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The cascaded control approach is widely used to control the modular multilevel converter (MMC). Such approach allows to manage all MMC state variables in a decoupling manner based on modes separation. This separation introduces conditions related to control objectives response time resulting in slow dynamics. This will limit the use of the potential of MMC energy that is considered as a freedom for ac and dc grids ancillary services. On another side, robustness properties for a given control are also of a great interest when considering unmodeled uncertainties and disturbances. Starting from these requirements, a linear feedback dead-beat control is proposed in this article to accelerate the inner loops and consequently the outer ones (control objectives). The proposed control, based on exact discrete-time model of the MMC in which the sampling period is considered a priory in the control design, is synthetized by taking into account the control outputs saturation. The stability proof of the control and the robustness analysis as well as experimental results under fault grid operations highlighted on small-scale MMC will be presented in this article. The comparison with a continuous-time sliding mode control shows the advantage of the proposed control regarding the response time and undesired oscillation reduction.

International audience; This paper investigates the impact of embedded Voltage Source Converter-based High Voltage Direct Current (VSC-HVDC) links on AC grids transient stability. Firstly, using Transient Energy Functions (TEF), it is demonstrated that VSC-HVDC links controlled to track constant power references, do not inherently improve transient stability of the surrounding AC grid as an AC line naturally does. Then, a control law using the feedback linearization technique on a simple but representative power system is derived. The control law highlights and combines the three main actions the VSC-HVDC link can offer to enhance rotor angle stability: fast power reallocation, injection of synchronising power and injection of damping power. The control law is implemented and validated in EMT simulation. It is then shown that an HVDC link can assure the synchronisation of different AC areas even if no AC transmission lines interconnect them. Through another case study, it is shown how the HVDC link can help to share dynamic frequency reserves in order to not jeopardise the stability of the system. A last example investigates the effect of a DC fault on AC transient stability and how the control can help improving the system response.

International audience; This paper proposes a comprehensive methodology for determining the converter droop settings to ensure the voltage security in a multi-terminal direct current (MTDC) grid. The novelty lies in the introduction of the concept of over- and under-voltage containment reserves in analogy to the frequency containment reserves in AC systems. This not only gives a distinction of the contribution between the converters in rectifying and inverting modes, but also significantly facilitates the sizing of the necessary amount of reserves within their available headroom capacity of power. In particular, the constraints of converter outages, converter rating, and DC voltage deviations are all taken into account in the design of reserves. The effectiveness of the proposed approach is demonstrated by a contingency power flow analysis algorithm and EMT simulations of a four-terminal MTDC grid.

Large interconnected power networks are arguably some of the most complicated man-made systems to understand and characterize. This becomes even more complicated due to the surge of renewables that are connected (possible via HVDC lines) to the network. Faults, such as the tripping of an electricity line, can easily occur in a network, which can cause undesired oscillatory behaviour. This paper proposes an output-feedback controller that aims at diminishing these oscillations. The presented controller consists of a state-feedback gain and a Kalman filter and is tuned by employing an in this work identified model. The proposed controller ensures a lower bound on the closed-loop damping coefficients of the network.

Frequency control is considered to be an important function of multi-terminal HVDC (MTDC) systems. Sharing frequency containment reserves (FCRs) among interconnected AC systems using flexible HVDC technology is particularly attractive in the European context. However, coordination of the contribution between systems with different sizes, quality requirements and dynamic characteristics requires harmonized rules and well-defined control strategies. If the controllers are not properly designed, they can lead to disproportional supports, noncompliance with the existing regulation framework, or even degradation of the frequency quality. This paper analyzes several frequency control solutions for MTDC systems in terms of the adequacy of the expected contribution to the frequency containment process. The performance analyses are then confirmed using load-frequency models coupled with a three-terminal DC system. It is revealed that certain control solutions result in insufficient performance with respect to the desired FCR provision. The proposed distributed solution for each pair of converters can be the most compliant with the existing framework while keeping the highest degrees of freedom.

This paper presents a distributed supplementary control for embedded Multi-Terminal VSC-HVDC (MTDC) grids to enhance the transient stability of the surrounding AC grid. Firstly, the need of supplementary controllers for embedded MTDC grids is demonstrated via the study of the Transient Energy Functions (TEF) of a simple hybrid AC/DC power system. Then, the proposed control structure is presented. This control aims to enhance the angle stability of the surrounding AC system via the modulation of the active power references of the converters. The objective of the control is to enhance AC transient stability while keeping the power balance of the DC grid even if converters reach their active power limits. The proposed control uses frequency, and angle measurements at the Point of Common Coupling (PCC) of the converters. The idea behind the proposed strategy is to match the control actions, and limits of each pair ( $i,j$ ) of converters. If converter $i$ modulates its power, converter $j$ modulates the same amount of power in the opposite direction. The concept of virtual links is used in this paper to represent this matching. Finally, the proposed controller is tested on a modified version of the IEEE 39 bus system using EMT simulations.

International audience; For real-time power system dynamic monitoring, it is important to provide accurate estimations of the network's critical electro-mechanical modes, which are time-varying frequency and damping values. This paper employs a framework for designing a multisine probing signal that, when applied in the control inputs of one of the power electronics-based grid actuators, is able to provide a damping estimation with user specified variance. The employed framework is demonstrated through simulations in a nonlinear simulator using models of varying complexity.

This paper attempts to shed light on potential stability issues in MMC-based HVDC systems. In particular, the focus is given to the influence of converter control parameters on the small-signal stability of an HVDC system equipped with large fault current limiting DC reactors. Those DC reactors are often required to reduce the rate-of-rise in fault currents and thus to limit the currents below the maximum interruption capability of DC Circuit Breakers (DCCBs). However, the introduction of large DC reactors can degrade the system stability. The small-signal stability analysis of an MMC-based HVDC system model, including control loops, DC reactors, and frequency-dependent HVDC cables, corroborates the unstable behavior of the system in the presence of large DC reactors. Furthermore, the influences of the bandwidth of the closed-loop power controller and the DC voltage droop parameter on the stability margin of the system are investigated. The obtained results suggest that special attention should be paid to the design and parameter of the controller in each control mode when MMC-based HVDC systems are equipped with large DC reactors.

This paper studies the dynamic interactions between the AC grids and the DC system. In this work, we focus on MMC-HVDC links interconnecting offshore wind farms and AC systems. The onshore converter is controlled in DC-voltage control mode on the DC side and in grid-forming on the AC side. The authors show the importance of DC-voltage loop design when controlling the MMC in grid-forming mode and its consequences on the MMC internal energy. In the conclusion, some recommendations are made regarding different potential solutions for supporting the DC voltage.

International audience; In recent years, the growth of renewable energy production has encouraged the development of new technologies, such as High-Voltage Direct Current (HVDC) networks, that enhance the integration of such energy sources to power transmission grids. However, this type of technology introduces new challenges in the way power transmission systems are controlled and operated, as faster and more complex control strategies will be needed in a domain which nowadays relies heavily on human decisions. In this context, Discrete Event Systems (DES) modeling and Supervisory Control Theory (SCT) are powerful tools for the development of a supervisory control to be deployed in the grid. This paper presents an application of the SCT to HVDC grids and proposes an implementation method for the resulting supervisors. The proposed method is capable of integrating decentralized and discrete-event controllers that interact with the continuous-time physical system. The language chosen for the implementation is C code, as it can be easily incorporated in power system simulation software, such as EMTP-RV. The method is validated by the simulation of the start-up of a point-to-point link in the EMTP-RV software.

Due to the complexity of the system, the control of the modular multilevel converter (MMC) constitutes an intense research activity. The stored energy inside the MMC presents a new degree of freedom, which can be exploited to provide ancillary services (oscillation damping for example). In order to do so, the response time of the energy loop has to be as fast as possible. However, when a cascaded approach is used to control the structure, this purpose cannot be achieved without fast inner loops. This paper presents a novel inner loops controller in order to obtain a high response dynamic. These controllers have been developed based on exact discrete-time models obtained from an analytic calculation of exponential of matrices. A pole placement method using feedback control has been chosen to derive their control laws. For stability matters, a pole location analysis is used to set appropriately the controller parameters, which are the sampling period and the controller gains. After validation with offline simulations and in order to show the advantages of the proposed controllers compared to the existing solutions, experimental tests have been performed using a real small-scale MMC.

International audience; This paper presents the nonlinear control of a Fully-Fed Synchronous Machine based Variable Speed Pumped Storage Plant (FFSM PSP). First, a model is developed and the control objective is established followed by the control design. The control algorithm is designed using Feedback Linearization robustified by a Second Order Sliding Mode Control (SOSMC). Using both techniques allows a fast response of the system while relaxing the conditions on the Sliding Mode Control and avoiding the known chattering problem. The control is compared with the industrial standard PI controller from the dynamic response point of view and also during short-circuits.

The growth of renewable energy production is changing the future of power transmission systems. In recent years, High-Voltage Direct Current (HVDC) technologies based on Modular Multilevel Converters (MMC) are embraced by industry and academia as a solution for the efficient integration of renewable energies into electrical grids. Faster and more complex control strategies will be needed in this domain which nowadays relies heavily on human decision. This paper proposes a Discrete Event System (DES) approach to manage the control responses to deploy in an HVDC grid. Based on Discrete Event Systems (DES) modelling and Supervisory Control Theory (SCT), this paper proposes a method for synthesizing a supervisory control for HVDC systems, which focuses on local observations and limits the number of events to be communicated. The method is validated by simulation for the start-up of a point-to-point link.

International audience; This paper attempts a detailed comparison of some of the solutions for the black start of the Offshore Wind Power Plants with Diode Rectifier based HVDC transmission. The major challenges and control requirements to ensure the black start operation are explained following a brief review of the existing capabilities of wind generators. The various solutions surveyed as part of the study are presented along with a detailed comparison. Moreover, a case study is simulated, supported by calculations to highlight the power requirements of the offshore grid during black start, enabling further assessment of the black start solutions discussed.

Modeling Modular Multilevel Converters requires a special attention due to the strong associations between the accuracy and the complexity of models on one hand and the accuracy and simulation speed on the other hand. This paper investigates different implementation techniques for MMC models and gives an overview about their development and rapidity.

This paper proposes a new approach to tuning voltage droop parameters in an MMC-based multi-terminal HVDC system. Using the new degree of freedom offered by the virtual capacitor control, the transient behavior of the DC voltage can be improved without adverse effects on the connected AC grids.

International audience; Electromechanical oscillations are inherent to power networks. Although it is possible to partially damp these oscillations, it is impossible to eliminate them completely. This oscillatory behavior can lead to major breakdowns in power networks, especially when the damping is relatively low. It is therefore important to provide accurate estimations of the network’s damping values. These estimation can be obtained via system identification for which a probing signal needs to be designed. This paper presents a framework for designing a specific probing signal that is able to provide accurate damping estimations with a user-defined variance. A power spectrum of the probing signal is determined by solving an optimization problem with Linear Matrix Inequality constraints. The objective function is defined as a weighted sum of the probing signal’s power and a level of disturbance caused by probing the network. A desired level of the damping estimation’s variance is set as a constraint. The time-domain realization of the obtained power spectrum is described by a multisine, which is the actual probing signal applied to the network. The employed framework is demonstrated through nonlinear simulations using the Kundur with an embedded HVDC link and NORDIC 44 networks.

In this article, the interactions between AC grid and existing VSC control modes are analyzed. First, three VSC control modes, namely grid-feeding, grid-supporting and grid-forming, are compared with each other in order to assess VSC/grid coupling level. Then, in order to underscore the growing role of VSCs in transmission systems, an elementary benchmark network is considered. It includes an equivalent SM (Synchronous Machine), a VSC, a load and a transmission line with a varying electrical distance. Thereafter, a modal analysis is conducted on this model to study the interactions between the different VSC controls and the SM dynamics using a Matlab/Simulink environment. The converter penetration rate is represented by a variable power ratio between the converter and the machine, while the electrical distance by an RL dynamic impedance. This approach makes it possible to assess the stability limits on the VSC share imposed by the system strength. Negative interactions are identified and recommendations for novel converter control strategies proposed. Besides, the influence of the AVR with the VSC in grid-forming as well as PLL-related stability issues with the VSC in grid-feeding or grid-supporting are shown to be the key limiting factors for increasing the penetration of PE-based sources.

International audience; The role of Modular Multilevel Converters (MMCs) in HVDC grid greatly differs depending on whether it is an offshore or an onshore station. From the common point in their control schemes, an unexploited ability of the MMC-the controllability of the internally stored energy-is identified in both offshore and onshore applications. The virtual capacitor control, previously proposed by the authors, makes use of this degree of freedom to provide energy contribution to the DC grid. The impact of this control is demonstrated by time-domain simulations of a five-terminal HVDC grid.

International audience; In recent years, different protection strategies for high-voltage direct current (HVDC) grids have been developed by the industry and academia for the reliable and safe operation of direct current grids. The proposed strategies have different impacts on the AC networks where HVDC grids are connected. In the case of embedded HVDC grids embedded in a synchronous AC network, a partial loss of the HVDC grid might cause the desynchronisation of the AC grid. Therefore, it is of utmost importance to assess the impact of those protection strategies into the stability of the whole network. The objective of this study is to propose a methodology for the transient stability assessment of a simple but representative AC grid in case of DC fault. After validation of the methodology, some HVDC link protection criteria are defined in terms of the Critical Time to Return to Operation. These criteria will be helpful for the design of HVDC protection systems or for the sizing of future HVDC links in order to respect the constraints of the existing protection strategies.

International audience; The problem of modeling and control of multi-terminal high-voltage direct-current transmission systems is addressed in this paper, which contains five main contributions. First, to propose a unified, physically motivated, modeling framework — based on port-Hamiltonian representations — of the various network topologies used in this application. Second, to prove that the system can be globally asymptotically stabilized with a decentralized PI control that exploits its passivity properties. Close connections between the proposed PI and the popular Akagi's PQ instantaneous power method are also established. Third, to reveal the transient performance limitations of the proposed controller that, interestingly, is shown to be intrinsic to PI passivity-based control. Fourth, motivated by the latter, an outer-loop that overcomes the aforementioned limitations is proposed. The performance limitation of the PI, and its drastic improvement using outer-loop controls, is verified via simulations on a three-terminal benchmark example. A final contribution is a novel formulation of the power flow equations for the centralized references calculation.

International audience; The modular multilevel converters (MMCs) have emerged as the most suitable converter technology for HVDC applications. Besides the recognized advantages over conventional voltage source converters, one of the remarkable features of the MMC is its ability to store energy in the distributed submodule capacitors. This important feature can be used to mitigate the fluctuations of the DC voltage, which is inherently volatile against power disturbances compared to the frequency of conventional AC systems. This paper proposes a novel control strategy, called virtual capacitor control, which enables the utilization of the energy storage capability of the MMC to attenuate voltage fluctuations of HVDC systems. With the proposed control, the MMC behaves as if there were a physical capacitor whose size is adjustable and can be even bigger than the physical capacitor embedded in the converter. This control allows the system operator to optionally adjust this virtual capacitor of each MMC station and, thus, it provides an additional degree of freedom to the HVDC system operation. The EMT simulations of a 401-level MMC-based HVDC link system show the effectiveness of the proposed control to improve dc voltage transient dynamics.

This paper deals with the identification of High Voltage Direct Current (HVDC) cables in order to obtain an accurate model. The context of large penetration of renewable energy sources in electric production requires to consider new power grids. Nowadays the HVDC multi-terminal networks are going to develop, and with them, new identification and control problems appear. We propose an output-error method to the parametric estimation of HVDC cable models. A π-model, which takes into account the coupling between core and screen of the cable, is estimated. The approach is tested with simulated noise-free data given by the Wideband cable model developed on EMTP-RV software. The goal is to evaluate if the studied model represents the high-frequency behavior of the cable and the feasibility to estimate the parameters of such a model.

International audience; Ensuring that the DC voltage remains within an acceptable range is a major concern for HVDC systems. In DC systems, the capacitance is the dominant factor that determines the volatility of the DC voltage against sudden disturbances in analogy to inertia of the AC system characterizing the rate of change of the frequency. As a solution to this problem, the authors of this paper previously proposed a novel control method for Modular Multilevel Converter (MMC), named Virtual Capacitor Control. This enables to make the MMC behave as if there were a physical capacitor whose size is adjustable. Thus, it is possible to attenuate the fluctuations of the DC voltage by virtually enhancing the equivalent capacitance of the system. This paper presents a method to determine the required size of this virtual capacitor to limit the peak of the DC voltage to a desired value in the case of the HVDC grid collecting the power generated by wind farms where a master/slave control may be applied. Its advantages are explicated with analysis on the DC voltage dynamics, and its feasibility is verified by EMT simulations of a three-terminal DC grid.

Purpose Self-commuted voltage source converter (VSC) can significantly extend the flexibility and operability of an HVDC system and be used to implement the concept of multi-terminal HVDC (MTDC) grid. To take full advantage of MTDC systems, its overall behaviour must be characterized in quasi static and dynamic states. Based on the numerous literatures, a dedicated two-level VSC model and its local controllers and DC grid voltage regulators are developed for this purpose. Furthermore, the requirement of the system to guarantee all the physical constrains must be well assessed and concrete demonstrations must be provided by numerical simulations. Design/methodology/approach First, a two-level VSC model and its local controllers and DC grid voltage regulators are developed. Then, DC cable models are investigated and their characteristics are assessed in the frequency domain. Those developed models are combined to form a three-terminal HVDC grid system on Matlab/Simulink platform. To analyze the stability of this electrical system, the dynamics of the system against variations of power dispatch are observed. Findings To analyze the stability of this electrical system, the dynamics of the system against variations of power dispatch are observed. The differences in the DC grid voltage dynamics and the power flow of the converter stations coming from the embedded primary controls are analysed, and the technical requirements for both cases are assessed. Originality/value In this paper, the dynamic stability of an MTDC system has been analysed and assessed through an adequate simulation model, including its control scheme and the cable models. The interest of the improved PI model for cables is highlighted.

International audience; The complex topology of the Modular Multilevel Converter (MMC) requires some additional controllers to keep its functionalities. One of the important requirements on the MMC control is to balance the energy stored in the distributed capacitors in the arms on the three legs. However, due to the superimposed internal DC and AC power flows in the converter, the energy stored in the arms contains intrinsic oscillations. This paper provides a thorough analysis on those intrinsic oscillations on the internal energy of the MMC. Based on the analysis, a novel analytic filter is proposed, which enables to extract average value of the energy while keeping other internal dynamics stable. The proposed filter is implemented on an EMTP-RV platform. The simulation demonstrates its improved dynamic response and reduction of the internal losses compared to the existing solutions.

The main objective of the proposed work is to perform stator flux and torque high dynamics response related to specific railway requirements such as anti-slid re-adhesion control. Moreover, this type of application takes into account DC bus voltage and current limitations. In addition, systems controlled by pulse width modulation (PWM) line side converters, injects harmonic current into the feeding overhead line. Therefore, it is necessary to consider an additional harmonic constraint (harmonic shape) as an entire part of the global control system in order not to interfere with signaling systems. Consequently, the high dynamics control objectives must be considered together with the PWM constraint and voltage/current limitations, as a single control task. Real-time simulation as well as experimental results for a specific railway test bench will be presented to highlight the performances of such control algorithm.