Due to modularity and easy scalability, modular multilevel converters (MMCs) are deemed the most suitable for high-voltage and medium-voltage power conversion applications. However, large module capacitors are usually required in MMCs to store large circulating power of line-frequency and its harmonics that flow through the capacitors. Even though several methods for minimizing the circulating power have been proposed in the literature, there is still the need for a systematic and simplified approach of addressing these control strategies and evaluating their efficacy. Moreover, the generally accepted feedback control architecture for the MMC is complicated, derived through a rigorous mathematical analysis, and therefore, not easy to intuitively comprehend. Recently, a method of modeling of the MMC based on state-plane analysis and coordinate transformation, is proposed in the literature. Based on the state-plane analysis, two kinds of circulating power in the MMC are identified that are orthogonal to each other. This means these two circulating power can be controlled individually without affecting each other. To control these circulating power, in the literature, a decoupled equivalent circuit model is developed through the coordinate transformation which clearly suggests a means for minimizing these circulating power. Further extending this work, in this thesis, the existing control concepts for reducing the circulating power are unveiled in a systematic and simplified manner utilizing the decoupled equivalent circuit model. A graphical visualization of circulating power using the state-planes is provided for each control strategy to readily compare its efficacy. Moreover, the generally accepted control architecture of the MMC is presented in an intuitive and simplified way using the decoupled circuit model. The important physics related to control implementation, originally hidden behind the complicated mathematics, is explained in detail. / Master of Science / A power converter is an electrical device that converts electrical energy from one form to another in order to be compatible with the load demand. A typical power converter consists of semiconductor switches, inductor, capacitor etc. These power converters are required in a wide range of applications: automotive and traction, motor drives, renewable energy conversion, energy storage, aircraft, power generation, transmission, and distribution, to name a few. Many of these applications are continuously increasing their power capacity to handle the escalating demands of energy that exist due to rising population numbers, industrialization, urbanization etc. Consequently, it has been a responsibility of power electronics engineers and researchers to develop power converters that can handle high voltages and high currents. Multilevel power converters have been the key-enabling developments that can withstand high-voltages while using traditional low-voltage semiconductor switches. Several multilevel converters such as the neutral point clamped converter, flying capacitor converter, cascaded H-bridge converter, modular multilevel converter (MMC) etc. have been developed and commercialized in the last two decades. Among them, the MMC is a widely accepted topology for medium- and high-voltage power conversion applications. In an MMC, several modules are stacked together in series, and each module consists of semiconductor switches and a capacitor. The series connection of the modules enables the MMC to handle high-voltage power conversion using low-voltage traditional semiconductor switches. The voltage rating of an MMC can be easily scaled-up by simply increasing the number of modules in each arm. Moreover, since several identical modules are connected in each arm, the structure of the MMC is highly modular which helps greatly in manufacturing and design. Nonetheless, in MMCs, generally large circulating power flow to the capacitor in each module, which leads to significant voltage ripples. To suppress these voltage ripples, a large capacitor is required in each module, leading to large size and weight of the converter. In the literature, several control strategies have been proposed to minimize the circulating power. However, there is still the need for a systematic and simplified approach of addressing these control strategies and evaluating their efficacy. Moreover, the generally accepted feedback control architecture for the MMC is complicated, derived through a rigorous mathematical analysis, and therefore, not easy to intuitively comprehend. Recently, a decoupled equivalent circuit model has been developed in the literature. This model clearly explains the process of power flow in the MMC between input and output and the nature of the circulating power. The equivalent circuit model provides the circulating power, that are orthogonal to each other, meaning they can be controlled individually without affecting each other. Moreover, the equivalent circuit model clearly suggests a means for minimize the circulating power by providing two "ideal" control laws. Further extending this work, in this thesis, the existing control concepts for reducing the circulating power are unveiled in a systematic and simplified manner utilizing the decoupled equivalent circuit model. Moreover, the generally accepted control architecture of the MMC is presented in an intuitive and simplified way via the decoupled circuit model. The important physics related to control implementation, originally hidden behind the complicated mathematics, is explained in detail.

A novel multilevel converter that is especially suited for high speed multi-megawatt switched reluctance motor drives operating at the medium voltage level is presented. The drive is capable of variable speed, four-quadrant operation. Each phase leg of the converter contains an arbitrary number of cascaded cells connected in series with the phase winding. Each cell contains a half-bridge chopper connected to a capacitor. The converter is named the cascaded chopper cell converter. The modular nature of the converter with the ability to add redundant cells makes it very reliable, which is a key requirement for medium voltage drive applications. A comprehensive control algorithm that overcomes the challenges of balancing and controlling cell capacitor voltages is also proposed. A suitable startup algorithm to limit startup current and switching losses, as well as ensure that cell capacitor voltages remain controlled at startup, is suggested. Details of the drive design such as component sizing and control parameter selection are also discussed. A detailed simulation model is developed and explained, and simulation results are provided for primary validation. Operation with standard current and speed control is first simulated. Then a scheme that gives way to a controller that operates the drive in single-pulse mode is developed and presented. This single-pulse control scheme controls the turn-on and turn-off angles, as well as the energization voltage level, in order to obtain high efficiency. Practical considerations related to the drive such as reliability, efficiency, and cost considerations are also discussed. Finally, a detailed comparison of the proposed converter to another competing converter is performed. Besides its scalability to high voltages and powers, the reliability and efficiency of the proposed converter makes it also a candidate for sub-megawatt applications requiring minimum downtime, or any application where high efficiency or improved performance is required. A small part of this work is also dedicated to brushless dc machines. Control methods for a new converter for brushless dc machines are proposed and verified via simulation. The main advantage of this converter with the proposed control is that it allows exact control of torque or speed up to twice the rated speed, without resorting to current phase advancing or other flux-weakening techniques. / Ph. D.

Cette thèse est dédiée aux convertisseurs multiniveaux et aborde les problématiques liées à la compensation des perturbations générées sur un réseau électrique, telles que celles produites par les fours à arc. Elle est composée de quatre chapitres couvrant les thématiques de la modélisation des réseaux électriques, des convertisseurs de tension, du contrôle commande et des stratégies de compensation, accompagnés de simulations et de résultats expérimentaux obtenus sur des équipements industriels de forte puissance. Les applications réseaux étant diverses et variées, les convertisseurs multiniveaux sont ici étudiés dans le but d’être raccordés directement sur des réseaux de distribution. Pour cela, un état de l’art des différentes topologies de convertisseurs de tension (classiques et multiniveaux) est présenté et les topologies dites modulaires, sont retenues pour une étude plus poussée. Ces convertisseurs utilisent des modules de puissance à base de ponts en H, de ½ ponts en H ou de ponts en H 3-niveaux connectés en cascade. Ils permettent ainsi de créer différents types de configurations ou couplages appelés dans ce mémoire : étoile, triangle et étoiles symétriques. Les différents modules et les stratégies pour les commander sont étudiés autour d’un composant de puissance (de type IGBT 2.5kV/1.5kA). A travers les domaines électrique et thermique, une méthode est proposée afin d’estimer les pertes, les températures de jonction et déterminer ainsi les limites d’utilisation d’un tel composant de puissance. Le dimensionnement et la fiabilité de ces convertisseurs est également abordé pour chacune des configurations envisagées, afin de dégager les avantages et inconvénients pour une application réseau. D’une façon générale, la stratégie de contrôle des convertisseurs multiniveaux est ardue, principalement lié au fait que de multiples sources de tensions continues doivent être contrôlées. Dans cette optique, des stratégies de contrôle sont proposées et validées en simulation selon les types de modules et de configurations utilisés pour la compensation des perturbations d’un four à arc. Enfin, la dernière partie de ces travaux est consacrée aux résultats expérimentaux sur la base d’un compensateur industriel dénommé DSVC (Dynamic Static Var Compensator), pour la compensation des fours à arc. Les différents résultats obtenus sur plusieurs sites industriels ont ainsi permis la validation des travaux exposés dans ce mémoire / This thesis is dedicated to the multilevel converters and addresses issues related to compensation for disturbance generated on an electrical network such as those produced by arc furnaces. It is composed of four chapters covering the themes of modeling of electrical networks, voltage converters, control and compensation strategies, with simulations and experimental results obtained on high power industrial equipment. There are many networks applications and multilevel converters are here considered to be directly connected to distribution networks. Therefore, a state of the art of different voltage converters, classics and multilevel topologies, is presented and the topologies called modular are retained for further studies. These converters use modular power cells made of H bridges, ½ bridges or 3-level H bridges connected in cascade. They allow to create different types of configurations or couplings called in this memory: star, delta and double stars. The different modules and the strategies to control them are investigated around the same switching power component (IGBT 2.5kV/1.5kA). Through electrical and thermal fields, a method is proposed to estimate their losses, junction temperatures in order to determine the limits of use of such a component of power. Sizing and reliability of these converters is also discussed for each considerer configurations in order to identify the advantages and disadvantages for a network application. Generally, the multilevel converters control strategy is difficult because of the multiple sources of DC voltages to control. In this context, control strategies are proposed and validated in simulation according to the types of modules and configuration used to compensation for disturbance of an arc furnace. Finally, the last part of this thesis is devoted to the experimental results based on an industrial compensator DSVC (Dynamic Static Var Compensator) for arc furnace compensation. The different results obtained at several industrial sites have thus allowed the validation of the various works exposed in this thesis

Ce mémoire s’inscrit dans le contexte général de la continuité de service des convertisseurs multiniveaux, lors de la défaillance d’un de leurs composants de puissance. Les structures concernées sont les topologies suivantes, largement utilisées dans les applications industrielles : Neutral Point Clamped (NPC) et Neutral Point Piloted (NPP) ou T-Type. Dans un premier temps, afin de limiter le taux de pannes du convertisseur, une commande contribuant à l’accroissement de la durée de vie des composants de puissance est tout d’abord proposée. Pour se faire, nous minimiserons sur chaque période le nombre de commutations des composants commandables à l’ouverture et à la fermeture. Cette idée a pour origine le fait qu’un convertisseur multiniveaux permet de générer le même niveau de tension de sortie à partir de plusieurs séquences de commutations différentes. Le principe de la commande proposée sera développé de manière générale, puis appliqué aux cas de structures type « Pont en H » à 5 niveaux, de type NPP (ou T-Type) et NPC. Ensuite, nous étudierons la continuité de service en mode nominal d’un convertisseur « Pont en H » à 5 niveaux, de type NPP (ou T-Type), suite à la défaillance en circuit ouvert d’un composant de puissance. Nous proposerons tout d’abord un diagnostic du défaut, constitué d’une première étape de détection, suivie d’une localisation précise du composant défaillant. Une topologie originale de convertisseur à tolérance de pannes permettra de garantir la continuité de service du système, en modifiant sa commande en adéquation avec le composant défaillant localisé. Des architectures électroniques numériques reconfigurables basées sur des composants FPGA (Field Programmable Gate Array) seront dédiées au diagnostic et à la reconfiguration de la commande ; elles permettront d’atteindre des performances temporelles élevées. L’ensemble des résultats présentés dans ce mémoire sera validé par modélisation/simulation, puis expérimentalement sur un banc de test / This thesis deals with continuity of service of multilevel power converters, during the failure of one of their power components. The studied converter topologies are the following, widely used in industrial applications: Neutral Point Clamped (NPC) and Neutral Point Piloted (NPP) or T-Type. First, to reduce the failure rate of the converter, an advanced control is proposed ; it increases the lifetime of the power components by minimizing the number of switchings over a period. This idea is based on the fact that a multilevel converter makes possible to generate the same output voltage level from several different switching sequences. The principle of the proposed control will be developed in a general way. Then, it is applied to the cases of 5-level "H-bridge" topologies, NPP (or T-Type) and NPC. Then, the continuity of service in nominal mode is studied for a 5 level "H-brige" NPP (or T-Type) converter, when an open circuit failure occurs on a power component. We first propose a fault diagnosis, consisting in a fault detection step, followed by the location of the faulty component. Then, an original fault-tolerant converter topology will ensure the continuity of service of the system, by modifying the control according to the localized faulty component. Reconfigurable digital electronic architectures based on Field Programmable Gate Array (FPGA) components will be dedicated to the diagnosis and the reconfiguration of the control; they will perform high temporal performances. All the results presented in this paper are validated by modeling and simulation. Then, they are experimentally validated on a test bench

The HVDC, High Voltage Direct Current, is important when it comes to upgrading the energy system to a renewable, sustainable and efficient system. This master thesis is investigating what is happening during the most decisive fault cases when the HVDC station is operating with inherent overload. An inherent overload operating area is defined and simulations are performed in PSCAD/EMTDC to study the transient behavior of the fault currents and overvoltages.

Les principaux critères de comparaison des convertisseurs sont le rendement, la masse, le volume, le coût et la fiabilité. Le contexte environnemental et économique et le développement des applications nomades ouvrent à l’électronique de puissance un domaine d’application de plus en plus vaste. Mais pour imposer cette technologie, il faut sans cesse améliorer ces performances et les compromis entre celles qui sont antagonistes (augmentation du rendement et diminution de la masse par exemple…) ce qui amène naturellement à la problématique de conception et d’optimisation. Le cas spécifique de l’aéronautique n’échappe pas à la règle et les contraintes y semblent encore plus fortes. La réduction de la masse, du volume et l’augmentation du rendement et de la fiabilité sont parmi les défis principaux actuels, et la transition de systèmes hydrauliques ou pneumatique vers des systèmes électriques laisse espérer à une amélioration des performances globales de l’avion. Les architectures des convertisseurs sont un moyen efficace d’améliorer les convertisseurs parce qu’ils permettent de réduire les contraintes au sein des convertisseurs tout en améliorant les formes d’onde en entrée et/ou en sortie. Parallèlement, les composants classiques en silicium ont bénéficié de larges avancés au cours de ces dernières décennies et approchent de leurs limites théoriques. Pour espérer une amélioration, des technologies en rupture sont désormais nécessaires. Au cours de ces dernières années, les technologies de semi-conducteurs dit « à grand gap », essentiellement à base de Nitrure de Gallium ou de Carbure de Silicium (resp. GaN et SiC) se sont considérablement amélioré et sont d’ores et déjà plus performant que les composants Si dans de nombreux cas. Les semi-conducteurs étant généralement plus performants lorsqu’ils ont une tenue en tension plus faible, on envisage ici de cumuler plusieurs avantages en envisageant la mise en série de composants GaN basse-tension pour améliorer l’intégration des convertisseurs de puissance. Dans un premier temps, un convertisseur multi-niveaux élémentaire de type Flying Capacitor (FlyCap) est mis en oeuvre. Des condensateurs de puissance intégrés sont utilisés, ce qui pourrait permettre de réduire l’empreinte de ces composants et de proposer une dissipation thermique commune par le dessus des composants. L’utilisation de composant au temps de commutation réduit est critique pour la fiabilité des convertisseurs. Une étude de l’influence des paramètres physique du circuit électrique sur les inductances parasites de la maille de puissance et de commande est menée permettant de mettre en évidence des règles de conception dans le but d’améliorer la fiabilité des convertisseurs. Dans un second temps, l’équilibrage dynamique de la topologie FlyCap qui est critique pour les formes d’onde et la sureté de fonctionnement est étudié. La prise en compte des pertes dans les semi-conducteurs permet d’améliorer l’estimation de la dynamique d’équilibrage. Une base de réflexion sur le dimensionnement d’un équilibreur passif est également proposée pour optimiser sa dynamique et les pertes associées. Un prototype expérimental à 5 cellules de commutation est présenté permettant d’atteindre une tension d’entrée de 270 V avec des composants 100V. / Performance, weight, volume, cost and reliability are key criteria to compare converters. Environment and economical context and the development of mobile applications lead electronics to have a wider field of application. Improving performances and tradeoff between conflicting characteristics (high efficiency and reduced weight for example) is thus constantly needed to impose this technology, which calls for design and optimization methods and tools. The specific case of aeronautics is no exception and there is in this field a high demand. Mass and volume reduction, efficiency and reliability improvement is one of the most important challenges, and the change from hydraulic and pneumatic systems to electric systems is expected to allow a global improvement of aircraft performances. Converter’s topology is a good candidate to improve and reduce the size of converters because it can reduce stress while improving the input and/or output waveforms. Meanwhile, conventional silicon components have taken advantage of wide advances in recent decades and are now close to their theoretical limits. To hope for a significant improvement, breaking technologies are now needed. In recent years, GaN and SiC Wide Band Gap semiconductors have seen significant development and are already often better than Si power devices. Lowvoltage semiconductors are generally better than higher voltage ones. Thus, we consider here cumulating advantages with a serial arrangement of low voltage GaN semi-conductors to improve power converter’s integration. First, a basic multilevel Flying Capacitor GaN-based converter is implemented. The integration of power capacitors is proposed to evaluate this technology, which could reduce the footprint of these components and could allow a common heatsink dissipation through the top of the components. Very fast turn-on and turn-off of GaN devices is critical for safe operation due to parasitic inductances. A study of physical parameters of the electrical circuit on parasitic inductances of power and control loop is conducted to lay down design rules in order to improve the reliability of converters. Secondly, dynamic balancing of Flying Capacitor which is critical for the waveforms and reliability is studied. Semi-conductor’s losses are considered to improve the estimation of dynamic balancing. A method for the design of a passive balancer is also proposed to optimize the balancing and associated losses. An experimental prototype with 5 switching cells is presented to achieve an input voltage of 270 V with 100 V rated voltage devices.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This Master Thesis presents an AC Power Source (ACPS) study contribution through the proposal, design and implementation of a novel hybrid ACPS topology. In general, the proposed hybrid topology is defined from the series connection between a Modular Multilevel Converter (MMC), called main amplifier, and a Linear Power Amplifier (LPA), called correction amplifier. With this connection, the proposed ACPS enables the output waveform synthesis with high fidelity when compared to the reference waveform, also with a high bandwidth. The main contribution of the proposed topology is to allow the simplification of the main amplifier input stage, since the MMC requires a common DC bus for providing power to the load. Throughout this study, a linear amplifier DC bus design is presented, since it influences directly the ACPS performance. Regarding the main amplifier, dynamic models are presented for the control system design, which will ensure the circulating component minimization in the MMC poles, as well as ensuring the converter power flow balance by controlling the sum and subtraction of the capacitor voltages. Additionally, the pole inductors design considering the current ripple at the switching frequency is also presented. The ACPS prototype consists of eight half-bridge submodules, triggered by the control system implemented on a Digital Signal Processor (DSP) and through the selection algorithm implemented on a Field-Programmable Gate Array (FPGA). Finally, experimental results are provided in order to guarantee the employed methodology in the main and correction amplifiers design, through bench test prototype. / Esta Dissertação contribuiu com o estudo de fontes CA de potência (AC Power Source ACPS), através da proposta, desenvolvimento e implementação de uma nova topologia híbrida de ACPS. De forma geral, a topologia híbrida proposta é definida a partir da conexão série entre um Conversor Multinível Modular (Modular Multilevel Converter MMC), denominado amplificador principal, e um Amplificador Linear de Potência (Linear Power Amplifier LPA), denominado amplificador de correção. Com esta conexão, a ACPS proposta sintetiza uma forma de onda de saída com elevada fidelidade em relação à forma de onda de referência, juntamente com elevada banda-passante. A principal contribuição da topologia proposta é a possibilidade de simplificação do estágio de entrada do amplificador principal, uma vez que o MMC requer apenas um barramento CC para o fornecimento de potência à carga. No decorrer deste trabalho, também é apresentada uma análise para o projeto do barramento CC do amplificador linear, uma vez que o mesmo influencia diretamente no rendimento da ACPS. Em relação ao amplificador principal, são apresentados os modelos dinâmicos para o projeto do sistema de controle, que deve garantir a minimização da componente circulante dos polos do MMC, bem como garantir o balanço de potência do conversor através do controle da soma e da subtração das tensões dos capacitores das células. Adicionalmente, é apresentada uma análise para o projeto dos indutores dos polos em função da ondulação de corrente na frequência de chaveamento. O protótipo da ACPS é composto por oito submódulos meia-ponte, acionados através do sistema de controle implementado em um Processador Digital de Sinais (Digital Signal Processor DSP) e através do algoritmo de do balanço das tensões implementado em uma FPGA (Field-Programmable Gate Array). A partir da implementação da ACPS em laboratório, são apresentados os resultados experimentais com o propósito de comprovar a metodologia empregada no projeto dos amplificadores principal e de correção, bem como da estratégia de controle.

Le système de transport d’électricité doit évoluer pour satisfaire les besoins du marché de l’électricité et de l’insertion de la production renouvelable. Les systèmes de transport dits HVDC se développent. Les interfaces d’électroniques de puissance vont jouer un rôle majeur et doivent faire preuve d’une extrême fiabilité, d’une grande efficacité et rester économiquement abordables.La technologie MMC (Convertisseur Modulaire Multi-niveaux) connaît un essor par rapport à des technologies classiques, comme le convertisseur trois-niveaux. Sa topologie étant complexe, deux niveaux de contrôle peuvent être définis. Le premier niveau porte sur le contrôle des interrupteurs pour équilibrer les tensions des sous-modules. Le second niveau contrôle les courants, la puissance et l’énergie dans le système.Cette thèse est axée sur ce deuxième niveau de contrôle. Une approche hiérarchisée et formelle, basée sur l’inversion du modèle pour le contrôle de l’énergie du MMC est présentée. Pour ce contrôle, différentes méthodes ont été proposées et comparées. Cela implique de développer une modélisation, mettre en place un contrôle. Différents modèles et contrôles ont été développés.Le MMC est généralement intégré dans une liaison HVDC où deux stations AC/DC ont un contrôle différent. Un soin particulier doit être apporté à la station dédiée au contrôle de la tension. En effet, la gestion de l’énergie dans le MCC est un point critique pour la stabilité de la tension.Enfin, les différents types de contrôle évoqués ont été étudiés dans le cas d’une liaison HVDC. Il a été montré que les échanges entre le bus DC et les MMC jouent un rôle important pour la régulation de la tension du bus DC / In future, the capability of the electric power transmission continues to grow due to renewable energy production and the needs of electrical market. Consequently, many HVDC transmission systems are developed. Definitely the power electronic interfaces will play a key role to provide high reliability, good efficiency and cost effectiveness for this AC/DC conversion.Recently, the Modular Multilevel Converter (MMC) has taken the advantage over the more classical converter as three-level VSC. Since MMC topology is complex, two different control levels may be distinguished: the control of the switches mainly orientated on the balance of hundreds of voltage on the elementary submodules, the higher level control whose aim is to control the currents, power and energy in the system.This thesis is oriented mainly on the latter. It discusses a hierarchical and formal approach for the MMC to control the energy in all the storage elements. At first it is shown that an energy control is required mandatory. Secondly, it supposes to develop an energetic model which is inverted to design the energy control. Then different solutions of control have been developed and discussed.In the majority of applications, MMC is integrated in an HVDC point to point link where the two AC/DC substations have different roles. A specific attention has to be paid on the station which controls the voltage since the way to manage the energy in the MMC has a critical role in the DC voltage stability.Finally, all these types of control have been tested and discussed on an HVDC. It is shown that the exchange between the DC bus and the MMC placed on both sides play a key role in the DC bus voltage regulation.

Calculate solutions of a dynamic MMC energy-based model, when the system variables, i.e. the voltages and currents, are given as periodic signals. The signals are represented by a finite number distinct frequency components. As a result, the arm energies and cell voltages are given in this signal domain and can easily be translated to time domain as well.:cplx_series.m cplx_series_demo.m energy_series.m denergy_series.m check_symmetry.m transf2arm.m LICENSE.GNU_AGPLv3 sconv2.m

Grid-connected high-power converters are found in high-voltage direct current transmission (HVDC), static compensators (STATCOMs), and supplies for electric railways. Such power converters should have a high reliability, high efficiency, good harmonic performance, low cost, and a small footprint. Cascaded converters are promising solutions for high-voltage high-power converters since they allow the combination of excellent harmonic performance and low switching frequencies. A high reliability can also be achieved by including redundant submodules in the chain of cascaded converters. One of the emerging cascaded converter topologies is the modular multilevel converter (M2C). This thesis aims to bring clarity to the dimensioning aspects and limiting factors of M2Cs. The dc-capacitor in each submodule is a driving factor for the size and weight of the converter. It is found that the voltage variations across the submodule capacitors will distort the voltage waveforms and also induce alternating components in the current that is circulating between the phase-legs. It is, however, shown that it is possible to control the alternating voltage by feed-forward control. It is also shown that if the circulating current is controlled, the injection of a second-order harmonic component can extend the operating region of the converter. The reason for this is that when the converter is operating close to the boundary of overmodulation the phase and amplitude of the second-order harmonic is chosen such that the capacitors are charged prior to the time when a high voltage should be inserted by the submodules. The controller that is used must be able to balance the sbmodule capacitor voltages. Typically, an increased switching frequency will enhance the performance of the balancing control scheme. In this thesis it is shown that the capacitor voltages can be balanced with programmed modulation, even if fundamental switching frequency is used. This will, however, increase the voltage ripple across the aforementioned capacitors. In order to quantify the requirements on the dc-capacitors a general analysis is provided in this thesis which is based on the assumption that the capacitor voltages are well balanced. It is found that for active power transfer, with a 50 Hz sinusoidal voltage reference, the capacitors must be rated for a combined energy storage of 21 kJ/MW if the capacitor voltages are allowed to increase by 10% above their nominal values. / <p>QC 20121127</p>