This thesis investigates the disparities in losses between 2D-based design simulations and a 3D realization of solenoidal inductors featuring distributed gaps. The inductor geometry entails a solenoidal copper winding enveloped by sintered ferrite rings and end caps, with the air gap required for energy storage distributed over multiple smaller discrete gaps. The simulated 3D structure possesses higher losses than its 2D cross-section due to inherent structural features. The research culminates in two contributions. First, a practical two-variable design approach is presented, leveraging matrix algebra to succinctly represent the decision quantities as functions of the two most important variables to the application. The procedure results yield several informative plots that assist in selecting a design that meets the efficiency and thermal limits. Second, a detailed explanation is provided on the 3D loss effects, along with the recommended design considerations and a method to estimate the dominant 3D loss effect using simple 2D simulations. The design recommendations address a 26-fold increase in the core loss of the outer ferrite rings. They also reduce the copper loss due to the termination effect by 55% using spacer ferrite layers. A simple 2D simulation method is proposed to accurately predict the increased 3D copper loss due to the axial shift of the winding to within 3% and runs 60 times faster than the equivalent 3D simulation. Additionally, a derived equation for the optimal turn spacing aligns with the simulation results with <6% error, offering practical insights for design optimization. These results enable the design of a low-loss solenoidal inductor and accurate loss estimations without running lengthy and complicated 3D simulations. A 13 µH, 150 Arms solenoidal inductor prototype for operation in a 10 kV-to-400 V, 50 kW converter cell serves as empirical validation, corroborating the efficacy of the proposed analysis and design methodology. / Master of Science / It is common to rely on a 2D cross-section of the structure to facilitate the design procedure for inductors, essential components used in electronic circuits to control and convert energy. Two-dimensional simulations of inductors are preferred due to their modeling simplicity, running speed, and low processing power requirement compared to 3D simulations. This thesis investigates the disparities in losses between 2D-based design simulations and a 3D realization of solenoidal inductors featuring distributed gaps. The inductor geometry entails a helical copper winding enveloped by rings and end caps made of a magnetic material. There are multiple small air gaps between the magnetic rings that are required for energy storage, and having multiple small gaps instead of a single large one is referred to as "distributed gaps". The simulated 3D structure possesses higher losses than its 2D cross-section due to inherent structural features. The research culminates in two contributions. First, a practical two-variable design approach is presented, leveraging matrix algebra to succinctly represent the decision quantities as functions of the two most important variables to the application. The procedure results yield several informative plots that assist in selecting a design that meets the efficiency and thermal limits. Second, a detailed explanation is provided on the 3D loss effects, along with the recommended design considerations and a method to estimate the dominant 3D loss effect using simple 2D simulations. The design recommendations address a 26-fold increase in the loss of the outer rings and reduce the copper loss by 55%. A simple 2D simulation method is proposed to accurately predict the increased 3D copper loss to within 3% and runs 60 times faster than the equivalent 3D simulation. Additionally, a derived equation for the optimal turn spacing aligns with the simulation results with <6% error, offering practical insights for design optimization. These results enable the design of a low-loss solenoidal inductor and accurate loss estimations without running lengthy and complicated 3D simulations. A 13 µH, 150 Arms solenoidal inductor prototype for operation in a 10 kV-to-400 V, 50 kW converter cell serves as empirical validation, corroborating the efficacy of the proposed analysis and design methodology.

Among the multilevel (ML)-voltage source converters (VSCs) for medium voltage (MV) and high power (HP) applications, the most used power topology is the three level (3L)-neutral point clamped (NPC)-VSC, due to its features such as common direct current (DC)-bus capability with medium point, absence of switches in series-connection, low part count, and straightforward control. The use of MV-insulated gate bipolar transistor (IGBT) modules as power switches offers further advantages like inexpensive gate drivers and survival capability after short-circuit. However, the IGBT modules have a reduced life cycle due to thermal stress generated by load cycles. Despite the advantages of the 3L-NPC-VSC, its main drawback is the uneven power loss distribution among its power devices. To address this issue and to improve other characteristics, more advanced ML converters have been developed. The 3L-active neutral point clamped (ANPC)-VSC allows an improved power loss distribution thanks to its additional IGBTs, which increase the number of feasible zero-states, but needs a loss balancing scheme to choose the proper redundant zero-state and a more complex commutation sequence between states. The 3L-neutral point piloted (NPP)-VSC improves the power loss distribution thanks to the use of series-connected switches between the output terminal and the positive and negative DC-link terminals. Other advanced power topologies with higher amount of levels include the 5L-ANPC-VSC, which has a flying capacitor per phase to generate the additional levels; and the 5L-stacked multicell converter (SMC), which needs two flying capacitors per phase. The goal of this work is to is to evaluate the performance of the aforementioned NPC-type ML converters with common DC-link, included the ones with flying capacitors, in terms of the power loss distribution and the junction temperature of the most stressed devices, which define, along with the nominal output voltage, the maximum power the converter can deliver. A second objective of this work is to describe the commutations of a MV 3L-ANPC-VSC phase leg prototype with IGBT modules, including all the intermediate switching states to generate the desired commutations.:Figures and Tables V Glossary XIII 1. Introduction 1 2. State of the art of medium voltage source converters and power semiconductors 5 2.1. Overview of medium voltage source converters 5 2.1.1. Multilevel Voltage Source Converter topologies 6 2.1.2. Application oriented basic characteristic of IGCTs and IGBTs 10 2.1.3. Market overview of ML-VSCs 11 2.2. IGBT modules for MV applications 12 2.2.1. Structure and Function 12 2.2.2. Electrical characteristics of the IGBT modules 15 2.2.3. Power losses and junction temperatures estimation 17 2.2.4. Packaging 19 2.2.5. Reliability and Life cycle of IGBT modules 21 2.2.6. Market Overview 23 2.3. Summary of Chapter 2 23 3. Structure, function and characteristics of NPC-based VSCs 25 3.1. The 3L-NPC-VSC 25 3.1.1. Power Topology 25 3.1.2. Switching states, current paths and blocking voltage distribution 26 3.1.3. Modulation of three-level inverters 28 3.1.4. Power loss distribution 32 3.1.5. “Short” and “long” commutation paths 33 3.2. The 3L-NPP-VSC 34 3.2.1. Power Topology 34 3.2.2. Switching states, current paths and blocking voltage distribution 35 3.2.3. Power Loss distribution 36 3.3. The 3L-ANPC-VSC 37 3.3.1. Power Topology 37 3.3.2. Switching states, current paths and blocking voltage distribution 38 3.3.3. Commutations and power loss distribution 39 3.3.4. Loss balancing schemes 57 3.4. The 5L-ANPC-VSC 60 3.4.1. Power Topology 60 3.4.2. Switching states, current paths and blocking voltage distribution 61 3.4.3. Commutation sequences 62 3.4.4. Power Loss distribution 70 3.4.5. Modulation and balancing strategies of capacitor voltages 70 3.5. The 5L-SMC 74 3.5.1. Power Topology 74 3.5.2. Switching states, current paths and blocking voltage distribution 75 3.5.3. Commutations and power loss distribution 78 3.5.4. Modulation and balancing strategies of capacitor voltages 80 3.6. Summary of Chapter 3 81 4. Comparative evaluation and performance of NPC-based converters 83 4.1. Motivation and goal of the comparisons 83 4.2. Basis of the comparison 83 4.2.1. Simulation scheme 85 4.2.2. Losses and thermal models for (4.5 kV, 1.2 kA) IGBT modules 86 4.2.3. Operating points, modulation, controllers and general parameters 88 4.2.4. Life cycle estimation 94 4.3. Simulation results of the 3.3 kV 3L-VSCs 97 4.3.1. Loss distribution and temperature at equal phase current 97 4.3.2. Maximum phase current 109 4.3.3. Life cycle 111 4.4. Simulation results of the 6.6 kV 5L and 3L-VSCs 115 4.4.1. Loss distribution and temperature at equal phase current 115 4.4.2. Maximum phase current 120 4.4.3. Life cycle 128 4.5. Summary of Chapter 4 132 5. Experimental investigation of the 3L-ANPC-VSC with IGBT modules 135 5.1. Goal of the work 135 5.2. Description of the 3L-ANPC-VSC test bench 136 5.2.1. Medium voltage stage 136 5.2.2. Gate drivers and digital signal handling 138 5.2.3. Measurement equipment 139 5.3. Double-pulse test and commutation sequences 140 5.3.1. Description of the double-pulse test for the 3L-ANPC-VSC 140 5.3.2. Commutation sequences for the double-pulse test 142 5.4. Commutation measurements 142 5.4.1. Switching and transition times 144 5.4.2. Type I commutations 145 5.4.3. Type I-U commutations 150 5.4.4. Type II commutations 150 5.4.5. Type III commutations 157 5.4.6. Comparison of the commutation times 157 5.4.7. Stray inductances of the “short” and “long” commutations 163 5.5. Summary of Chapter 5 167 6. Conclusions 169 Appendices 173 A. Thermal model of IGBT modules 175 A.1. General “Y” model 175 A.2. “Foster” thermal circuit 177 A.3. “Cauer” thermal circuit 178 A.4. From “Foster” to “Cauer” 179 A.5. Temperature comparison using “Foster” and “Cauer” networks 181 B. The “Rainflow” cycle counting algorithm 183 C. Description of the wind generator example 187 C.1. Simulation models 188 C.1.1. Wind turbine 188 C.1.2. Synchronous generator, grid and choke filter 189 C.1.3. Converters 189 C.2. Controllers 190 C.2.1. MPPT scheme 190 C.2.2. Pitch angle controller 191 C.2.3. Generator side VSC 192 C.2.4. Grid side VSC 193 D. 3D-surfaces of the maximum load currents in NPC-based converters 195 Bibliography 201 Bibliography 201 / Unter den Multilevel-Spannungsumrichtern für Mittelspannungs- und Hochleistungsanwendungen ist die am häufigsten verwendete Leistungstopologie der NPC-VSC, wegen seinen Merkmalen wie die Gleichstrom-Bus fähigkeit mit mittlerem Punkt, das Fehlen von Schaltern in Reihenschaltung, eine geringe Anzahl von Bauteilen und eine einfache Steuerung. Die Verwendung von Bipolartransistor Modulen mit isolierter Gate-Elektrode als Leistungsschalter bietet weitere Vorteile wie kostengünstige Gatetreiber und Überlebensfähigkeit nach einem Kurzschluss. Die IGBT-Module haben jedoch aufgrund der durch Lastzyklen erzeugten thermischen Belastung eine verkürzte Lebensdauer. Trotz der Vorteile des 3L-NPC-VSC ist der Hauptnachteil die ungleichmäßige Verteilung der Leistungsverluste zwischen den Leistungsgeräten. Um dieses Problem zu beheben und andere Eigenschaften zu verbessern, wurden fortgeschrittenere ML-Konverter entwickelt. Das 3L-ANPC-VSC ermöglicht dank seiner zusätzlichen IGBTs eine verbesserte Verlustleistungsverteilung, wodurch die Anzahl der möglichen Null-Zustände erhöht wird, es ist jedoch ein Verlustausgleichsschema erforderlich, um den richtigen redundanten Null-Zustand, und benötigt auszuwählende komplexere Kommutierungssequenz zwischen Zuständen. Das 3L-NPP-VSC verbessert die Verlustleistungsverteilung durch die Verwendung von in Reihe geschalteten Schaltern zwischen der Ausgangsklemme und den positiven und negativen Zwischenkreisklemmen. Andere fortgeschrittene Leistungstopologien mit einer höheren Anzahl von Stufen umfassen den 5L-ANPC-VSC, der pro Phase einen fliegenden Kondensator zur Erzeugung der zusätzlichen Stufen aufweist; und den 5L-SMC, der pro Phase zwei fliegende Kondensatoren benötigt. Das Ziel dieser Arbeit ist es, die Leistung der oben genannten NPC-VSC, einschließlich der mit fliegenden Kondensatoren, hinsichtlich der Verlustleistungsverteilung und der Sperrschichttemperatur der am stärksten beanspruchten Geräte zu bewerten. Diese definieren zusammen mit der Nennausgangsspannung die maximale Leistung, die der Umrichter liefern kann. Ein zweites Ziel dieser Arbeit ist die Beschreibung der Kommutierungen eines MV 3L-ANPC-VSC- Prototyps mit IGBT-Modulen einschließlich aller Zwischenschaltzustände, um die gewünschten Kommutierungen zu erzeugen.:Figures and Tables V Glossary XIII 1. Introduction 1 2. State of the art of medium voltage source converters and power semiconductors 5 2.1. Overview of medium voltage source converters 5 2.1.1. Multilevel Voltage Source Converter topologies 6 2.1.2. Application oriented basic characteristic of IGCTs and IGBTs 10 2.1.3. Market overview of ML-VSCs 11 2.2. IGBT modules for MV applications 12 2.2.1. Structure and Function 12 2.2.2. Electrical characteristics of the IGBT modules 15 2.2.3. Power losses and junction temperatures estimation 17 2.2.4. Packaging 19 2.2.5. Reliability and Life cycle of IGBT modules 21 2.2.6. Market Overview 23 2.3. Summary of Chapter 2 23 3. Structure, function and characteristics of NPC-based VSCs 25 3.1. The 3L-NPC-VSC 25 3.1.1. Power Topology 25 3.1.2. Switching states, current paths and blocking voltage distribution 26 3.1.3. Modulation of three-level inverters 28 3.1.4. Power loss distribution 32 3.1.5. “Short” and “long” commutation paths 33 3.2. The 3L-NPP-VSC 34 3.2.1. Power Topology 34 3.2.2. Switching states, current paths and blocking voltage distribution 35 3.2.3. Power Loss distribution 36 3.3. The 3L-ANPC-VSC 37 3.3.1. Power Topology 37 3.3.2. Switching states, current paths and blocking voltage distribution 38 3.3.3. Commutations and power loss distribution 39 3.3.4. Loss balancing schemes 57 3.4. The 5L-ANPC-VSC 60 3.4.1. Power Topology 60 3.4.2. Switching states, current paths and blocking voltage distribution 61 3.4.3. Commutation sequences 62 3.4.4. Power Loss distribution 70 3.4.5. Modulation and balancing strategies of capacitor voltages 70 3.5. The 5L-SMC 74 3.5.1. Power Topology 74 3.5.2. Switching states, current paths and blocking voltage distribution 75 3.5.3. Commutations and power loss distribution 78 3.5.4. Modulation and balancing strategies of capacitor voltages 80 3.6. Summary of Chapter 3 81 4. Comparative evaluation and performance of NPC-based converters 83 4.1. Motivation and goal of the comparisons 83 4.2. Basis of the comparison 83 4.2.1. Simulation scheme 85 4.2.2. Losses and thermal models for (4.5 kV, 1.2 kA) IGBT modules 86 4.2.3. Operating points, modulation, controllers and general parameters 88 4.2.4. Life cycle estimation 94 4.3. Simulation results of the 3.3 kV 3L-VSCs 97 4.3.1. Loss distribution and temperature at equal phase current 97 4.3.2. Maximum phase current 109 4.3.3. Life cycle 111 4.4. Simulation results of the 6.6 kV 5L and 3L-VSCs 115 4.4.1. Loss distribution and temperature at equal phase current 115 4.4.2. Maximum phase current 120 4.4.3. Life cycle 128 4.5. Summary of Chapter 4 132 5. Experimental investigation of the 3L-ANPC-VSC with IGBT modules 135 5.1. Goal of the work 135 5.2. Description of the 3L-ANPC-VSC test bench 136 5.2.1. Medium voltage stage 136 5.2.2. Gate drivers and digital signal handling 138 5.2.3. Measurement equipment 139 5.3. Double-pulse test and commutation sequences 140 5.3.1. Description of the double-pulse test for the 3L-ANPC-VSC 140 5.3.2. Commutation sequences for the double-pulse test 142 5.4. Commutation measurements 142 5.4.1. Switching and transition times 144 5.4.2. Type I commutations 145 5.4.3. Type I-U commutations 150 5.4.4. Type II commutations 150 5.4.5. Type III commutations 157 5.4.6. Comparison of the commutation times 157 5.4.7. Stray inductances of the “short” and “long” commutations 163 5.5. Summary of Chapter 5 167 6. Conclusions 169 Appendices 173 A. Thermal model of IGBT modules 175 A.1. General “Y” model 175 A.2. “Foster” thermal circuit 177 A.3. “Cauer” thermal circuit 178 A.4. From “Foster” to “Cauer” 179 A.5. Temperature comparison using “Foster” and “Cauer” networks 181 B. The “Rainflow” cycle counting algorithm 183 C. Description of the wind generator example 187 C.1. Simulation models 188 C.1.1. Wind turbine 188 C.1.2. Synchronous generator, grid and choke filter 189 C.1.3. Converters 189 C.2. Controllers 190 C.2.1. MPPT scheme 190 C.2.2. Pitch angle controller 191 C.2.3. Generator side VSC 192 C.2.4. Grid side VSC 193 D. 3D-surfaces of the maximum load currents in NPC-based converters 195 Bibliography 201 Bibliography 201

This work presents a 6.5-kV 1-kA SiC bipolar diode module for megawatt-range medium voltage converters. The study comprises a review of SiC devices and bipolar diodes, a description of the die and module technology, device characterization and modelling and benchmark of the device at converter level. The effects of current change rate, temperature variation, and different insulated-gate bipolar transistor (IGBT) modules for the switching cell, as well as parasitic oscillations are discussed. A comparison of the results with a commercial Si diode (6.5 kV and 1.2 kA) is included. The benchmark consists of an estimation of maximum converter output power, maximum switching frequency, losses and efficiency in a three level (3L) neutral point clamped (NPC) voltage-source converter (VSC) operating with SiC and Si diodes. The use of a model predictive control (MPC) algorithm to achieve higher efficiency levels is also discussed. The analysed diode module exhibits a very good performance regarding switching loss reduction, which allows an increase of at least 10 % in the output power of a 6-MVA converter. Alternatively, the switching frequency can be increased by 41 %.

This work presents a 6.5-kV 1-kA SiC bipolar diode module for megawatt-range medium voltage converters. The study comprises a review of SiC devices and bipolar diodes, a description of the die and module technology, device characterization and modelling and benchmark of the device at converter level. The effects of current change rate, temperature variation, and different insulated-gate bipolar transistor (IGBT) modules for the switching cell, as well as parasitic oscillations are discussed. A comparison of the results with a commercial Si diode (6.5 kV and 1.2 kA) is included. The benchmark consists of an estimation of maximum converter output power, maximum switching frequency, losses and efficiency in a three level (3L) neutral point clamped (NPC) voltage-source converter (VSC) operating with SiC and Si diodes. The use of a model predictive control (MPC) algorithm to achieve higher efficiency levels is also discussed. The analysed diode module exhibits a very good performance regarding switching loss reduction, which allows an increase of at least 10 % in the output power of a 6-MVA converter. Alternatively, the switching frequency can be increased by 41 %.:1 Introduction 2 State of the art of SiC devices and medium-voltage diodes 2.1 Silicon carbide diodes and medium-voltage modules 2.2 Medium-voltage power diodes 3 Characterization of the SiC PiN diode module 37 3.1 Introduction 3.2 Experimental setup 3.3 Experimental results: static behaviour 3.4 Experimental results: switching behaviour 3.5 Comparison with 6.5-kV silicon diode 3.6 Oscillations in the SiC diode 3.7 Summary 4 Comparison at converter level 4.1 Introduction 4.2 Power device modelling 4.3 Determination of maximum converter power rating 4.4 Analysis 4.5 Increased efficiency through model predictive control 4.6 Summary 5 Conclusion