are called Module Integrated Converters (MIC). The most important requirements for these systems are the higher possible efficiency - in order to take advantage of the supplied solar energy – and the pure sinusoidal output current. The main purpose of this thesis is to contribute to the field of the dispersed PV power generation. Thus, it focuses on the thorough analysis, the behaviour optimization, the components losses estimation, the parameterization and finally the optimal design of Flyback current source inverter (Flyback CSI). The main objectives fulfilled in this thesis are: • The detailed analysis of the inverter behaviour for two different semiconductor control strategies. • The precise losses calculation of all the components of the Flyback CSI. • The optimal design of the Flyback CSI, which is based on maximizing the weighted efficiency. • The implementation of the semiconductor control via a digital microcontroller, eliminating the existing analogue control. Initially, the study focuses on a first control technique that forces the inverter to function in Discontinuous Conduction Mode (DCM). On the other hand, a second control technique that forces the inverter to function on the Boundary between Continuous and Discontinuous Mode (BCM) is proposed. This new control technique is named i-BCM (improved BCM) and it is an improved version of the BCM control technique found in the literature. This new control scheme significantly improves the power factor of the inverter output. The inverter injects pure sinusoidal current to the grid. The two different control strategies form different circuit conditions. Analytical expressions for the average and the rms value of the current, flowing through the components (semiconductors, transformers e.t.c), for both cases are developed. In addition, new operating boundaries of the semiconductors for the safe operation of the inverter based on the analysis of the voltage and current that stresses the semiconductors, are proposed. Special attention is given on the calculation of the voltage deviation on the output filter capacitor. This voltage deviation is caused by the switching operation of the inverter and affects the selection of the semiconductors and the voltage level that can handle. Furthermore, the conduction losses and the switching losses of the semiconductors are determined through analytical, mathematical equations. Because of the inverter high switching frequency, the transformer losses (copper and core), are calculated with special attention to detail. For this reason, an in depth examination of the existing literature takes place that leads to the selection of the appropriate core and copper loss models. The models are adequately adjusted to the circuit conditions of the Flyback inverter topology. The system is parameterized along with the losses analysis. All the equations are manipulated in such a way that simplifies the determination of all the variables and all the constants of the inverter and the loss dependent parameters. Consequently, special emphasis is given to the manipulation of the analytical equations, without affecting the accuracy, in order to express the losses using the minimum number of independent variables. Therefore, the study is complete but the complexity is eliminated and the independent design variables are only four. The optimization problem is the maximization of the weighted efficiency. The optimal design of the Flyback CSI is implemented based on this formulation. As a next step, the objective (or cost) function, the design variables and constants, the constraints and their range need to be defined. The weighted efficiency is the objective function whereas the input and the output specifications of the inverter are the design constants. After an extensive literature research, a stochastic optimization method is chosen as the most appropriate to determine the values of the four design variables in order to achieve the highest weighted efficiency. A new iterative algorithm, which uses the losses equations, is developed to achieve the optimal design of the Flyback CSI for both control strategies. Moreover, the control of the inverter is implemented via a digital microcontroller, eliminating the existing analogue control. This changes the way of controlling the inverter and offers flexibility and limitless possibilities in implementing and adopting various control strategies. Specifically, under the i-BCM control scheme, the need for measuring the current of the transformer windings is eliminated by using an appropriate algorithm. The microcontroller used in this research is dspic30F4011 developed by Microchip. Its good computational capacity and the variety of peripherals enable the automation of some functions such as connection and disconnection from the grid and the integration of the maximum power point tracking (M.P.P.T.) on the same digital unit. Finally, laboratory prototypes are implemented, based on the optimal parameters calculated for every case, using the proposed optimization method. The experimental procedure confirmed the theoretical approximations. A high precision power analyser was used. Furthermore, the beneficial effect of the combined use of the two control power techniques on the power density is also studied.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-05-08T00:11:48Z No. of bitstreams: 1 NAYARA BRANDÃO DE FREITAS – DISSERTAÇÃO (PPGEE) 2016.pdf: 3718233 bytes, checksum: f4f88b8a316139fc246558ded5f688d9 (MD5) / Made available in DSpace on 2018-05-08T00:11:48Z (GMT). No. of bitstreams: 1 NAYARA BRANDÃO DE FREITAS – DISSERTAÇÃO (PPGEE) 2016.pdf: 3718233 bytes, checksum: f4f88b8a316139fc246558ded5f688d9 (MD5) Previous issue date: 2016-06-23 / O tema desenvolvido consiste no estudo, caracterização e análise de conversores multiníveis CA/CC/CA monofásicos/monofásicos, monofásicos/bifásicos e monofásicos/trifásicos aplicados a sistemas de conversão e compensação de energia, empregando IGBTs (Transistor Bipolar de Porta isolada) como dispositivos semicondutores. No decorrer do trabalho, diversas topologias são analisadas e comparadas utilizados critérios como quantidade de barramentos CC, valores das tensões dos barramentos CC, WTHD (Distorção Harmônica Total Ponderada) das tensões chaveadas, frequências de chaveamentos dos IGBTs e perdas por condução e chaveamento. Os sistemas de controle das variáveis dos conversores estudados são apresentados e o controle individual dos barramentos CC é abordado com destaque. Implementações experimentais foram utilizadas para comprovar a teoria apresentada e mostrar a viabilidade dos sistemas. / This work consists in the study, characterization, anda analysis of AC/DC/AC multilevel converters are applied to conversion and compensation systems and employ and IGBTs (Insulated Gate Bipolar Transistor) as power semiconductor device. Many topologies are analyzed and compared considering the number of DC-links, DC-links voltages values, WTHDs (Weighted Total Harmonic Distortion) of the generated voltages, and semiconductors conduction and switching losses. The control systems of the studied converters are presented and the individual control of the DC-links voltages in highlighted. Experimental results are provided in order to prove the theoretical results and the viability of the systems.

Enhancing performance of power electronics converters has always been an interesting topic in the power electronics community. Over the years, researchers and engineers are developing new high performance component, novel converter topologies, smart control methods and optimal design procedures to improve the efficiency, power density, reliability and reducing the cost. Besides pursuing high performance, researchers and engineers are striving to modularize the power electronics converters, which provides redundancy, flexibility and standardization to the end users. The trend of modularization has been seen in photovoltaic inverters, telecommunication power supplies, and recently, HVDC applications. A systematic optimal design approach for modular power converters is developed in this dissertation. The converters are developed for aerospace applications where there are stringent requirement on converter form factor, loss dissipation, thermal management and electromagnetic interference (EMI) performance. This work proposed an optimal design approach to maximize the nominal power of the power converters considering all the constraints, which fully reveals the power processing potential. Specifically, this work studied three-phase active front-end converter, three-phase isolated ac/dc converter and inverter. The key models (with special attention paid to semiconductor switching loss model), detailed design procedures and key design considerations are elaborated. With the proposed design framework, influence of key design variables, e.g. converter topology, switching frequency, etc. is thoroughly studied. Besides optimal design procedure, control issues in paralleling modular converters are discussed. A master-slave control architecture is used. The slave controllers not only follow the command broadcasted by the master controller, but also synchronize the high frequency clock to the master controller. The control architecture eliminates the communication between the slave controllers but keeps paralleled modules well synchronized, enabling a fully modularized design. Furthermore, the implementation issues of modularity are discussed. Although modularizing converters under form factor constraints adds flexibility to the system, it limits the design space by forbidding oversized components. This work studies the influence of the form factor by exploring the maximal nominal power of a double-sized converter module and comparing it with that of two paralleled modules. The tradeoff between modularity and performance is revealed by this study. Another implementation issue is related to EMI. Scaling up system capacity by paralleling converter modules induces EMI issues in both signal level and system level. This work investigates the mechanisms and provides solutions to the EMI problems. / Ph. D. / As penetration of power electronics technologies in electric power delivery keeps increasing, performance of power electronics converters becomes a key factor in energy delivery efficacy and sustainability. Enhancing performance of power electronics converters reduces footprint, energy waste and delivery cost, and ultimately, promoting a sustainable energy use. Over the years, researchers and engineers are developing new technologies, including high performance component, novel converter topologies, smart control methods and optimal design procedures to improve the efficiency, power density, reliability and reducing the cost of power electronics converters. Besides pursuing high performance, researchers and engineers are striving to modularize the power electronics converters, enabling power electronics converters to be used in a “plug-and-play” fashion. Modularization provides redundancy, flexibility and standardization to the end users. The trend of modularization has been seen in applications that process electric power from several Watts to Megawatts. This dissertation discusses the design framework for incorporating modularization into existing converter design procedure, synergically achieving performance optimization and modularity. A systematic optimal design approach for modular power converters is developed in this dissertation. The converters are developed for aerospace applications where there is stringent v requirement on converter dimensions, loss dissipation, and thermal management. Besides, to ensure stable operation of the onboard power system, filters comprising of inductors and capacitors are necessary to reduce the electromagnetic interference (EMI). Owning to the considerable weight and size of the inductors and capacitors, filter design is one of the key component in converter design. This work proposed an optimal design approach that synergically optimizes performance and promotes modularity while complying with the entire aerospace requirement. Specifically, this work studied three-phase active front-end converter, three-phase isolated ac/dc converter and three-phase inverter. The key models, detailed design procedures and key design considerations are elaborated. Experimental results validate the design framework and key models, and demonstrates cutting-edge converter performance. To enable a fully modularized design, control of modular converters, with focus on synchronizing the modular converters, is discussed. This work proposed a communication structure that minimizes communication resources and achieves seamless synchronization among multiple modular converters that operate in parallel. The communication scheme is demonstrated by experiments. Besides, the implementation issues of modularity are discussed. Although modularizing converters under form factor constraints adds flexibility to the system, it limits the design space by forbidding oversized components. This work studies the impact of modularity by comparing performance of a double-sized converter module with two paralleled modules. The tradeoff between modularity and performance is revealed by this study.

This work is focused on innovative construction of the industrial radial sealless pump and mainly on construction of the three phase DC/AC converter based on new semiconductor technology SiC. These new semiconductor devices allow move switching frequency up to 100 kHz. For such high switching frequency new non-conventional topology of the output filter was designed. This high frequency is currently unusual in three-phase application with output voltage 400V. High switching frequency reduces size of wound components of the output filter and its presence is accepted in terms of total weight and price of the whole system. Clear sinus waveform of the output converter voltage reduces torque ripple, EMC and extend the lifetime and reliability of mechanical parts and the whole pump drive. Three phase synchronous motor is directly placed into the pump body and is designed as slotless motor. In the inlet area is the classical bearing replaced by active magnetic bearing. It is used due to possibility to pump aggressive liquids or substances where high level of cleanness has to be guaranteed.

Indiana University-Purdue University Indianapolis (IUPUI) / The substantial increase demand for electrical energy requires high efficient apparatus dealing with energy conversion. Several technologies have been suggested to implement power supplies with higher efficiency, such as multilevel and interleaved converters. This thesis proposes an energy conversion unit with an optimized number of output voltage levels per number of switches nL=nS. The proposed five-level four-switch per phase converter has nL=nS=5/4 which is by far the best relationship among the converters presented in technical literature. A comprehensive literature review on existing five-level converter topologies is done to compare the proposed topology with conventional multilevel converters. The most important characteristics of the proposed configuration are: (i) reduced number of semiconductor devices, while keeping a high number of levels at the output converter side, (ii) only one DC source without any need to balance capacitor voltages, (iii) high efficiency, (iv) there is no dead-time requirement for the converters operation, (v) leg isolation procedure with lower stress for the DC-link capacitor. Single-phase and three-phase version of the proposed converter is presented in this thesis. Details regarding the operation of the configuration and modulation strategy are presented, as well as the comparison between the proposed converter and the conventional ones. Simulated results are presented to validate the theoretical expectations. In addition a fault tolerant converter based on proposed topology for micro-grid systems is presented. A hybrid pulse-width-modulation for the pre-fault operation and transition from the pre-fault to post-fault operation will be discussed. Selected steady-state and transient results are demonstrated to validate the theoretical modeling.