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This article deals with DC voltage dynamics of Multi-Terminal HVDC grids with energy-based controlled Mo\-dular Multilevel Converters (MMC) adopting the commonly used power-voltage droop control technique for power flow dispatch. Special focus is given on the energy management strategies of the MMCs and their ability to influence on the DC voltage dynamics. First, it is shown that decoupling the MMC energy from the DC side by controlling the energy to a fixed value, regardless of the DC voltage level, causes large and undesired DC voltage transient after a sudden power flow change. Second, the Virtual Capacitor Control technique is implemented in order to improve the results, however, its limitations on droop-based MTDC grids are highlighted. Finally, a novel energy management approach is proposed to improve the performance of the later method. These studies are performed with detailed MMC models suitable for the use of linear analysis techniques. The derived MTDC models are validated against time-domain simulations using detailed EMT MMC models with 400 sub-modules per arm.

The Modular Multilevel Converter (MMC) represents the recent development among the diverse available topologies of VSC and is allegedly the most suitable solution for converters in HVDC transmission systems. This paper investigates the stability of modular multi-level converters based HVDC system connected to a weak ac grid. Small signal stability based on eigenvalues analysis is used to study the interaction between the weak ac grid and the converter. The impact of control parameters, mainly the synchronization system (i.e., Phase Locked Loop) on the stability of the MMC is also considered in frequency domain. Finally, time-domain simulations and frequency domain analysis are carried out using MATLAB/Simulink and symbolic toolbox to validate the effectiveness of the proposed study.

The interconnections of offshore wind farms have raised the interest of Multi-Terminal DC (MTDC) grids with voltage source converters, specifically with the Modular Multilevel Converter (MMC) topology. For controlling the DC bus voltage, the droop control strategy proves to be one of the most effective since it allows a shared effort between the different converters connected to the DC grid. Furthermore, these MTDC grids may likely result in multivendor schemes, where each converter could have different control strategies among them. Specially on the way that the internal energy of the MMC is managed, which may have an important impact on the DC voltage dynamics. This paper proposes a simplified model to represent the dynamic behavior of the DC grid including converters which highlights the droop gain and the energy management of the converter as main influential parameters. The performance of this model was assessed by comparisons with EMT simulations on a representative case study with different parameters.

The average value model of the Modular Multilevel Converter (MMC) is in general non-linear with time periodic variables. Recent developments demonstrated how the MMC model can be transformed into a a Steady-State Time Invariant (SSTI) representation allowing for linearization of the model. While previous modeling efforts for small-signal eigenvalue analysis considered mainly the classical Circulating Current Suppressing Controller (CCSC), this paper presents an approach for representing a complete energy-based control system in a set of Synchronously Rotating Frames (SRFs). This is obtained by separating the state variables according the their frequency components and applying corresponding Park transformations. The resulting model is based on existing controllers implemented in the stationary abc frame, and enables small-signal stability studies of MMCs with such control systems. Simulations results comparing an EMT type MMC model with the complete SSTI system validate the proposed approach.

This paper presents a small signal eigenvalue analysis applied to a droop-controlled HVDC terminal based on the Modular Multilevel Converter (MMC) topology. The applied linearised model is derived from previous modelling efforts recently proposed in the literature, which rely on the application of three Park transformations at different frequencies (w, −2w and 3w) applied to associated variables defined within the MMC model. The investigated configuration is controlled under the well-known Circulating Current Suppression Controller (CCSC). The developed small-signal model is utilized to evaluate two different approaches for calculating the insertion index for modulation of the MMC, and to reveal potential stability problems in the system. It is demonstrated by participation factor analysis that the potentially unstable modes of the system under the investigated control strategy are linked to the uncontrolled zero-sequence component of the common-mode current resulting from the CCSC

The Modular Multilevel Converter (MMC) is a most promising converter technology for the High Voltage DC application. The complex topology of the MMC requires several additional controllers to balance the energy in the capacitors which are distributed all over the converter. Typically, there is a requirement of two controls; one is the regulation of the total energy in each leg, and the other is the distribution of the energy between the upper and the lower arms. This paper presents control strategies for the latter one being capable of distributing the energy only by internal power flow, so that undesired interference with the associated grids can be completely avoided. The proposed controls are achieved by forcing the common mode currents to be balanced while keeping the classic cascaded control structure as much as possible. The effectiveness and advantage of the proposed solutions are demonstrated by simulations.

The Modular Multilevel Converter (MMC) has enhanced the feasibility of Multi-Terminal DC grids (MTDC). For controlling the DC bus voltage in the MTDC grids, the droop control is the most promised technique. This paper evaluates the dynamic impact of the way of controlling the MMC on the MTDC grids. Results are compared with a simplified model that highlights the key elements for the dynamic behavior of the DC bus voltage, the droop parameter and the equivalent DC bus capacitor.

The Modular Multilevel Converter (MMC) represents the recent development among the diverse available topologies of VSC and is allegedly the most suitable solution for converters in HVDC transmissions. This paper presents an Average Value Model (AVM) of the MMC that still includes the characteristic internal dynamics that are non-existent in traditional 2-level VSCs. This AVM and its control are described and linearized in order to obtain a state-space model of the MMC that can easily be used as a subsystem for multi-terminal HVDC (MTDC) grids. A case study showing a 401-level MMC-based HVDC link simulated in the EMTP-RV software validates the proposed state-space representation of the MMC.

This paper proposes an advanced control strategy for Modular Multilevel Converters (MMC) integrated in Multiterminal DC grid. In this present work, a three terminal MMC-MTDC system connecting onshore AC systems with an offshore wind farm is setup. Firstly, the voltage droop control associated to the conventional cascaded controllers for MMC stations is studied, the dynamic behavior of the DC voltage is analyzed and some drawbacks are outlined. In order to improve the dynamic behavior of the controlled DC bus voltage and the stability of MTDC system, an optimal multivariable control strategy of each MMC converter is proposed and integrated in a voltage droop controller strategy. The designed advanced controller allows to improve the overall DC grid stability and to reach the droop values designed on static considerations with acceptable dynamic behavior. By means of numerical simulations in EMTP-RV software, it is shown that the proposed control strategy performs well the stability of MTDC grid with 400- level model for MMC compared with the classic existing control methods.

This article deals with power flow coordination of a HVDC grid used to connect offshore wind farms to several mainland grids. The coordination of the DC grid is achieved thanks to a centralized control which monitors and sends proper setpoints to manage power flow. This controller is equipped with a dedicated algorithm which enables to guarantee as much as possible the desired power transfer and cope with wind power forecast errors. Moreover, this HVDC grid controller is used as interface for the AC transmission system operator to redistribute power flow among grid side converter stations in order to de-risk AC contingencies and avoid wind power spillage. Simulations results obtained from an EMT model of a five-terminal MTDC grid with Modular Multilevel Converters prove the effectiveness of the proposed methodology in normal operation as well as the system restoration after a wind farm disconnection.

This paper focuses on simplified models of the Modular Multilevel Converter suitable for large-scale dynamic studies, in particular simulations under the phasor approximation. Compared to the existing literature, this paper does not a priori adopt the modeling approach followed for the original twolevel or three-level Voltage Source Converter. On the contrary, a model is derived following a physical analysis that preserves its average internal dynamic behavior. An equivalent control structure is proposed and various alternatives are highlighted. The proposed model with its controllers has been implemented in a phasor simulation software and its response has been validated against a detailed Electromagnetic Transient model. Finally, an illustrative example is presented with the application of the proposed model on a large grid consisting of AC areas interconnected with a multi-terminal DC grid.

The modular multilevel converter (MMC) is the most promising solution to connect HVDC grids to an HVAC one. The installation of new equipment in the HVDC transmission systems requires an economic study where the power losses play an important role. Since the MMC is composed of a high number of semiconductors elements, the losses estimation becomes complex. This paper proposes a simulation-based method for the losses estimation that combines the MMC averaged and instantaneous model in a modular way. The method brings the possibility to compare performances for different modules technologies as well as different high and low level control techniques. The losses characteristics within the MMC are also discussed. The passive losses are taken into account for the first time.

Modular Multilevel Converters (MMC) are becoming increasingly popular with the development of HVDC connection and, in the future, Multi Terminal DC grid. A lot of publications have been published about this topology these last years since it was first proposed. Many of them deal with converter control methods, other address the method of estimating losses. Usually, the proposed losses estimation techniques are associated to simple control methods For VSC (Voltage Sources Converters) topology, the losses minimization is based on the limitation of the RMS currents values. This hypothesis is usually extended to the control of MMC, by limiting the differential currents to their DC component, without really being checked.

Analyse de stabilité en petit signaux des Convertisseurs Modulaires Multiniveaux et application à l’étude des MMC dans des Réseaux HVDC Ces travaux de thèse portent essentiellement sur la modélisation, l’analyse et la commande des convertisseurs de type MMC intégrés dans un contexte MTDC. Le premier objectif de ce travail est d’aboutir à un modèle dynamique du convertisseur MMC, exprimé dans le repère dq, permettant d’une part, de reproduire avec précision les interactions AC-DC, et d’exprimer, d’autre part, la dynamique interne du convertisseur qui peut interagir également avec le reste du système. Le modèle développé peut être linéarisé facilement dans le but de l’exploiter pour l’étude de stabilité en se basant sur les techniques pour les systèmes linéaires à temps invariant. Ensuite, selon le modèle développé dans le repère dq, différentes stratégies de contrôle sont proposées en fonction de systèmes de contrôle-commande existantes dans la littérature mis en places pour le convertisseur MMC. Étant donné que l’ordre du système est un paramètre important pour l’étude des réseaux MTDC en présence de plusieurs stations de conversion de type MMC, l’approche de réduction de modèles à émerger comme une solution pour faciliter l’étude. En conséquence, différents modèles à ordre réduit sont développés, et qui sont validés par la suite, par rapport au modèle détaillé, exprimé dans le repère dq. Finalement, les modèles MMC développés ainsi que les systèmes de commande qui y ont associés sont exploités, pour l’analyse de stabilité en petits signaux des réseaux MMC-MTDC. Dans ce sens, la stratégie de commande associée à chaque MMC est largement évaluée dans le but d’investiguer les problèmes majeurs qui peuvent surgir au sein d’une configuration MTDC multi-constructeurs. Mots clés «Réseaux à courant continu multi-terminaux», «Convertisseur modulaire multiniveaux», «Modélisation dans l’espace d’états», «Stabilité en pétits signaux». Small-signal stability analysis of Modular Multilevel Converters and application to MMC-based Multi-Terminal DC grids This thesis deals with the modeling and control of MMCs in the context of MTDC. The first objective is to obtain an MMC model in dq frame which can reproduce accurately the AC- and DC- interactions, while representing at the same time the internal dynamics which may interact with the rest of the system. This model is suitable for linearization and stability studies, among other linear techniques. Then, based on the developed dq model, different control strategies are developed based on state-of-the-art MMC controllers. Since the dimension of the system is a limiting factor for studying MTDC grids with many MMCs, different reduced-order models are presented and compared with the detailed dq model. Finally, the developed MMC models with different controllers are used for the MTDC studies. The impact of the selected controllers for each MMC is evaluated to highlight the potential issues that may occur in multivendor schemes. Keywords «HVDC transmission», «Modular multilevel converter», «State-Space modeling», «SmallSignal stability analysis», «Interoperability in MTDC grids».