This paper presents a dynamic phasor-based state-space modelling framework for modular multilevel converters (MMCs) using multiple dq reference frames (DQsym). The main contribution is the development of a numerically stable state-space solver tailored to multi-dq dynamic phasor models. The solver employs integration and a systematic matrix update mechanism to consistently incorporate switching events within the unified state-space formulation, allowing harmonic interactions and topology changes to be captured without manual reconfiguration. The proposed framework is implemented as a standalone MATLAB/Simulink library to facilitate time-domain simulation and to provide a structured basis for future eigenvalue-based small-signal stability studies. The approach is validated on a point-to-point HVDC system and benchmarked against an EMT model. Results demonstrate that the DQsym-based implementation achieves EMT-level fidelity while maintaining state-space structure suitable for scalable, system-level analysis of converter-dominated grids.

Modern power systems with high penetration of inverter-based resources (IBRs) exhibit fast dynamics and complex harmonic interactions that challenge conventional modelling tools. Electromagnetic transient (EMT) simulations provide high fidelity but are computationally demanding for large-scale studies due to small time-step requirements, whereas conventional phasor-domain models neglect harmonic and higher-frequency effects to allow for larger time-steps. This paper proposes a unified dynamic-phasor-based framework (DQsym), implemented as a MATLAB/Simulink library, that combines dynamic phasors with multiple rotating reference frames and defines explicit algebraic rules for harmonic-domain operations compatible with state-space formulations, enabling systematic assembly of interconnected system-level models beyond isolated component representations. The formulation supports modelling across multiple harmonic orders and is expressed in state space, providing a natural pathway for future integration with small-signal analysis and control design tools, although such extensions are outside the scope of this paper. The approach is validated through: 1) benchmark case demonstrating higher-order harmonic modelling capability and 2) simulations of an IEEE 9-bus system expanded with point-to-point HVDC transmission based on a modular multilevel converter (MMC), where the framework reproduces fundamental and second-harmonic dynamics indicating that DQsym reproduces the overall harmonic pattern and closely matches the fundamental component compared with EMT results. The proposed framework provides a structured and accurate harmonic-domain modelling tool for the analysis of IBR-rich power systems.

The growing High-Voltage Direct Current transmission networks require modern control strategies in converter stations to ensure reliable operation and uninterrupted energy supply, particularly under unstable and low Short-Circuit ratio conditions. Conventional Grid Following converters become unstable in low Short-Circuit ratio scenarios, while modern Grid Forming converters, though more robust, exhibit slower dynamic response in high Short-Circuit ratio scenarios. This paper presents a hybrid control switching strategy based on polytopic Lyapunov functions that combines the strengths of Grid Following Control and Grid Forming Control strategies. Switching between these control strategies occurs at defined hyperplanes of polytopes derived from the state-space equations, enabling the system to maintain fast and stable performance under changing Short-Circuit ratio conditions of the grid. Because the method is grounded in polytopic Lyapunov function theory, it demonstrates inherent large-signal stability. This proposed Hybrid Control Strategy is validated using real-time ^ő simulations, showing robust performance during Short-Circuit ratio variations, highlighting its potential for future High-Voltage Direct Current systems.

With the growing integration of Modular Multilevel Converters (MMCs) in Multi-Terminal Direct Current (MTDC) transmission systems, there is a growing need for control strategies that balance economic efficiency with robust dynamic performance. This paper presents an enhanced Optimal Power Flow (OPF)-based framework for hybrid AC-MTDC systems, incorporating a novel droop control strategy that jointly coordinates DC-voltage and AC-frequency regulation. By embedding frequency control loops into the MMCs, the method enables system-wide coordination that enhances power sharing and improves resilience under disturbances. The proposed strategy dynamically adjusts converter operating points to minimize generation costs and DC-voltage deviations, balancing economic objectives with system stability. A modified Nordic test system integrated with a four-terminal MTDC grid is used to validate the approach. Optimization is performed using Julia, while the system's dynamic performance is evaluated through electromagnetic transient simulations with the EMTP software. Case studies across multiple scenarios demonstrate that the proposed droop control achieves markedly improved frequency and voltage robustness over active power control, while incurring lower generation costs than the adaptive droop benchmark. The results highlight the ability of the proposed strategy to deliver cost-effective operation without compromising performance, offering a promising solution for the coordinated control of future hybrid AC-DC transmission networks.

The increasing integration of renewable energy, particularly offshore wind, introduces significant uncertainty into hybrid AC-HVDC systems due to forecast errors and power fluctuations. Conventional control strategies typically rely on fixed setpoints and neglect frequency deviations, which compromise system stability under rapid renewable variations. To address the challenge, this paper presents an optimal power flow (OPF)-based adaptive control framework for hybrid AC-MTDC systems with offshore wind integration. To enable the time-coupled OPF to produce anticipatory setpoints under wind variability, a Random Forest-based wind-speed forecast is integrated as an uncertainty-aware data source, providing the OPF with an informed view of the wind trajectory over the dispatch horizon. The resulting baseline setpoints are further adjusted in real time through an adaptive droop control scheme that simultaneously regulates DC voltage and AC frequency to enhance robustness across a broad class of disturbances. The effectiveness of the proposed framework is validated through hardware-in-the-loop simulations against three benchmark control modes, demonstrating consistent and balanced performance under wind-forecast uncertainty, AC-side load steps, and DC-side faults.

This paper describes an advanced algorithm for current control in a modular multilevel power converter. The proposed algorithm is based on deadbeat model predictive control, which is further enhanced by applying an artificial neural network. Rather than supplanting the existing predictive controller, the neural network is used to supplement it, thereby improving control performance. The reference current tracking capability is enhanced under all operating conditions, particularly in cases where the reactive elements of the converter exhibit a relatively high resistive component. By introducing the neural network, the inherent delay of model predictive control in such scenarios is virtually eliminated, which reduces the overall control error. The network is trained offline on a set of control inputs obtained by optimizing the current response in a wide range of operating modes. Algorithm verification is performed for a three-phase modular multilevel converter in different steady-state and transient conditions. A state-of-the-art high-fidelity real-time simulator is used in both the algorithm development and verification stages.

The displacement of synchronous generation by converter-interfaced resources is reshaping power system dynamics and has made resonance stability, a category newly recognized in modern stability framework, an increasingly pressing concern. Compared with converter-driven stability, however, resonance stability has received limited systematic treatment and still lacks a unifying perspective that connects its diverse manifestations. This paper revisits resonance from a unified, mechanism-oriented viewpoint, interpreting it as an oscillatory phenomenon arising from strong coupling among closely spaced mechanical, electrical, electromechanical, or control modes of different subsystems or control loops. On this basis, resonance is classified into four types according to the interacting modal pairs, thereby placing classical subsynchronous resonance, electromechanical modal resonance, and emerging converter-related resonances within a single framework. Representative incidents are first reviewed to show how the dominant patterns have evolved from synchronous-machine interactions toward broadband, converter-dominated ones. The main analysis methods are then surveyed and mapped to the resonance types they best address. Finally, mitigation strategies are organized by resonance type around three basic levers: damping injection, impedance reshaping, and modal detuning. The review aims to provide a coherent basis for interpreting mechanisms, selecting methods, and designing mitigation measures in converter-dominated power systems.

This paper proposes the use of Model Predictive Control (MPC) with an exponential cost function for the Modular Multilevel Converter (MMC), which is widely recognized as a preferred converter topology for integrating and converting renewable energy sources into electrical energy. MPC provides a superior control strategy in the presence of system constraints, a straightforward control design, facilitates the inclusion of multiple control objectives through a flexible cost-function formulation, and offers excellent control performance. By formulating an appropriate cost function, an MMC’s operational goals can be effectively achieved through MPC. However, non-exponential MPC approaches typically employ a rectangular moving-horizon window whose length matches the chosen prediction horizon, which can affect closed-loop stability. The results based on the non-exponential cost further reveal that the choice of prediction horizon notably influences the numerical conditioning of MPC algorithms. In particular, as the prediction horizon lengthens, the numerical condition tends to degrade rapidly when a large control horizon is used. This research work uses an exponentially weighted moving horizon window to overcome these issues. Employing the exponential-based cost function further significantly reduces the condition number of the Hessian matrix, thereby improving the numerical properties of the MPC. We further analyze the effects of different constraints, observing that the MPC strictly adheres to them and that the control variable influences the response of the MMC plant’s performance. We further compared our results with those of other controllers and analyzed performance metrics, demonstrating that the exponential MPC is effective in this case. Additionally, the results presented in this paper demonstrate the prescribed degree of stability and highlight the importance of fine-tuning key MPC parameters for the MMC model. The exponential-based MPC is validated for the MMC under scenarios involving small and large active and reactive power disturbances, considering offline simulations.

The rapid expansion of offshore wind and solar is placing increasing pressure on transmission infrastructure, challenging energy security, sustainability, and affordability. In response, global policy initiatives are advancing high-voltage direct current (HVDC) "express energy highways"to efficiently transfer bulk renewable power. Voltage-source converter (VSC)-based multi-Terminal HVDC (MT-HVDC) grids offer a scalable offshore solution but require advanced control to manage their fast nonlinear dynamics and low inertia. This paper presents a real-Time control and dispatch framework for a five-Terminal radial-mesh VSC-MMC HVDC grid. A model predictive control (MPC) strategy is developed, automatically coded from Simulink, and deployed on a real-Time target for controller-hardware-in-The loop (CHIL) validation using an RTDS® simulator. The setup includes dynamic braking resistors, DC breakers, and integrated human machine and dispatch interfaces for real-Time tuning and supervisory control. Comparative testing under power setpoint changes and AC/DC fault scenarios shows that the proposed MPC achieves more accurate active and reactive power tracking with lower overshoot, improves damping of post-fault oscillations, and enables seamless coordination between local and system-level operations. These results confirm the practical feasibility and operational resilience of MPC-based control for future offshore MT-HVDC systems.

Hybrid AC/voltage source converter-based multi-terminal DC (VSC-MTDC) power grids play a crucial role in enabling long-distance power transmission and flexible interconnection between AC grids. To fully leverage the functional advantages of such systems, it is essential that they operate in or close to optimal power flow (OPF) conditions. To address this, ACDC-OpFlow is developed as an open-source and cross-language framework for solving AC/DC OPF problems. Its core innovation lies in a unified modeling structure that supports MATLAB, Python, Julia, and C++, with Gurobi used as a consistent solver backend. This framework is beginner-friendly and allows users to work in their preferred programming languages. Both text-based and graph-topology results are provided to help users understand the system-wide power flow distribution and operational status. This work presents the design concept of ACDC-OpFlow, showcases representative example results, and discusses the performance differences observed in multiple programming language implementations.

The increased use of High-Voltage Direct Current transmission networks requires appropriate control strategies for the converter stations, which are crucial to ensure uninterrupted energy supply. In this paper, a Polytopic Lyapunov Function-based Hybrid switching control strategy is implemented to combine the merits of Grid Following and Grid Forming control strategies by switching alternatively from one to another at the polytopes’ hyperplanes to ensure good system response even for faulty conditions. The state space equations of the control strategies are used to form the state hyperplanes for the switching rule. Since the hybrid switching control is based on the Polytopic Lyapunov Function, the system is inherently Large Signal Stable. The results obtained by real-time-based simulations using RTDS verify the designed control for various transient phenomena.

Unlike synchronous generators, the fault response of grid-forming (GFM) inverter-interfaced distributed generators (IIDGs) is notably governed by the selection of control and current limiting strategies rather than inherent physical traits. While recent research has focused on the sequence domain fault model of GFM IIDGs, a research gap exists in elucidating the influence of control and current limiting schemes on this model's characteristics. This article aims to fill this void by examining how different control and current limiting schemes influence the positive and negative sequence impedances in the phasor-domain fault model of GFM IIDGs. This investigation encompasses droop-based, virtual synchronous machine-based, and virtual oscillator-based reference generation controls alongside rotating and stationary reference-frame-based voltage controls. Furthermore, saturation-based, latching-based, circular and virtual impedance-based current limiting schemes are analyzed. To achieve this goal, a thorough numerical simulation study is conducted. Findings indicate that outer reference generation controls exhibit minimal impact. Conversely, the choice of voltage control and various current limiting schemes emerge as the predominant factors shaping the sequence models of GFM IIDGs. These analyses and results are instrumental in devising reliable protection strategies within inverter-based grids, as a comprehensive understanding of electrical elements in the sequence domain is imperative for effective protective measures.

The widespread use of modular multilevel converters (MMCs) in the evolution of complex power grids presents new challenges for grid stability. MMCs have highly nonlinear impedance characteristics due to their complex internal dynamics and intricate control architectures. Due to practical constraints, physics-based models cannot accurately compute these impedances, and the use of closed-box measurement techniques is time-consuming, resulting in a limited amount of data available for impedance characterization. Thus, using current methods to estimate impedances over a wide range of operating points can be unreliable. This paper presents a transfer learning-based framework for MMC impedance characterization using system-level parameters as operating point variables. The proposed approach predicts both AC and DC side impedances simultaneously by extrapolating impedances derived using state-space modeling approaches to real-time electromagnetic transient (EMT) simulations. Finally, the method is evaluated on a practical converter from the CIGRE B4 DC grid test system for various types of controllers and scenarios involving unknown parameters.

This editorial introduces the Special Issue “Methodologies and Applications of Digital Twin for Renewable-Dominant Power Systems”, which highlights key research addressing the challenges associated with integrating renewable energy sources into power systems. Digital twins provide an advanced framework for modeling, simulation, and optimization of these complex systems, driven by the need to address the impact of power electronics and multi-source energies. The contributions featured in this issue focus on the application of DT technologies in renewable-dominant systems, offering solutions for enhancing system stability, optimization, and operational efficiency.

Unscheduled event handling capability and swift recovery from transient events are indispensable study areas to ensure reliability in offshore multiterminal high-voltage dc (MT-HVdc) grids. This article focuses on enhancing the reliability of half-bridge modular multilevel converters (HB-MMCs) in MT-HVdc grids by introducing a predictive dc fault ride-through (DC-FRT) recovery controller and fault separation devices. A novel dc protection-informed zonal DC-FRT scheme for HB-MMCs is proposed, incorporating a model predictive planner for optimized control inputs based on local and interstation measurements and converter constraints. A real-time digital simulator environment simulates the approach, which improves lower level control during fault interruption and suppression by utilizing fault detection and location information. In addition, the study examines two control schemes to assess the impact of communication delays in MT-HVdc grids, a critical factor for system stability and reliability during faults. These schemes include a centralized scheme with delays in input and output signals and a decentralized approach focusing on external signal delays. Both are compared against a baseline centralized control with no delays. These approaches explore alternatives for the placement of the proposed controller, considering potential delays in interstation high-speed communication. The findings underscore the significance of the proposed DC-FRT control in reinforcing MT-HVdc systems against faults, which contributes to efficient recovery and grid stability.

The modular multilevel converter (MMC) uses many power electronic components in the high voltage direct current (HVDC) application. One of the major concerns in half-bridge MMC is the fault in the converter submodules. It raises the question of whether the reliability and high-quality performance of the MMC can be increased significantly as the active device controls the power flow between the AC- and DC-sides. During the SM fault within the MMC leg, the unbalance is introduced in-side the MMC converter. The unbalanced voltage within the leg of the MMC will continuously introduce an AC-current component on the DC-side of the converter. Thus, the hybrid proportional-internal (PI) control and proportional-resonant control (PR) is introduced in controlling the power flow within the internal MMC to eliminate the AC-current component and ensure pure DC-current in the internal MMC. This study investigates the internal power flow control of a three-phase rectifier MMC with symmetric and asymmetric SM fault conditions. Compared with conventional control methods, the proposed control can tolerate SM faults and eliminate the AC-current component within the converter, increasing the converter's performance. Simulation results are included and discussed to verify the proposed control.