A transmissão de energia em corrente contínua, a partir de conversores fonte de tensão, é oportuna ao progresso do sistema elétrico de potência e tem permitido vantajosas aplicações. Muito se dá, devido ao emprego na conexão de sistemas com frequências distintas, além da redução de perdas na transmissão, provida pelas características operacionais destes. VSCs também promovem o controle do fluxo de potência, possibilitando uma efetiva contextualização no âmbito das redes inteligentes. Diante deste cenário, este estudo pretende construir um perfil de corrente através do Cálculo de Curto-Circuito Probabilístico, que emprega a Simulação de Monte Carlo, para prover as informações ao desenvolvimento de projetos de equipamentos, ajustes da proteção e controle de sistemas de transmissão em corrente contínua. A Simulação de Monte Carlo requer muitas iterações, tendo um custo computacional elevado. Se forem executadas em programas comerciais, exige um tempo elevado para leitura dos sinais em arquivos. Devido a isso, um programa de código livre usando linguagem C++, foi desenvolvido para possibilitar acesso aos sinais de interesse ainda em memória, reduzindo desta forma o tempo computacional. Além disso, para melhorar a performance, foram usadas técnicas de processamento paralelo e de computação em nuvem. Desta forma, este estudo contribui com informações indispensáveis ao projeto de equipamentos de proteção dos sistemas de transmissão em corrente contínua de forma a cooperar com o desenvolvimento consistente desta tecnologia. / Transmitting electrical power in direct current using a VSC is suitable for the progress of these systems and has remarkable and advantageous applications. This happens in order to connect two systems with distinct frequencies. This type of line is also used in the reduction of losses in transmission over long distances, provided by their operating characteristics. These converters also promote the control of power flow between distinct generation units, making them effective in the context of Smart Grids. Based on this, the purpose of this research is to construct a profile of a current using a Probabilistic Short-Circuit Analysis by Monte Carlo Simulation to provide basic data to the optimum development of design equipment in protection and control. The Monte Carlo Simulation requires many iterations to find an optimal result. An open source program using C++ language was developed to describe all the system models variables in order to decrease the computation time, as it is time consuming to read signals stored on a disk using commercial software. Moreover, in order to lower computation costs, parallel process techniques and cloud computing were used. Therefore, this study contributes to the literature by providing essential information for designing equipment for Direct Current transmission protection systems.

A transmissão de energia em corrente contínua, a partir de conversores fonte de tensão, é oportuna ao progresso do sistema elétrico de potência e tem permitido vantajosas aplicações. Muito se dá, devido ao emprego na conexão de sistemas com frequências distintas, além da redução de perdas na transmissão, provida pelas características operacionais destes. VSCs também promovem o controle do fluxo de potência, possibilitando uma efetiva contextualização no âmbito das redes inteligentes. Diante deste cenário, este estudo pretende construir um perfil de corrente através do Cálculo de Curto-Circuito Probabilístico, que emprega a Simulação de Monte Carlo, para prover as informações ao desenvolvimento de projetos de equipamentos, ajustes da proteção e controle de sistemas de transmissão em corrente contínua. A Simulação de Monte Carlo requer muitas iterações, tendo um custo computacional elevado. Se forem executadas em programas comerciais, exige um tempo elevado para leitura dos sinais em arquivos. Devido a isso, um programa de código livre usando linguagem C++, foi desenvolvido para possibilitar acesso aos sinais de interesse ainda em memória, reduzindo desta forma o tempo computacional. Além disso, para melhorar a performance, foram usadas técnicas de processamento paralelo e de computação em nuvem. Desta forma, este estudo contribui com informações indispensáveis ao projeto de equipamentos de proteção dos sistemas de transmissão em corrente contínua de forma a cooperar com o desenvolvimento consistente desta tecnologia. / Transmitting electrical power in direct current using a VSC is suitable for the progress of these systems and has remarkable and advantageous applications. This happens in order to connect two systems with distinct frequencies. This type of line is also used in the reduction of losses in transmission over long distances, provided by their operating characteristics. These converters also promote the control of power flow between distinct generation units, making them effective in the context of Smart Grids. Based on this, the purpose of this research is to construct a profile of a current using a Probabilistic Short-Circuit Analysis by Monte Carlo Simulation to provide basic data to the optimum development of design equipment in protection and control. The Monte Carlo Simulation requires many iterations to find an optimal result. An open source program using C++ language was developed to describe all the system models variables in order to decrease the computation time, as it is time consuming to read signals stored on a disk using commercial software. Moreover, in order to lower computation costs, parallel process techniques and cloud computing were used. Therefore, this study contributes to the literature by providing essential information for designing equipment for Direct Current transmission protection systems.

Ce travail de thèse a pour finalité de présenter différentes méthodologies pour l’analyse de réseaux à courant continue haut tension (HVDC). La théorie fondamentale de l‘analyse de sensitivité s’applique sur l’analyse des systèmes électriques de puissance dans les différentes étapes de la production et la transmission de l’énergie. Des outils de bases concernant cette théorie sont devenus populaires et très utilisés.En pratique, les facteurs de participation représentent un exemple de ces outils, utilisés depuis longtemps. Ils ont été proposés par (Perez-Arriaga et al., 1982). Le but des facteurs de participation est la réduction des modèles des systèmes ayant une dynamique particulière comme celle des systèmes électromécaniques. Aussi, les facteurs de participation sont utilisés pour comprendre les relations entre les variables d’état et les valeurs propres des systèmes. Nous présentons la théorie fondamentale de la sensitivité analytique dans laquelle les facteurs de participation sont basses. Pour une bonne compréhension de ces éléments de base de cette théorie, quelques exemples sont présentés. Nous présentons une formulation différente pour l’analyse par sensitivité paramétrique (Barrera Gallegos et al., 2016).Enfin, les deux méthodologies sur des exemples des réseaux HVDC. Notre comparaison permet d’exposer les limites de l’utilisation des facteurs de participation sur des réseaux HVDC.En conclusion, la nouvelle méthodologie est plus générale comparée aux facteurs de participation. Egalement, la nouvelle méthodologie, par sensitivité paramétrique, nous donne plus d’informations sur les caractéristiques dynamiques des réseaux HVDC. / The work presented in this thesis presents different methodology for parametric sensitivity of high voltage dc networks(HVDC).The fundamental theory of modal analysis has been applied for analysis of the power electrical systems in its different stages of production and transmission of energy. Tools derived from these fundamentals have become popular with its use. Among the tools used in dynamic analysis, participation factors have been used for a long time. Proposed by (Perez-Arriaga et al., 1982), they give a metric for relating states and eigenvalues of a system. The objective of the participation factors is to analyze systems with particular dynamics such as electromechanical systems. The participation factors is a tool that helps in the reduction of systems. Firstly, we present the fundaments of the sensitivity analysis upon which the participation factors are based on. The principle is illustrated with several examples.We propose a new formulation for sensitivity analysis using parametric sensitivity (Barrera Gallegos et al., 2016).In the latter, the application of participation factors and parametric sensitivity analysis is performed using HVDC networks. This comparison exposes the limitation of the participation factors for the general analysis of HVDC grids.In conclusion, the new methodology is a better and general alternative compared to traditional participation factors employed for analysis of HVDC grids. In addition, the new technique of parametric sensitivity produces several novel information related to the dynamic characteristics of the HVDC grid.

Τα τελευταία χρόνια έχει αρχίσει να διαδίδεται με γρήγορους ρυθμούς η μέθοδος μεταφοράς ισχύος μέσω συνεχούς ρεύματος. Προς αυτή την κατεύθυνση ώθηση έδωσε η ανάπτυξη νέων ημιαγωγικών διακοπτικών στοιχείων οδηγώντας σε περεταίρω ανάπτυξη και χρήση των συστημάτων μεταφοράς με συνεχές ρεύμα. Σε αυτή τη διπλωματική εργασία μελετάται ένα σύστημα μεταφοράς ισχύος με διασύνδεση συνεχούς ρεύματος (HVDC), που συνδέεται ανάμεσα σε δυο εναλλασσόμενα ηλεκτρικά δίκτυα με και χωρίς φορτίο. Την διασύνδεση συνεχούς ρέματος πραγματοποιούν δυο back-to-back AC/DC μετατροπείς VSC, που αναλαμβάνουν τους ρόλους του ανορθωτή και του αντίστροφα ισχύος. Οι μετατροπείς χρησιμοποιούν την διαμόρφωση πλάτους παλμού PWM. Αρχικά μελετάται θεωρητικά το μοντέλο των μετατροπέων και του back-to-back HVDC συστήματος και στην συνέχεια σχεδιάζεται και αναλύεται η λειτουργία του ανάμεσα σε δυο δίκτυα εναλλασσομένου ρεύματος με ή χωρίς την ταυτόχρονη παρουσία φορτίου. Τέλος προσομοιώνεται το σύστημα μέσω του λογισμικού Matlab και συγκεκριμένα της εφαρμογής Simulink για την εξαγωγή συμπερασμάτων. / In the past few years the method of power transmission by means of direct current has expanded rapidly. To this direction a push forward has been given by the development of new semi-conductive switching valves leading to a further development of transmission systems by direct current. In this thesis what is considered is a power transmission system via direct current HVDC connected between two AC electric networks with or without load. The direct current connection is achieved through back-to-back AC/DC converters VSC which undertake the role of rectifier and that of inverter of power. The converters use the Pulse Width Modulation (PWM). At first the converter model and the back-to-back HVDC system is theoretically approached and in the process what is designed and analyzed is its function between two networks of AC current with or without the simultaneous presence of load. Finally the system is simulated through software Matlab and specifically the application of simulink in order to draw conclusions.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The worldwide increase in the popularity of high voltage direct current (HVDC) power transmission application has led to questions regarding the performance of high voltage alternating current (HVAC) insulators when energized under HVDC excitation. These questions have led researchers conduct numerous research projects worldwide. A particular question NamPower (the power utility in Namibia) has faced is: how do these insulators perform and age when energized under HVDC excitation in heavily polluted environments? This question was only partly answered by some insulator ageing tests conducted under laboratory conditions for HVDC excitation. However, the natural ageing tests on insulators, which are preferred, have to date been confined predominantly to HVAC excitation voltages. Thus, this research was initiated to investigate the natural ageing performance of insulators under both HVAC and HVDC excitations, when subjected to harsh marine pollution environments. This research project involved performance and ageing tests on three identical sets of line insulators made from different insulator materials, energised under HVAC and both polarities HVDC excitations respectively. The tests were conducted at Koeberg insulator pollution test station (KIPTS), which is a natural marine pollution insulator test station located near Cape Town, along the west coast of South Africa, approximately 50 m from the sea. The set of insulators consisted of EPDM silicone alloy rubber, HTV silicone rubber, RTV silicone rubber coated porcelain, Porcelain and Glass insulators. The HVAC excitation voltage was chosen as 12.7 kV r.m.s. phase-to-ground and it was decided to use a HVDC excitation voltage equal to this value. The research results showed that the insulators made from HTV silicone rubber performed better than the insulators made from EPDM silicone alloy rubber under all excitation voltages. It is also showed that RTV silicone rubber coated porcelain insulators performed better than Glass and Porcelain insulators under all excitation voltages. / AFRIKAANSE OPSOMMING: Die wêreld wye toename in gewildheid van hoë spanning gelyk stroom (HSGS) krag transmisie aplikasie het gelei na vrae oor die effektieweteit van hoë spanning wissel stroom (HSWS) insolators in HSGS aplikasies. Hierdie vrae het gelei na baie navorsings projekte. Een vraag waarmee NamPower (die krag voorsienings maatskapy in Namibia) gekonfronteer was, was hoe gaan die insolators wat onderworpe is aan ’n HSGS toevoer reageer in ’n baie besoedelde omgewing. Hierdie vraag was slegs gedeeltelik beantwoord deur verouderings toetse op insolators wat gedoen is in ’n labaratorium met ’n HSGS toevoer. Inteendeel, die meeste natuurlike verouderings toetse op insolators, soos verkies, is meestal gedoen met ’n HSWS toevoer. Om hierdie rede was hierdie navorsing begin om natuurlike verouderings toetse te doen op insolators onderworpe beide aan HSWS en HSGS toevoere binne ’n marien besoedelde omgewing. Hierdie navorsings projek gaan oor prestering en verouderings toetse op drie, identiese, transmissie lyn insolator stelle, wat onderskeidelik onderworpe was aan HSWS en beide polariteite HSGS toevoere. Die toetse was gedoen by Koeberg insolator besoedeling toets stasie (KIBTS) wat naby Kaapstad geleë is langs die weskus van Suid Africa omtrent 50 m van die see. ’n Stel toets insolators bestaan uit EPDM silikon allooi rubber, HTV silikon rubber, RTV silikon rubber bedekte porselein, Porselein en Glas insolators. Die HSWS waarde waarmee die insolators getoets was, was 12.7 kV w.g.k., fase-na-grond, en dit was besluit om ’n HSGS waarde gelyk aan hierdie spannings waarde te gebruik. Die navorsings resultate wys dat insolators wat gemaak is met HTV silikon rubber presteer beter as insolators wat met EPDM silikon allooi rubber gemaak is onder al die verskillende toevoere. Dit wys ook dat RTV silikon rubber bedekte porselein presteer beter as Porselein en Glas insolators onder al die verskillende toevoere.

Modern day power systems present an open access environment, inspiring participation from small scale and large power suppliers. With multiple players in the system driven by the market, proper monitoring and control of system becomes a major concern. This transformation is accompanied by dynamic consumption patterns and rising power demands. The expanding network encompassing EHV/AC network, HVDC and FACTS devices, along with increased penetration of renewable sources, viz. solar and wind energy at medium and low voltage levels, adds to the problem. Independent System Operators (ISO) are entrusted with ensuring smooth operation, and employing proper preventive measures to eliminate a possible cascade tripping leading to a partial or large-scale blackout. To aid the operator in the process of ensuring secure operation of the grid, there are many tools that provide required information and guidance. Power flow tracing is one such tool that aids the operator in congestion management, transmission pricing, transaction evaluation, loss allocation and reactive power optimization. In this thesis, a novel active power flow tracing approach is proposed that takes into account, the real-time operating conditions and network topology. It provides the decomposition of active power flow in a line into respective components injected by various generators in the system. It also provides the contribution of the generators to various loads in the system. The approach is simple and computationally fast, making it an ideal tool to aid preventive control decisions. Based on the proposed active power flow tracing, a congestion management approach is developed. The approach indicates the least number of generators that need to be coordinated for generation rescheduling, so as to alleviate overloading in affected transmission lines and transformers. The approach also takes into consideration the operating constraints on the system, while computing the optimal rescheduling amongst selected generators using LP technique. The thesis also presents a real power loss allocation approach based on the proposed power flow tracing. Loss allocation is an important part of tariff design as the cost associated with losses amounts to a sizable fraction of total revenue collected from the loads. The approach provides information as to how losses are distributed among loads and how much each generator is providing for the loss share of each load. The approaches developed in the thesis are illustrated on a sample 10-bus equivalent system, IEEE 30-bus, and IEEE 39-bus systems. Results for typical case studies are presented for practical systems of 72-bus equivalent and 203-bus equivalent of Indian Southern grid.

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.

Transformers emit a characteristic humming noise due to magnetostriction which is the continuous change in dimensions during magnetization. The noise is amplified if the induced frequencies match the core’s natural frequencies, consequently avoiding geometries that create resonance is critical in order to fulfill customer sound level requirements. In this thesis, a high voltage direct current transformer core with two main limbs and two return limbs is studied. Using finite element analysis (FEA), the core can be modeled and analyzed in a computer environment. The main contributors of noise are the first bending and longitudinal resonance modes. Data for how these modes change with geometric alterations is collected and stored through parametric studies. An analytical expression is then constructed through Rayleigh’s energy method with added coefficients that can be correlated to FEA datasets achieving a verified model via data-fitting. A satisfactory model is created for both resonance modes. / Transformatorer avger ett karaktäristiskt surrande ljud. Ljudet uppkommer på grund av magnetostriktion vilket är förändringar i geometri som uppkommer då kärnan kontinuerligt magnetiseras. Ljudet förstärks om induktionsfrekvenserna matchar kärnans naturliga frekvenser, så att undvika kärngeometrier som skapar resonans är viktigt för att klara ljudnivåkrav som kunden har. I denna studie betraktas resonansfenomenet i en högspänningstransformator för likström (HVDC) med två lindade ben och två sidoben. Med avstamp i en finita elementanalys (FEA) kan kärnan modelleras och analyseras i en datormiljö. Data för hur resonansmoderna som bidrar mest till ljud förändras med förändringar av geometriska parametrar samlas genom parametriska studier. I detta fall analyseras de första böj- och longitudinella resonansmoderna. Ett analytiskt uttryck skapas sedan med hjälp av Rayleigh’s energimetod där coefficienter anpassas efter FEA-datan. Detta leder slutligen till en verifierad modell som fungerar väl för uppskattning av de båda relevanta resonansmoderna.

Satisfaire les besoins en énergie de manière responsable est possible grâce aux énergies renouvelables, notamment éoliennes et solaires. Cependant ces centres de captation d’énergie sont éloignés dans zones de consommation. Le transport de l’énergie via des réseaux HVDC (haute tension courant continu) permet un rendement et une flexibilité avantageuse face au transport HVAC (haute tension courant alternatif). Ceci est rendu possible grâce aux convertisseurs utilisant l’électronique de puissance. Les récents développements sur les semi-conducteurs à large bande interdite, plus particulièrement le carbure de silicium (SiC) offrent la possibilité de concevoir ces convertisseurs plus simples, utilisant des briques technologiques de plus fort calibre (≤ 10 kV). Cependant le packaging, essentiel à leur bon fonctionnement, ne suit pas ces évolutions. Dans cette thèse, nous explorons les technologies actuelles ainsi que les limites physique et normatives liées au packaging haute tension. Des solutions innovantes sont proposées pour concevoir un module de puissance haute tension, impactant que faiblement les paramètres connexes (résistance thermique, isolation électrique et paramètres environnementaux). Les éléments identifiés comme problématiques sont traités individuellement. La problématique des décharges partielles sur les substrats céramiques métallisés est développée et une solution se basant sur les paramètres géométriques a été testée. Le boitier standard type XHP-3 a été étudié et une solution permettant de le faire fonctionner à 10 kV à fort degré de pollution a été développée. / The supply of carbon-free energy is possible with renewable energy. However, windfarms and solar power plants are geographically away from the distribution points. Transporting the energy using the HVDC (High Voltage Direct Current) technology allow for a better yield along the distance and result in a cost effective approach compared to HVAC (High Voltage Alternative Current) lines. Thus, there is a need of high voltage power converters using power electronics. Recent development on wide bandgap semiconductors, especially silicon carbide (SiC) allow a higher blocking voltage (around 10 kV) that would simplify the design of such power electronic converters. On the other hand, the development on packaging technologies needs to follow this trend. In this thesis, an exploration of technological and normative limitation has been done for a high voltage power module design. The main hot spot are clearly identified and innovative solutions are studied to provide a proper response with a low impact on parasitic parameters. Partial Discharges (PD) on ceramic substrates is analyzed and a solution of a high Partial Discharge Inception Voltage (PDIV) is given based on geometrical parameters. The XHP-3 like power modules are studied and a solution allowing a use under 10 kV at a high pollution degree (PD3) is given.

La multiplication des projets HVDC de par le monde démontre l'engouement toujours croissant pour cette technologie de transport de l'électricité. La grande majorité de ces transmissions HVDC correspondent à des liaisons point-à-point et se basent sur des convertisseurs AC/DC de type LCC ou VSC à 2 ou 3 niveaux. Les travaux de cette thèse se focalisent sur l'étude, le contrôle et la commande de systèmes HVDC de type multi-terminal (MTDC), avec des convertisseurs de type VSC classique ou modulaire multi-niveaux. La première étape consiste à obtenir les modèles moyens du VSC classique et du MMC. La différence fondamentale entre ces deux convertisseurs, à savoir la possibilité pour le MMC de stocker et de contrôler l'énergie des condensateurs des sous-modules, est détaillée et expliquée. Ces modèles et leurs commandes sont ensuite linéarisés et mis sous forme de représentations d'état, puis validés en comparant leur comportement à ceux de modèles de convertisseurs plus détaillés à l'aide de logiciels de type EMT. Une fois validés, les modèles d'état peuvent être utilisés afin de générer le modèle d'état de tout système de transmissions HVDC, qu'il soit point-à-point ou MTDC. La comparaison d'une liaison HVDC à base de VSCs classiques puis de MMCs est alors réalisée. Leurs valeurs propres sont étudiées et comparées, et les modes ayant un impact sur la tension DC sont identifiés et analysés. Cette étude est ensuite étendue à un système MTDC à 5 terminaux, et son analyse modale permet à la fois d'étudier la stabilité du système, mais aussi de comprendre l'origine de ses valeurs propres ainsi que leur impact sur la dynamique du système. La méthode de décomposition en valeurs singulières permet ensuite d'obtenir un intervalle de valeurs possibles pour le paramètre de"voltage droop", permettant ainsi le contrôle du système MTDC tout en s'assurant qu'il soit conforme à des contraintes bien définies, comme l'écart maximal admissible en tension DC. Enfin, une proposition de "frequency droop" (ou "statisme"), permettant aux convertisseurs de participer au réglage de la fréquence des réseaux AC auxquels ils sont connectés, est étudiée. Le frequency droop est utilisé conjointement avec le voltage droop afn de garantir le bon fonctionnement de la partie AC et de la partie DC. Cependant, l'utilisation des deux droop génère un couplage indésirable entre les deux commandes. Ces interactions sont mathématiquement quantifiées et une correction à apporter au paramètre de frequency droop est proposée. Ces résultats sont ensuite validés par des simulations EMT et par des essais sur la plate-forme MTDC du laboratoire L2EP. / HVDC transmission systems are largely used worldwide, mostly in the form of back-to-back and point-to-point HVDC, using either thyristor-based LCC or IGBT-based VSC. With the recent deployment of the INELFE HVDC link between France and Spain, and the commissioning in China of a three-terminal HVDC transmission system using Modular Multilevel Converters (MMCs), a modular design of voltage source converters, the focus of the scientific community has shifted onto the analysis and control of MMC-based HVDC transmission systems. In this thesis, the average value models of both a standard 2-level VSC and an MMC are proposed and the most interesting difference between the two converter technologies -the control of the stored energy in the MMC- is emphasised and explained. These models are then linearised, expressed in state-space form and validated by comparing their behaviour to more detailed models under EMT programs. Afterwards, these state-space representations are used in the modelling of HVDC transmission systems, either point-to-point or Multi-Terminal HVDC (MTDC). A modal analysis is performed on an HVDC link, for both 2-level VSCs and MMCs. The modes of these two systems are specifed and compared and the independent control of the DC voltage and the DC current in the case of an MMC is illustrated. This analysis is extended to the scope of a 5-terminal HVDC system in order to perform a stability analysis, understand the origin of the system dynamics and identify the dominant DC voltage mode that dictates the DC voltage response time. Using the Singular Value Decomposition method on the MTDC system, the proper design of the voltage-droop gains of the controllers is then achieved so that the system operation is ensured within physical constraints, such as the maximum DC voltage deviation and the maximum admissible current in the power electronics. Finally, a supplementary droop "the frequency-droop control" is proposed so that MTDC systems also participate to the onshore grids frequency regulation. However, this controller interacts with the voltage-droop controller. This interaction is mathematically quantified and a corrected frequency-droop gain is proposed. This control is then illustrated with an application to the physical converters of the Twenties project mock-up.