Electrical engineering, Polytechnique Modular multilevel converters (MMCs) may contain numerous IGBTs. The modeling of such converters for electromagnetic transient type (EMT-type) simulations is complex. Detailed models used in MMC-HVDC simulations may require very large computing times. Simplified and averaged models have been proposed in the past to overcome this problem. In this paper existing averaged and simplified models are improved in order to increase their range of applications. The models are compared and analyzed for different transient events on a MMC-HVDC system.

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This is an author-deposited version published in: https://sam.ensam.eu Handle IDAbstract-The present paper deals with the post-fault synchronization of a voltage source converter based on the droop control. In case of large disturbances on the grid, the current is limited via current limitation algorithms such as the virtual impedance. During the fault, the power converter internal frequency deviates resulting in a converter angle divergence. Thereby, the system may lose the synchronism after fault clearing and which may lead to instability. Hence, this paper proposes a theoretical approach to explain the dynamic behavior of the grid forming converter subject to a three phase bolted fault. A literal expression of the critical clearing time is defined. Due to the precise analysis of the phenomenon, a simple algorithm can be derived to enhance the transient stability. It is based on adaptive gain included in the droop control. These objectives have been achieved with no external information and without switching from one control to the other. To prove the effectiveness of the developed control, experimental test cases have been performed in different faulted conditions.

This paper demonstrates that the sum and difference of the upper and lower arm voltages are suitable variables for deriving a generalized state-space model of an MMC which settles at a constant equilibrium in steady-state operation, while including the internal voltage and current dynamics. The presented modelling approach allows for separating the multiple frequency components appearing within the MMC as a first step of the model derivation, to avoid variables containing multiple frequency components in steady-state. On this basis, it is shown that Park transformations at three different frequencies (+ω, −2ω and +3ω) can be applied for deriving a model formulation where all state-variables will settle at constant values in steady-state, corresponding to an equilibrium point of the model. The resulting model is accurately capturing the internal current and voltage dynamics of a three-phase MMC, independently from how the control system is implemented. The main advantage of this model formulation is that it can be linearised, allowing for eigenvalue-based analysis of the MMC dynamics. Furthermore, the model can be utilized for control system design by multi-variable methods requiring any stable equilibrium to be defined by a fixed operating point. Time-domain simulations in comparison to an established average model of the MMC, as well as results from a detailed simulation model of an MMC with 400 sub-modules per arm, are presented as verification of the validity and accuracy of the developed model.

Real-time (RT) simulation is a highly reliable simulation method that is mostly based on electromagnetic transient simulation of complex systems comprising many domains. It is increasingly used in power and energy systems for both academic research and industrial applications. Due to the evolution of the computing power of RT simulators in recent years, new classes of applications and expanded fields of practice could now be addressed with RT simulation. This increase in computation power implies that models can be built more accurately and the whole simulation system gets closer to reality. This Task Force paper summarizes various applications of digital RT simulation technologies in the design, analysis, and testing of power and energy systems. INDEX TERMS Applications, design, distribution networks, electric power circuits, hardware-in-theloop (HIL), modeling, rapid prototyping (RP), real-time (RT) simulation, testing, transmission networks. I. INTRODUCTION D IGITAL real-time (RT) simulators exploit advanced digital hardware and parallel computing methods to solve differential equations characterizing the system

This survey paper discusses the fundamentals of power systems modelling in the presence of large amounts of converter-interfaced generation (CIG). By referring to real-life events characterised by anomalous dynamics associated to the presence of CIG, the concepts of narrow versus broad band signals are first recalled along with the limitation of the meaning of apparent power, power factor and reactive power. In this regard, the adequacy of the phasor representation of voltages and currents waveforms is thoroughly discussed. Then, with respect to the central subject of control of power converters, a revised definition of grid-following and grid-forming converters is provided along with a thorough discussion of their associated controls and a comprehensive classification for both classes of converters. Several applications inspired by actual case studies are included in the paper in order to provide realistic application examples.

Renewable generation is mainly connected through converters. Even if they provide more and more ancillary services to the grid, these may not be sufficient for extremely high penetrations. As the share of such generating units is growing rapidly, some synchronous areas could in the future occasionally be operated without synchronous machines. In such conditions, system behaviour will dramatically change, but stability will still have to be ensured with the same level of reliability as today. To reach this ambitious goal, the control of inverters will have to be changed radically. Inverters will need to move from following the grid to leading the grid behaviour, both in steady state and during transients. This new type of control brings additional issues on converters that are addressed in this study. A solution is proposed to allow a stable operation of the system together with a limited solicitation of inverters during transients.

Electrical Engineering, Polytechnique Montreal A Modular Multilevel Converter (MMC) control system based on converter energy storage is proposed in this paper for two different control modes: active power and dc voltage. The proposed control system decouples the sub-module (SM) capacitor voltages from the dc bus voltage. One of the practical applications is the management of active redundant SMs. A practical HVDC system with 401-level MMCs including 10% redundancy in MMC SMs, is used for validating and demonstrating the advantages of the proposed control system. This paper also presents a novel capacitor voltage balancing control based on max-min functions. It is used to drastically reduce the number of switchings for each SM and enhances computational efficiency.