A digital twin (DT) should continuously and accurately reflect the dynamic state of its physical twin (PT). In safety-critical and time-sensitive domains such as power systems, anomalies in PT data stemming from measurement or communication malfunctions, can compromise DT updates and the integrity of DT-driven applications. To overcome this risk, it is essential to identify and correct anomalous PT data prior to DT updates. However, conventional DT implementations lack mechanisms for evaluating PT data before executing updates, posing challenges to operational reliability and system safety. This paper proposes a trustworthy digital twin (TwDT) concept with the PT data evaluation function, supported by a denoising physics-informed autoencoder (De-PI-AE) algorithm. The PT data evaluation function of a TwDT comprises three key steps: i ) detection for direct updates using trustworthy data while flagging anomalous PT data, ii ) identification for localisation of the specific anomalous values, and iii ) estimation for correcting previously identified anomalous values. The inclusion of each component effectively forms an entire PT data evaluation function to ensure reliable and continuous updates. A power system digital twin (PSDT) is used to demonstrate the development and effectiveness of the proposed De-PI-AE algorithm to realise the TwDTs, highlighting its strong potential to be embedded into DT update process. The De-PI-AI solution outperforms other artificial intelligence-based (AI) algorithms, achieving detection (88.5%), identification (98.9%), and estimation (mean square error reduced by 98.8%) of the specific PT data anomaly. The proposed solution enables the detection, identification, and estimation under one framework, while achieving positive performance gains. The proposed TwDT with the PT data evaluation function can be adopted and expanded to more DTs within power systems and beyond.

Converter valve-side single-phase-to-ground (SPG) faults are among the most critical issues affecting the secure operation of modular multilevel converters (MMCs). However, the fault characteristics of these faults in symmetrical monopolar MMCs have not been thoroughly explored. This paper aims to fill this gay by theoretically investigating SPG faults in such systems. The analysis considers various influencing factors, including MMC grounding schemes and dc line types. The findings demonstrate that valve-side SPG faults cause dc voltage oscillations and therefore, large discharging currents from the distributed capacitors of dc lines. These scenarios are examined through mathematical analyses and verified through simulations of a generic MMC-HVDC system using PSCAD/EMTDC. The results accurately reveal the fault behaviors under different system conditions, providing valuable insights for the design of protection systems and insulation coordination for internal ac grounding faults in MMC stations.

Valve-side, single-phase-to-ground (SPG) faults in bipolar high-voltage direct current (HVDC) systems based on half-bridge modular multilevel converters (HB-MMCs) result in i) significant upper arm overvoltage, and ii) non-zero-crossing currents in the grid-side ac circuit breaker (ACCB). In this paper, a dc-link thyristor-based protection scheme is proposed to address both issues. The dc-link thyristor branches are installed in the dc terminal of each station. A dc short-circuit loop is formed following triggering the thyristor branch, redirecting currents from the upper arms to the branch, thus preventing continuous capacitor charging in the upper arms. Moreover, the creation of the dc short-circuit loop induces symmetrical components in the grid-side currents, which ensure current zero-crossings in the grid-side ACCB. The peak current flowing into the dc-link thyristor branch is also calculated to facilitate the design of the thyristor branch. The effectiveness of the proposed protection scheme is validated in an HB-MMC HVDC system simulated in PSCAD/EMTDC.

Power system digital twins (PSDTs) promise ad-vanced solutions to reshape power system applications by op-erating in parallel with their physical counterparts to generate valuable operational insights. Digital twins (DT) enable what-if scenario testing, which can evaluate the outcomes of hypothetical situations or events without disrupting the normal operation of actual power systems. The lack of a framework supporting different applications while simultaneously managing real-time and historical data hinders the execution of multiple simultaneous PSDT instances. The parallel execution of DT instances has the potential to improve the efficiency of performing and analysing the outcomes of multiple tests. This paper proposes a workflow for what-if scenario testing by using DT instances to evaluate different tests under actual operating scenarios or conditions in parallel. A case study adopts real-time simulators as a virtual physical twin (VPT) and two parallel DTs in a laboratory environ-ment, respectively. Real-time simulation-based DT instances are simultaneously executed for different tests under actual operating points as the current state of VPT. It demonstrates the use and deployment of DT-enabled what-if scenario testing to reinforce power system operation. The proposed workflow is expandable and flexible, providing a practical approach that enhances DT- based applications.

Conventional grid-forming (GFM) converters are exposed to the risk of losing synchronization during severe symmetrical faults, which leads to active power fluctuation along with long recovery time. This paper proposes a current-limiting GFM control method that is capable of limiting the fault current and maintaining grid synchronization during severe symmetrical faults. A current synchronization controller is developed to replace the power synchronization controller widely used in previous work, and is designed to work compatibly with the current limiter. When a symmetrical fault occurs, GFM converters with the proposed control directly transition to a faulty steady state and maintain a constant power angle until the fault is cleared. The system returns to the pre-fault steady state after a short recovery period. The static model of the proposed current-limiting GFM control is further developed to facilitate the transient stability analysis, which proves that the performance of the proposed GFM control is not affected by the fault duration and the converter is capable of maintaining synchronization with the grid regardless of the sag depth. The fault response of converters with the proposed GFM control is validated in the control hardware-in-the-loop model.

The broader use of modular multilevel converters (MMCs) in medium-voltage direct current (MVDC) systems combined with the multiple possible network topologies of a multiterminal dc (MTDC) network pose major challenges to fault analysis, short-circuit calculations and, eventually, system reliability. In order to evaluate dc fault levels in MTDC systems with MMCs, this paper derives an expanded RLC equivalent model for representing converters and networks with system characteristic matrices, based on which, state-space analysis can be implemented to facilitate fault current calculations. Analytical calculations and simulation results of MMC and MTDC branch currents across multiple scenarios and different configurations of an MTDC network with five converters identify fault influencing factors and reveal unique characteristics of fault analysis in MVDC systems.

High penetration of renewable energy resources in the power system results in various new challenges for power system operators. One of the promising solutions to sustain the quality and reliability of the power system is the integration of energy storage systems (ESSs). This article investigates the current and emerging trends and technologies for grid-connected ESSs. Different technologies of ESSs categorized as mechanical, electrical, electrochemical, chemical, and thermal are briefly explained. Especially, a detailed review of battery ESSs (BESSs) is provided as they are attracting much attention owing, in part, to the ongoing electrification of transportation. Then, the services that grid-connected ESSs provide to the grid are discussed. Grid connection of the BESSs requires power electronic converters. Therefore, a survey of popular power converter topologies, including transformer-based, transformerless with distributed or common dc-link, and hybrid systems, along with some discussions for implementing advanced grid support functionalities in the BESS control, is presented. Furthermore, the requirements of new standards and grid codes for grid-connected BESSs are reviewed for several countries around the globe. Finally, emerging technologies, including flexible power control of photovoltaic systems, hydrogen, and second-life batteries from electric vehicles, are discussed in this article.

Power system digital twins (PSDTs) are foreseen as an essential step toward future grids that will positively affect network monitoring, operation, and planning across the whole power industry. Existing frameworks for developing a DT are bounded to particular power system components, applications and/or users. This article proposes a modular framework for the implementation of PSDTs that is flexible, robust, and cost-effective. The modularity in design enables the expansion of the twin beyond power system components and facilitates the integration of multiple services and users, without affecting the functionality of existing modules. Each module can be independently built, modified, replaced, or exchanged with other modules, unlocking multiple, more advanced, dedicated, and multidomain applications for the operation and planning of power systems. The first step toward a PSDT is illustrated based on a real-time compatible model of the Australian National Electricity Market. The model can be seen as the core of one or more distinct modules in the DT, which can be adapted and scaled for particular applications. The EMT real-time compatible model is employed to demonstrate four potential services, including renewable energy integration and “what-if” scenario cases, which are expected applications in forward-looking PSDTs.

Publisher Copyright: © 2022 IEEE.

Distributed real-time simulation (D-RTS) has been proposed as an alternative solution for the simulation of large-scale power systems. D-RTS interconnects heterogeneous and remote real-time resources virtually in order to combine and extend their simulation capabilities. A reliable D-RTS framework is necessary to virtually interconnect subsystems and manage simulation data in real time. D-RTS has mainly been implemented to combine standalone models, which only shows the feasibility and increased computing capability. However, the behavior of D-RTS has not been appropriately assessed nor investigated for decoupling models. On this basis, this paper investigates power system model decoupling and verifies its implementation for the purposes of D-RTS. The IEEE Australian Benchmark model is used as a case study. The implementation, operation, and performance of the distributed model are benchmarked against its monolithic counterpart. Results validate the simulation of the distributed model under both steady-state and transient operation, demonstrating that power system models can be decoupled in order to perform real-time simulations in a distributed manner under certain conditions.

Frequency support from photovoltaic (PV) power plants is required with new grid codes. To provide frequency support, the PV system needs to regulate the PV power in such a way that a predefined amount power reserve is kept in the PV system. Accordingly, a dynamic flexible power point tracking algorithm (FPPT) for grid-connected PV power plants is introduced in this paper. The proposed algorithm regulates the average PV power by continuously sweeping some portion of the PV curve that includes the given power reference point. The proposed strategy is different from traditional static FPPT techniques as it ensures a predefined amount of power reserve in the PV system. This power reserve provides the flexibility of increasing the power injected into the grid that can be withdrawn with a fast dynamic. Compared to the traditional solutions, in the proposed algorithm, the PV injects a constant power into the grid without any fluctuations. Effectiveness of the proposed technique in providing frequency support in a two-stage grid-connected PV plan is demonstrated by simulation results.

The rapid increase in distributed generation (DG), especially commercial and household solar PV systems in distribution networks necessitates the development of tools that provide greater insights in the behaviour of large numbers of DGs. Simulation models do not accurately capture the response of DGs to grid disturbances, and analysis of a single inverter is not representative of the behaviour of other inverters. This paper presents the development and preliminary use of an aggregation tool that allows modeling of DG response to frequency disturbances based on experimental data across a distribution feeder. By altering different renewable energy (RE) penetration levels and/or composition of inverter models in a feeder the tool can model and observe a diverse range of responses to the same grid disturbance. The tool provides preliminary insight into whether a broader simplified model of DGs is possible in distribution networks and can assist network operators with managing systems with high renewable energy penetration.

The frequency response support has been added to the new standards and grid codes for the grid-connected photovoltaic (PV) systems, to retain the reliability and quality of the power system under the high penetration of renewable energy resources. This paper proposes an algorithm for the control of cascaded H-bridge (CHB)-based PV systems to achieve frequency response for them. The required power reference, based on the grid operation condition, is distributed among the sub-modules (SMs) of the CHB converter considering the available power from each SM and operational constraints of the system. The details of the proposed control algorithm are provided, while its effectiveness is evaluated on a 1.5-MW PV simulation setup, connected directly to a 6.6-kV grid.

Low losses are a major advantage of the modular multilevel converter (MMC) in high-power applications. Losses on the MMC depend on a number of parameters such as switching frequency, voltage balancing algorithm, the topology of the sub-module (SM). This paper investigates the impact of different power factors in the losses of different MMC SMs with a focus on HVDC applications. Considering 27 different SM topologies, we demonstrate that the operation mode of the converter (inverter / rectifier) and the power factor affect not only the average losses but also the minimum and maximum losses within a period due to the voltage balancing requirements.

The interoperability challenges of emerging modular voltage source converter (VSC) topologies HVDC systems should be addressed along with rapid transformation of power systems driven by the need for more interconnected networks. This paper derives a hybrid VSC-HVDC model and demonstrates the interoperability of emerging alternate arm converter (AAC) with the state-of-the-art modular multilevel converter (MMC) in HVDC systems. The study provides primary steps towards detailed analysis of AAC interoperability in complex dc grid configurations. A detailed set of results based on the 800 MVA hybrid VSC-HVDC system demonstrate the interoperability performance of the AAC under different operating scenarios and verify associated control functions.

Contrary to reliability analysis in power systems with the main mission on safely and securely withstanding credible contingencies in day-to-day operations, resilience assessments are centered on high-impact low probability (HILP) events in the grid. This paper proposes an autonomous load restoration architecture founded on IEC 61850-8-1 GOOSE communication protocol to engender an enhanced feeder-level resilience in active power distribution grids. Different from the past research on outage management solutions, most of which 1) are not resilience-driven; 2) are reactive solutions to local single-fault events; and 3) do not address both network built-in flexibilities and flexible resources. The proposed solution harnesses 1) the imported power and flexibility from the neighboring networks; 2) distributed energy resources; and 3) vehicle to grid capacity of electric vehicles aggregations to enhance the feeder-level resourcefulness for agile response and recovery. Through real-time self-reconfiguration strategies, the suggested solution is capable of coping both single and subsequent outage events, and will engender a heightened resilience before and during the contingency period. Moreover, a resilience evaluation framework, which quantifies the contribution of all resources involved in service restoration, is developed. Real-time performance of the designed architecture is evaluated on a real-world power distribution grid using a real-time hardware-in-the-loop platform. Numerical case studies through a number of diverse scenarios demonstrate the efficacy of the proposed restoration solution in practicing an enhanced resilience in power distribution systems in response to HILP scenarios.

Flexible power point tracking (FPPT) is control of active power generated by grid-connected photovoltaic power plants (GCPVPPs) to provide various grid-support functionalities, such as frequency response and voltage support. Fast transient response is required during grid voltage and frequency variations. An algorithm, based on dynamic voltage reference design and model predictive control for the dc-dc converter in GCPVPPs is introduced in this paper. The main novelty of the proposed algorithm is fast dynamic response based on the maximum capacity of the system. This feature enables fast FPPT operation in GCPVPPs. The proposed control algorithm results in several features for the FPPT operation, including: higher bandwidth, low power oscillations during steady-state, flexibility for adding constraints based on the operation conditions, and ease of implementation without requiring any complex control parameters tuning and design procedure. The transient performance of the proposed algorithm is evaluated under conditions of voltage sag and frequency deviation. Experimental results are also provided to demonstrate the effectiveness of the proposed algorithm when subjected to rapid changes in PV reference power.

Battery energy storage systems play a vital role in renewable energy based electric power grids. Inverters are essential to integrate DC energy storage devices such as batteries to AC power grids. In this paper, a cascaded boost inverter topology based single-phase grid-connected battery energy storage system is presented. A current feedback ripple reduction method is used to mitigate the second-order harmonic ripple component of the module battery current by 97% without using additional hardware components. Furthermore, the inter-module battery state of charge (SOC) balancing is achieved by controlling the amplitude of the boost inverter module output voltage. The operation of the cascaded boost inverter based battery energy storage system is theoretically analyzed and validated using simulation results.

The negative- and zero-sequence currents of a modular multilevel converter (MMC) under imbalanced ac-grid conditions increase the maximum voltage of the submodule (SM) capacitors, which should be kept below a maximum voltage limit. This paper investigates the impact of offset pulse-width modulation (OPWM) on the capacitor voltage of the MMC under imbalanced ac-grid conditions. It is demonstrated that OPWM increases the maximum operating range of the MMC for a given set of restrictions, as it leads to a reduction of capacitor voltage by utilizing the total number of the SMs in the arms. Simulation results from an 800-MVA MMC-based HVDC transmission system demonstrate the effect of OPWM in the operation of the converters and the efficacy of the method compared to standard modulation methods.

This paper develops an alternate arm converter (AAC) high-voltage direct current (HVDC) terminal model that is compatible with the existing benchmark models of modular multilevel converter (MMC) based HVDC and dc-grid benchmark models. The developed model is a first step towards an AAC-based point-to-point transmission system and the future development of multi-converter, multiterminal benchmark models that facilitate system level studies with multiple topologies. The topology, configuration, design considerations and parameters of the model are derived in order to provide a direct equivalence with the MMC-based system. Detailed simulation studies of the multilevel converter demonstrate the operation and performance of the AAC-based benchmark model and the associated control functions.

Hybrid transmission systems associated with line commutated converters (LLC) and voltage source converters (VSC) have gradually become a particular solution for high voltage direct current (HVDC) transmission. The full-bridge submodule (FBSM) based modular multilevel converter (FB-MMC) has gained significant attention for its dc voltage reversal and fault ride through capabilities. However, large capacitance is essential for high power transmission of FB-MMC, increasing cost and size rapidly. This paper analyzes the FBSM voltage fundamental frequency and second-order harmonic fluctuations of the FB-MMC with zero sequence voltage injection. The design principles of the FBSM capacitance are also presented compared with the one without zero sequence voltage injection under equivalent voltage ripple conditions. Finally, comparative simulation results on a FB-MMC system verify the correctness of the analyses.

Selective harmonic elimination (SHE) - pulse with modulation (PWM), when applied to multilevel converters (MCs), can be optimized in case a half-wave (HW) symmetry is implemented. This kind of symmetry is able to provide a wide variety of solutions. This paper proposes a novel method, based on optimization algorithms, which provides a universal formulation of the SHE-PWM problem with HW symmetry, in such a way that different equation systems are not required to find a solution when different switching patterns are considered. In this way, the proposed technique is able to search simultaneously both the switching patterns and their associated firing angles that solve the SHE-PWM problem, without using predefined waveforms. Therefore, the search process is significantly simplified and the flexibility to find solutions with different waveforms, throughout the reference modulation index, ma, range, is increased. Different sets of solutions provided by this method have been presented and simulation results, obtained from a five-level modular multilevel converter (MMC), have proved the validity of the new proposed technique.

Tolerance and component aging can cause significant differences in the capacitance values of the submodules (SMs) in a modular multilevel converter (MMC). Depending on the modulation technique, capacitance mismatches may produce uneven switching transitions of the SMs, hence imbalances in the power losses that can lead to reliability problems. In this paper, a new algorithm that helps to achieve evenly distributed switching and conduction losses within the converter SMs is presented. The proposed algorithm is based on a modification of the common voltage balancing algorithms, balancing a weighted function of voltage and losses. Even distribution of power losses is achieved at the cost of slightly increasing the capacitor voltage ripples. The effectiveness of the strategy has been demonstrated by simulation results of a high-power grid-connected MMC.

Due to the high penetration of the installed distributed generation units in the power system, the injection of reactive power is required for the medium-scale and large-scale grid-connected photovoltaic power plants (PVPPs). Because of the current limitation of the grid-connected inverter, the injected active power should be reduced during voltage sags. In order to obtain a constant dc-link voltage in a multi-string PVPP, the extracted power from PV strings should be equal to the injected power to the grid in all operating conditions (excluding power losses). Therefore, the extracted power of PV strings should be reduced during voltage sags. In this paper, an algorithm is proposed for determining the reference voltage of the PV string which results in a reduction of the output power to a certain amount. The proposed algorithm calculates the reference voltage for the dc/dc converter controller, based on the characteristics of the power-voltage curve of the PV string and therefore, no modification is required in the the controller of the dc/dc converter. Simulation results on a 50-kW PV string verified the effectiveness of the proposed algorithm in reducing the power from PV strings under different irradiation and reference power values.

The alternate arm converter (AAC) is a multilevel converter of the same family as the modular multilevel converter (MMC). Contrary to the MMC, the AAC offers dc-fault tolerant capabilities but requires complex submodule (SM) capacitor voltage/energy regulation and circulating current control. Such control is also limited due to the small overlap period where both arms conduct and energy between the arms can be exchanged. This paper develops a double-band hysteresis-based circulating current control strategy by introducing an asymmetric overlap period control of the director switches (DSs). The proposed controller ensures zero-current switching operation of the DSs, and increases the flexibility of SM capacitor voltage regulation owing to the asymmetric overlap period. It improves the performance of current control and energy regulation for the AAC at both near sweet-spot and non sweet-spot operation without disturbing the output voltages and currents. The performance and effectiveness of the proposed controller are illustrated through simulations on MATLAB-Simulink and PLECS.

Research on dc-fault tolerant multilevel converters has gained noticeable attention over recent years. The alternate arm converter (AAC) is one of such emerging multilevel converter topologies, and a hybrid topology of the two-level converter and the modular multilevel converter (MMC). Bipolar sub-modules (SMs) that can produce both positive and negative voltages are the building blocks of the AAC. This paper analyses the operation of an AAC with the full-bridge SM (FB-SM) and the cross-connected SM (CC-SM). The conduction and switching losses of the two SM configurations are evaluated and compared, in order to identify the suitability of CC-SM for AACs and its performance compared to the FB-SM. The CC-SM with identical semiconductor devices has reduced losses compared to the CC-SM with higher rated devices in the cross-connected path. It is concluded that the CC-SM does not offer advantages in the losses, construction, and application to the AAC, compared to FB-SM.

In this work, a Model Predictive Control (MPC) strategy that combines Finite-Control-Set MPC (FCS-MPC) with Selective Harmonic Elimination (SHE) modulation pattern in its formulation is proposed to govern power converters. The key idea here is to define a desired steady-state in terms of the converter current and voltage. To do this, based on the converter current (system state) reference, an associated predefined SHE pattern is used as control input reference. Both system state and control references are included in the cost function. Therefore, during transients, the resulting predictive controller prefers to track the converter current while preserving the SHE pattern during steady-state. Thus, a fast dynamic response can be achieved throughout transients while a predefined voltage and current spectrum with low commutation frequency is obtained in steady-state by adjusting only the weighting factor of the cost function. Simulation results of the proposed SHE-MPC strategy when governing a Cascaded H-Bridge (CHB) converter are presented to highlight the benefits of the proposed predictive controller.

Control of the circulating current in the modular multilevel converter (MMC) is one of the major tasks for the proper operation of the converter topology. This paper develops a controller for the circulating current of the MMC that utilises the redundant voltage levels in 2N+1 modulated MMCs in order to regulate the current to its reference. The main advantages of the approach are the elimination of control loops that generate the voltages for the control of the circulating current, simple implementation and very fast dynamic performance. The application of the control is also independent of the circulating current reference. The simplicity and effectiveness of the proposed controller is illustrated through simulations and experimental results.

In this paper, a new approach to the discontinuous modulation technique for the operation of the modular multilevel converter (MMC) is presented. Discontinuous modulation is based on adding a zero-sequence to the original modulation signals so that each MMC arm is clamped to the upper or lower terminals of the dc-link bus during some intervals. In combination with a circulating current control, the original discontinuous modulation can reduce the capacitor voltage ripple amplitudes and the switching power losses. However, additional submodules (SMs) are required to control the circulating current. This new approach presents a clamping algorithm that eliminates the requirement of additional SMs. As a result, the conduction losses are reduced while the capacitor voltage ripples are maintained low. Simulation and experimental results on a silicon-carbide-based MMC are reported and compared against the original discontinuous modulation and a conventional carrier-based pulse-width modulation.

The Cascaded H-bridge topology is ideal for implementing large-scale converters for photovoltaic (PV) applications. The improved quality of output voltage waveforms, high efficiency due to transformer-less connection and ability to employ multiple Maximum Power Point Tracking (MPPT) algorithms are just some advantages. The main disadvantage is the required overrating to facilitate converter operation at times of unequal PV generation. Unequal generation occurs due to shading, temperature inhomogeneity and faulty cells. Capacitor voltage balancing under such conditions typically requires an increase in the number of series connected cells to inject zero sequence voltage. However, leakage current and safety requirements often dictate a need for isolation between PV arrays and the cascaded converter. Therefore, this paper proposes a converter topology that avoids the cost of extra series connected cells by making additional use of the DC-DC converters that provide isolation. H-bridge capacitor sizes are also shown to be reduced. Simulation results are presented that confirm correct operation of the proposed approach.

Multilevel cascaded H-bridge converters are becoming popular for next generation large-scale photovoltaic power converters. However, the power generation levels in the three phases can be significantly unequal, especially in a large plant, owing to the non-uniform irradiance levels and/or ambient temperatures. This paper proposes the delta-connected cascaded H-bridge converter for large-scale photovoltaic farms. Compared to the existing star connection, the delta connection reduces the converter overrating required. Experimental results obtained from a 430 V, 10 kW, three-phase, seven-level, delta connected cascaded H-bridge converter prototype are provided to demonstrate the superiority of the delta connection.

Interleaved four-quadrant, single-phase rectifiers are widely used in traction applications as part of an AC-DC-AC conversion system. This paper presents selective harmonic elimination pulse-width modulation (SHE-PWM) patterns for single-phase interleaved PWM rectifiers based on both H-bridges and full-bridge NPCs (H-NPCs). SHE-PWM waveforms are defined so that the low-order harmonics of the combined voltage and input currents on the primary of the supply transformer are eliminated. The formulation of the problem and the acquisition of solutions becomes more challenging as the number of levels in the voltage waveform increases. Solutions based on reduced eliminated harmonics are proposed in order to increase the number of solutions as well as their continuity. It is shown that the proposed formulation improves the available solution space with minimal effect to the output. The theoretical analysis are verified through simulation studies.

The voltage ripple of the capacitors of the modular multilevel converter (MMC) increases when the converter output frequency decreases. This occurs in motor drive applications at low motor speeds, where the output frequency is reduced proportionally to the converter modulation index. In this paper, a discontinuous modulation technique for reducing the amplitude of the capacitor voltage ripples and the switching losses, especially at low modulation indices, is presented. The technique is based on adding a zero-sequence to the original modulation signals, clamping the MMC arms to the upper or lower rails of the fictitious dc-link bus. A current control strategy suitable for this modulation strategy is also proposed. Simulation results under various operating points are reported along with evaluation and comparison results against the conventional carrier-based pulse-width space-vector modulation.