Modern power systems are increasingly reliant on power electronics (PE), with high-power Modular Multilevel Converters (MMC)-based grid-forming (GFM) assets playing a vital role in ensuring voltage and frequency stability. However, time delays and fast controls of such devices compromise the system’s stability due to their nonpassivities. Moreover, there is a proliferation of different PE-interfaced nonlinear loads that introduce harmonic distortions. To address these issues, MMC-based GFM converters might be required to provide harmonic filtering and exhibit passive behavior for stable interaction with other grid components.Current saturation during faults or contingencies further complicates the operation of GFM converters, as it modifies dynamics and requires seamless transitions between current-limiting and GFM modes. Existing solutions are inadequate for current-controlled GFM (CC-GFM) structures, as they degrade passivity.This paper proposes a seamless current limitation strategy for CC-GFM converters that preserves passivity and harmonic filtering during normal operation while ensuring stable and seamless transitions during current saturation. The approach freezes the states of the voltage feedforward and harmonic filtering compensators, enabling continuous output and bumpless transitions. Controller hardware in the loop experimental results validate the proposed method, highlighting its effectiveness in maintaining the current within the converter current limit.

This paper presents a novel frequency-domain identification tool based on Electromagnetic Transient (EMT) simulations: Z-tool. This is the first open source program offering a versatile automated scan and state-of-the-art small-signal analysis of multi-terminal AC, DC and AC/DC power systems. The approach is introduced with an emphasis on implementation aspects and its use for stability assessment. Furthermore, the stability analysis capabilities are illustrated in a subsynchronous oscillation screening study. In addition, refinements to decrease the runtime, such as multi-frequency excitation and the exploitation of symmetry properties, are described and demonstrated for different systems. The identification error is time-step-dependent due to the nature of EMT routines. Moreover, the trade-off between significant time-savings, achieved by adopting the proposed developments, and loss of accuracy are quantified for basic power system components offering a useful guideline for their applicability and parameter selection.

Ensuring stability in converter-dominated power systems requires voltage source converters to be robust under varying grid conditions and grid uncertainties such as short-circuit ratio variations. This paper analyzes the robustness of a grid-forming (GFM) current-controlled quasi-stationary electrical model virtual synchronous machine. We investigate the applicability of -analysis to systems incorporating GFM converters and demonstrate that operating point variations induced by parameter uncertainties must be explicitly considered. Due to the system's inherent nonlinearity, neglecting these variations can lead to misleading stability conclusions. To address the limitations of the -analysis, we introduce a robustness analysis method based on a parameter-dependent operating point and symbolic linearization, which enables efficient eigenvalue computation without repeated relinearization. Performance is additionally evaluated using sensitivity function analysis with respect to power reference tracking and angle disturbance rejection. The results show that appropriate control parameter selection improves robust stability under grid uncertainties by reducing undesired interactions.

To transition towards a carbon-neutral power system, considerable amounts of renewable energy generation capacity are being installed in the North Sea area. Consequently, projects aggregating many gigawatts of power generation capacity and transmitting renewable energy to the main load centers are being developed. Given the electrical challenges arising from having bulk power capacity in a compact geographical area with several connections to the main grid, and a lack of a robust definition identifying the type of system under study, this paper proposes a general technical definition of such projects introducing the term Electrical Energy Hub (EEH). The concept, purpose, and functionalities of EEHs are introduced in the text, emphasizing the importance of a clear technical definition for future planning procedures, grid codes, regulations, and support schemes for EEHs and multiterminal HVDC (MTDC) grids in general. Furthermore, the unique electrical challenges associated with integrating EEHs into the power system are discussed. Three research areas of concern are identified, namely control, planning, and protection. Through this analysis, insights are provided into the effective implementation of multi-GW scale EEH projects and their integration into the power grid through multiple interconnections. Finally, a list of ongoing and planned grid development projects is evaluated to assess whether they fall within the EEH category

Although frequency-domain analysis is a powerful tool for small-signal stability assessment in power systems, its sensitivity analyses generally aim at selected frequencies, particularly around poorly damped or undamped modes. However, reliably identifying the unstable frequencies within the frequency-domain framework remains a significant challenge. This work introduces and demonstrates a robust method based on the Generalized Nyquist Criterion for estimating unstable oscillatory frequencies, which overcomes the exposed limitations of existing techniques.

This paper proposes a generalized passivity sensitivity analysis for power system small-signal stability. The method quantifies the impact of device parameters and subsystems on the passivity index at both the device and system levels. Explicit sensitivity expressions are derived by exploiting the particular structures of the admittance and nodal models. The proposed analysis identifies the dominant contributors to non-dissipative behavior, thereby enabling effective passivation strategies. These proposed analyses, based on the developed sensitivities, are validated across different parameters at the device and system levels. In addition, we demonstrate how to utilize the proposed method through case studies with different converter controls, showing its general applicability.

Grid-forming (GFM) control-based converters such as static compensators (STATCOM) are considered as promising solutions for their system support characteristics and robustness against weak grid conditions. Contrary to common belief, GFM converters can also exhibit weak-grid instability, and it is unclear to what extent they stabilize the network. This paper investigates how control design affects both the stable integration of GFM converters into weak grids and their resulting stabilizing effects on the interconnected power system, with particular emphasis on wind farm integration. The analysis reveals that weak-grid stability and system-level stabilization critically depend on the adopted control structure rather than on the grid-forming concept itself. This highlights the necessity of adopting different control design approaches for grid-following (GFL) and GFM converters by demonstrating the opposite effects of voltage feed-forward (VFF) action in the current controller on weak-grid stability. The influences of key GFM converter parameters, such as virtual impedance (VI), are analyzed in terms of passivity for stable integration into weak grids. Their impact on the frequency-dependent power flow Jacobian (FD-JB) is also evaluated for system stabilizing effects. The case studies confirm the findings that although the passivity approach is effective for the converter itself, the resulting stabilizing effect on the complete system can be different depending on its control design.

With the growing integration of converter-interfaced generating units in power systems, interactions between converters and grids have been observed across both low and high-frequency ranges, resulting from the diverse dynamics of these converters. Moreover, incorporating the complex dynamic model of converters, which involves a large number of state variables, increases the computational burden when using conventional methods to identify unstable and interaction modes. These modes are also influenced by the parameters of both converters and networks, necessitating numerous time-consuming re-computations of all eigenvalues for parametric variation analysis in large power systems. To address these challenges, this paper proposes a method that utilizes closely located open-loop modes and their displacement from open-loop to closed-loop modes to selectively identify interaction modes within power systems. The proposed method leverages the open-loop subsystem eigenvalues and the interconnections between state variables of different subsystems to determine the closed-loop eigenvalue using a second-order eigenvalue approximation, thereby avoiding the need for the calculation of all eigenvalues of the entire system. The interaction information is then used to obtain a reduced-order eigenvector approximation to improve the computation time as compared to the full-order system. The identified interaction modes and corresponding computation time using the proposed method are compared with the traditional modal participation method. The proposed method provides an efficient approach to identifying interactions between converters and the power system.

This letter derives explicit conditions and the exact frequency range in which rotated passivity can be applied within a unified integral quadratic constraint (IQC)-based stability framework for power-electronic-dominated grids. By analytically examining the short-circuit admittance of transmission lines, we show that the applicability of rotated passivity-based stability analysis depends solely on the passive grid, enabling a closedform expression for the critical frequency beyond which the rotated indices lose non-negativity. The results reveal that the corresponding stability criterion remains applicable for typical overhead transmission lines up to the fundamental frequency, whereas long uncompensated underground cables may impose significantly lower limits. These findings establish clear applicability boundaries and strengthen the practical use of rotated passivity in frequency-domain small-signal stability analysis.

Power quality is a growing concern in modern electrical power systems due to the increasing penetration of power electronic interfaced nonlinear loads and generation, which introduce voltage and current distortions. Active filter techniques have been developed to mitigate these distortions. Among these techniques, virtual harmonic impedance is the most desired for harmonic power sharing or general power quality improvements. However, existing methods often lack explicit passivity considerations, which can lead to adverse interactions with the grid resonances. This paper presents a control design for a grid-forming Modular Multilevel Converter (MMC)-based STATCOM with virtual harmonic impedance. The proposed method enables the selection of a harmonic impedance that improves power quality while ensuring a positive passivity index around the converter harmonic admittance, thus guaranteeing stable interactions with the grid. This control approach is based on a dq-frame feed-forward harmonic compensator. The paper outlines the tuning methodology to achieve a harmonic virtual impedance, operational boundaries, and robustness of the proposed approach. Simulation results in a harmonic benchmark system demonstrate that the proposed control achieves the desired harmonic impedance while maintaining a passive response, ensuring stable system performance.

In the near future, point-to-point High Voltage Direct Current (HVDC) systems are expected to evolve into multi-terminal and meshed HVDC grids, predominantly adopting a bipolar HVDC configuration. Normally, bipolar HVDC systems operate in balanced mode, i.e., near zero current flows through metallic or ground return. However, bipolar HVDC systems can also be operated in an unbalanced mode in case of a single converter pole or line conductor outage. A steady-state analysis of the unbalanced DC network requires solving a power flow problem including various converter control modes, as the steady-state behavior of the converters is governed by their control modes. This paper presents a comprehensive and unified power flow model for the balanced and unbalanced operation of bipolar HVDC grids, including various converter control modes on the AC and DC sides of the converters in a hybrid AC/DC system. It extends the basic control modes, developed for monopolar HVDC grids, to support the balanced as well as unbalanced operation of bipolar HVDC grids. Additionally, an AC-droop control, which defines a droop relationship between voltage magnitude and reactive power at the AC side of a converter, is incorporated into the modeling of bipolar HVDC systems. The functionality of the proposed model is demonstrated through a test case, and the power flow results are validated using PSCAD simulations. The impact of converter control modes on post-contingency system states is also investigated for single-pole contingencies. The proposed power flow model is implemented as an open-source tool using the Julia/JuMP framework. The accuracy and robustness of the model, as well as the developed tool, are demonstrated through large-scale test cases, including systems with up to 3,120 buses.

This paper presents a generic method for the steady-state periodic trajectory calculation of the modular multilevel converter (MMC) and MMC-based HVDC systems, which is a prerequisite to steady-state performance optimization and harmonic state-space-based small-signal stability analysis, among other applications. In the case of the MMC, the periodic trajectory determination is challenging due to nonlinearity and delays in the differential equations, in particular when control dynamics are taken into account. To this day, most methods rely on lengthy manipulations of waveform representations and cannot generally account for delays and nonlinearities other than products of variables. Hence, there has been missing a more efficient formulation capable of addressing the limitations of existing state-of-the-art methods. This paper fills this gap by presenting a highly flexible Fourier-based collocation method which seamlessly accounts for control dynamics, nonlinearity and delays. Being based in the time-domain, the developed method naturally accounts for nonlinearity in the differential equations and, being real-valued, it is solved efficiently with readily available root-finding Newton-based algorithms. In this paper, the proposed method is also applied to an illustrative simple RLC circuit as well as to a complete arm-averaged model of the MMC; it is validated against simulations and compared with a state-of-the-art shooting method.

The inherent complexity of modular multilevel converters (MMCs) poses challenges for computationally efficient simulation and detailed analysis. To address this, MMCs are often approximated as two-level voltage source converters (2L-VSCs) in studies. This paper identifies the conditions under which such simplifications are valid. Two MMC control strategies are analyzed: (1) uncompensated modulation (UCM), which combines circulating current suppression with total energy management, and (2) compensated modulation (CM), incorporating per-arm energy control. The dynamic and frequency coupling mechanisms between the AC side and internal MMC states are analyzed for each approach. Furthermore, a small-signal comparison of MMC and 2L-VSC dynamics is conducted through an advanced harmonic state-space (HSS) method to evaluate the eigenvalues and admittance/impedance of the systems. The findings demonstrate that the modulation strategy significantly influences whether the AC-side dynamics of MMCs align with those of 2L-VSCs. These insights provide a foundation for simplifying control, modeling, and operational strategies while maintaining accuracy and performance.

This letter proposes an AC/DC frequency-dependent power flow Jacobian analysis to identify the system support capabilities. In addition, the analyses reveal that system support capabilities do not necessarily enhance the system stability margin, suggesting that technical requirements of narrow-frequency-band and AC-side focused specifications may not lead to the expected performance of GFM.

This paper proposes a generalized passivity sensitivity analysis for power system stability studies. The method uncovers the most effective instability mitigation actions for both device-level and system-level investigations. The particular structure of the admittance and nodal models is exploited in the detailed derivation of the passivity sensitivity expressions. These proposed sensitivities are validated for different parameters at device-level and at system-level. Compared to previous stability and sensitivity methods, it does not require detailed system information, such as exact system eigenvalues, while it provides valuable information for a less conservative stable system design. In addition, we demonstrate how to utilize the proposed method through case studies with different converter controls and system-wide insights showing its general applicability.

The energy transition towards carbon-neutrality is rapidly changing power systems as more wind energy is increasingly being integrated. As the share of power electronics interfaced energy resources increases, stability concerns arise due to the devices’ distinct behavior with respect to traditional equipment. In this context, grid forming converter control (GFM) is highlighted as a system stabilizing solution. Especially, wind turbines (WT) with GFM functionalities are a potential technology to support system stability while providing renewable energy. However, the impact of GFM WT on traditional power stability phenomena related to synchronous generators (SG) requires further investigation. This paper conducts an analysis of the impact of GFM-WT modeling fidelity for conducting power system studies efficiently. In addition, we focus on inter-area modes and their interplay with low frequency turbine modes linked to the drive-train and GFM control. The validity and effectiveness of the proposed reduced-order models for small-signal stability analysis are demonstrated by frequency response comparison and an investigation of the model structure from a state-space perspective. Lastly, the impact of different GFM-WT drive-train and control parameters on inter-area oscillations is studied for a modified two-area power system. All the results discussed in this paper are validated through electromagnetic transient (EMT) simulation.