With the increasing penetration of renewable energy, synchronous generators (SGs) and voltage source converters (VSCs) synchronized via phase-locked loops (PLLs) are expected to coexist in modern power systems, leading to complex dynamic interactions. Traditional small-signal stability analyses of PLL-VSCs often simplify or neglect the electromagnetic transients of SG stator flux and AC network dynamics, leaving the impact mechanisms of these dynamics on PLL-dominated stability modes largely unexplored. To bridge this gap, this paper establishes a comprehensive small-signal model for a parallel SG-VSC system. Within a self-stabilization and en-stabilization analytical framework, the complex torque paths associated with AC network dynamics and SG stator flux are rigorously extracted via branch decomposition. By analytically evaluating the complex torque coefficients under diverse operating conditions, the underlying mechanisms by which these dynamics modulate the PLL synchronization stability are unveiled. The findings reveal critical influence patterns involving the VSC capacity ratio, active power setpoints, PLL control parameters, and electrical distance. Specifically, it is revealed how the coupling between SG flux/ network dynamics and PLL alters the damping and synchronizing torque of the PLL-VSC.

With the increasing penetration of voltage-source converters (VSC), unknown dynamics pose severe challenges to high-proportion renewable energy power systems. However, there is currently a lack of effective methods to study the dynamics of high-order nonlinear power systems. Therefore, considering the nonlinear effects, this paper proposes an extended normal form method (ENFM) to analyze the dynamics of high-order nonlinear systems at non-equilibrium points (NEP), and takes the VSC grid-connected system as an example. Furthermore, based on the proposed ENFM, the phenomenon of eigenvalue deviation is found, and a quantitative index is proposed to evaluate the boundary of linear modal analysis. Finally, the proposed method is applied in both the grid-following and grid-forming VSC grid-connected systems, and the results show the feasibility and effectiveness of the ENFM.

With the rapid development of renewable energy, the application of large-capacity converters is receiving increasing attention, which also poses a risk of electromagnetic oscillations. However, the analysis of small-signal stability of grid-connected converters mainly focuses on two-level (2L) converters, rather than other high-capacity converters, such as three-level neutral point clamped (3L-NPC) converters. Besides, there is a lack of research on small-signal modeling considering neutral point (NP) dynamics of 3L-NPC converters. In this study, the non-differentiability of NP dynamics is characterized, and a differentiable model of the 3L-NPC converter grid-connected system is established. Then, the linear time-periodic (LTP) small signal model considering the NP dynamics of the 3L-NPC converter is built using trajectory linearization, and its small-signal stability is analyzed. Finally, the effectiveness of the above analysis is verified in comparison with the detailed model.

To address the potential issue of excessive short-circuit current (SCC is used instead in the following) in modern power system incorporating Voltage Source Converters (VSC), this paper first introduces the SCC characteristics of VSC operating in active and passive control modes. It then investigates methods for calculating the current contributions of VSC under different control modes. Based on this foundation, a voltage-current droop control current-limiting strategy is initially proposed. Considering the need for reactive power active support due to the low inertia of power electronic equipment, an optimized control method is further proposed that balances both current-limiting and active support requirements. A two-terminal system model is built and simulated in MATLAB/Simulink to verify the effectiveness of the SCC optimized control method. This provides a valuable reference solution for addressing the issue of excessive SCC associated with the increasing number of VSC in future power system.

With the integration of large-scale renewable energy sources (RESs), the line commutated converter (LCC) based high-voltage direct-current (HVDC) inverter side suffers from degraded grid strength and escalating commutation failure (CF) risks. In comparison with the widely used grid-following (GFL) RESs, grid-forming (GFM) RESs exhibit the favorable characteristics of voltage sources. Therefore, the hybrid operation of GFL-/GFM-RESs holds great potential in voltage support and may help CF suppression. This paper first analyzes the impacts of RESs on the first and subsequent CFs, respectively. It reveals that GFM-RESs alleviate the deterioration of grid voltage induced by GFL-RESs, thereby suppressing the first CF. However, current fault ride-through controls of RESs cannot fulfill the reactive power dynamic demand during the CF recovery process and rarely help mitigate subsequent CFs. Moreover, the limited overcurrent capability of GFM-RES hinders its ability to ride through CF. Based on the mechanism analysis, a CF suppression strategy based on the hybrid GFL/GFM operation is proposed. The proposed strategy optimized the controls of RESs to fulfill reactive power dynamics and offer voltage support during the CF process. Case studies are undertaken on the studied system and the CIGRE benchmark, respectively. The simulation results confirm the effectiveness of the proposed strategy for suppressing CF.

The Doubly-Fed Induction Generator (DFIG) based wind turbine (WT) contains control loops and energy storage components operating across multiple timescales, leading to potential cross-timescale influence dynamics in DFIG-WT-dominated power systems. Previous analyses have primarily focused on single timescale dynamics or the interactions between control loops at different timescales, with limited attention given to the cross-timescale influences between control loops and energy storage components. This paper aims to reveal the cross-timescale influence mechanism of current control at the AC-current-control timescale on the dynamics of the DC capacitor at the DC-voltage-control timescale. Modal analysis is a mature method used to uncover the cross-timescale influence phenomena and laws of current control on the dynamics of the DC capacitor. Subsequently, an equivalent circuit model is established to analyze the mechanism by which current control affects the dynamics of the DC capacitor. Finally, the conclusions are validated through simulations based on a four-machine two-area power system and the power grid of Northwest China.

ABSTRACT When renewable energy is exported through an islanded modular‐multilevel‐converter‐based high‐voltage direct‐current (MMC‐HVDC) system, the sending‐end converter station usually operates in voltage‐frequency (VF) control mode to support the alternating‐current (ac) voltage and frequency. The renewable energy side behaves as a current source. This source characteristic mismatch makes the power absorbed by the VF‐controlled converter difficult to regulate directly. Under converter blocking faults, the power balance may be rapidly disturbed. The resulting power imbalance can cause dc overvoltage and arm overcurrent within several milliseconds to tens of milliseconds. However, MMC‐HVDC converters have limited overvoltage and overcurrent withstand capability, and conventional security control devices are usually too slow for this transient process. To address this problem, this paper studies blocking faults at both sending‐end and receiving‐end converter stations. The mechanism of power uncontrollability in the VF‐controlled converter is analyzed. Operating power‐margin design principles are proposed for safe dc transmission operation. The influence of renewable energy integration topology is also investigated. A coordinated direct‐power control strategy among multiple converter stations is further developed to rapidly redistribute unbalanced power. An electromagnetic transient model of a practical MMC‐HVDC grid project is used for verification. The results show that the proposed method can improve post‐fault power coordination and suppress dc overvoltage and arm overcurrent within the designed operating margins.

With the integration of large-scale renewable energy sources (RESs), the line commutated converter (LCC) based high-voltage direct-current (HVDC) inverter side suffers from degraded grid strength and escalating commutation failure (CF) risks. In comparison with the widely used grid-following (GFL) RESs, grid-forming (GFM) RESs exhibit favorable characteristics of voltage sources. Therefore, the hybrid operation of GFL-/GFM-RESs holds great potential in voltage support and may help CF suppression. This paper first analyzes the impacts of RESs on the first and subsequent CFs, respectively. It reveals that GFM-RESs alleviate the deterioration of grid voltage induced by GFL-RESs, thereby suppressing the first CF. However, current fault ride-through controls of RESs cannot fulfill the reactive power dynamic demand during the CF recovery process and rarely help mitigate subsequent CFs. Moreover, the limited overcurrent capability of GFM-RES hinders its ride-through of CF. Based on the mechanism analysis, a CF suppression strategy based on the hybrid GFL/GFM operation is proposed. The proposed strategy optimized the controls of RESs to fulfill reactive power dynamics and offer voltage support during the CF process. Case studies are undertaken on the studied system and CIGRE benchmark, respectively. The simulation results verify the effectiveness of the proposed strategy for CF suppression.

In many countries, the negative sequence current control (NSCC) has been the national standard for connecting renewable energy to power systems. At the same time, the original relationship of voltage source converters (VSCs), commonly used in renewable power generation, shows inherent periodic time-varying characteristics. Considering the pros and cons of the different small-signal models for nonlinear time-varying systems, the comprehensive analysis based on linear time periodic (LTP) and harmonic state-space (HSS) models are introduced to studying the small-signal stability of power systems dominated by VSCs with NSCC. Considering the advantages of the LTP model in stability determination, the stable domains of control parameters are described. Additionally, the structural effect of the decoupled double synchronous reference frame (DDSRF), widely used for separating positive and negative sequences, is compared. Then, considering that the HSS model is a linear time-invariant (LTI) model, and its stability mechanism analysis method is mature, we characterize the interaction among controls based on the participation factor analysis. These comprehensive analysis results are beneficial for understanding the impact of NSCC on system dynamics and provide theoretical support for the optimization of NSCC and DDSRF. Finally, case studies validate the effectiveness of the analysis results.

Grid-forming (GFM) converters, which mimic the characteristics of synchronous generator (SG), having capable of providing inertia support to the grid, reducing the risk of oscillation and increasing the stability in weak grid. Due to these advantages, GFM converters are regarded as a promising technology in the modern power system. Similar to the SG, the fault current of GFM converter can reach an extremely high-level during grid fault which is out of the over-current ability of converters. The large fault current may cause severe damage to the power electronic devices of GFM converters. Thus, it is important to enhance the fault-ride-through (FRT) ability of the GFM converter. To address this issue, this paper conducts an in-depth dynamic analysis of the GFM converter and proposes a control method based on power retuning (PRT) by changing the power references of the GFM converter to maintain stability and restrict the fault current of the GFM converter during fault in an indirect way. Firstly, the relations between power and voltage phasor is built and the dynamic of the phasors is revealed. Subsequently, PRT control is proposed to improve the FRT ability of the GFM converter. Then, based on the geometric relations of the phasors, a detailed calculation of the power references is clearly presented to guide the adjustment of the PRT controller. Furthermore, considering the capacity of the GFM converter, the boundary of PRT controller is identified. Finally, simulation results are provided to verify the effectiveness of the PRT controller.

With the increasing penetration of wind power represented by Doubly Fed Induction Generator (DFIG) based wind turbines (WTs), the power system dynamics exhibit characteristics of multi-timescale. Moreover, the strong nonlinear characteristics of the system lead to cross-timescale coupled phenomena between multi-timescale dynamics in dynamic processes. However, previous studies typically employ linear methods to evaluate the stability of the equilibrium point neighborhood while ignoring the characteristics of cross-timescale caused by nonlinear effects. This paper addresses this gap by employing the normal form method (NFM) based on second-order Taylor expansions in the DFIG-WTs-dominated power systems. Subsequently, cross-timescale coupled modes and phenomena have been revealed. Furthermore, the frequency characteristics and damping characteristics of the coupled dynamics are analyzed. Finally, both cross-timescale phenomena are discovered and validated in real-time LAB(RT-LAB).

In recent years, renewable energy generation (RPG) has experienced rapid growth, and large-scale hydro–wind–photovoltaic storage (HWPS) bases have been progressively developed in southwest China, where hydropower resources are abundant. Ensuring the small-signal stability of such large-scale integrated systems has become a critical challenge. While considerable research has focused on the small-signal stability of grid-connected wind, photovoltaic, or energy storage systems (ESSs), studies on the stability of large-scale HWPS bases remain limited. Moreover, emerging grid codes require power electronic devices to maintain synchronization under unbalanced grid conditions. The time-varying rotating transformations introduced by positive-sequence (PS) and negative-sequence (NS) control render the conventional Park transformation ineffective. To address these challenges, this study develops a linear time-periodic (LTP) model of a large-scale HWPS base using trajectory linearization. Based on Floquet theory, the impacts of RPG station and ESS control parameters on system stability are analyzed. The results reveal that under the considered scenario, these control parameters may induce oscillations over a relatively wide frequency range. Specifically, low PLL and DVC bandwidths (BWs) are associated with the risk of low-frequency oscillations, whereas excessively high BWs may lead to sub-synchronous oscillations. The validity of the analysis is verified through comparison with time-domain simulations of the nonlinear model.

This study examines whether power systems using 100% phase-locked loop (PLL)-synchronized voltage-source converters (VSCs) can operate independently. While grid-forming (GFM) technology lacks a unified definition, independent operation remains its core requirement. Current views incorrectly associate PLL synchronization solely with grid-following (GFL) control, assuming that PLL-based equipment requires support from synchronous generators or GFM devices. We challenge this by revealing three essential conditions for independent operation in fully PLL-synchronized systems: stable device synchronization, controllable node voltages, and adjustable system frequency. Through detailed analysis and tests, we prove these requirements can be met in 100% VSC systems using PLL synchronization. This discovery breaks the traditional link between operational independence and synchronization methods. Our findings offer new insights for developing renewable-dominated grids. The above three conditions have been proven to be achievable in a 100% PLL-synchronized VSC system.

The dynamics of network power response play a crucial role in system stability. However, the integration of power electronic equipment leads to amplitude and angular frequency (abbreviated as “frequency”) time-varying characteristics of the node voltage during dynamic processes. As a result, traditional calculation methods for and characteristics of the power response of the network based on phasor and impedance lose their validity. Therefore, this paper undertakes mathematical calculations to reveal the power response of a network under excitation by voltage with time-varying amplitude and frequency (TVAF), relying on the original mathematical relationships and superimposed step response. Then, the multi-timescale characteristics of both the active and reactive power of the network are explored physically. Additionally, this paper reveals a new phenomenon of storing and releasing the active and reactive power of the network. To meet practical engineering requirements, a simplified power expression is presented. Finally, the theoretical analysis is validated through time-domain simulations.

Energy storage components and control loops in Doubly Fed Induction Generator (DFIG) based wind turbines (WTs) exhibit multi-timescale characteristics. This leads to multi-timescale dynamics in DFIG-WTs-dominated power systems. Previous studies primarily focused on single-timescale dynamic mechanisms using simplified models or on interaction phenomena between control loops with full-timescale models. The cross-timescale influence mechanisms between control loops and energy storage components were neglected. This study explores the cross-timescale influence mechanism of terminal voltage control at the voltage-control timescale on the rotor dynamics at the rotor-speed-control timescale in a DFIG-WTs-dominated power system. Modal analysis is a fundamental dynamic analysis method that reveals key participating elements. It uncovers the cross-timescale influence phenomena of terminal voltage control in rotor mode. Then, the cross-timescale coupling branch of terminal voltage control to the rotor is clarified. Moreover, an equivalent circuit for terminal voltage control is established. This circuit illustrates the dynamic coupling mechanism between the terminal control equivalent inductance and the load capacitance by integrating the circuits of the DFIG and the network. Additionally, the influence of terminal voltage control on rotor mode damping is explained. The conclusions are validated through simulations in the two-machine system, the four-machine two-area system, and the IEEE 39-bus system.

The design of electromagnetic oscillation stabilizers (EOSs) involves two critical steps: 1) selecting the installation location, and 2) designing the structures and parameters. The first step has been thoroughly addressed in the Part I paper within the linear time-periodic (LTP) framework, hence this Part II paper focuses on the second step. Specifically, this article first introduces a generalized periodic stabilization control (PSC) scheme, which is fundamentally a periodic output feedback control strategy. Unlike existing PSC theories, the proposed scheme imposes less restrictive solution conditions and exhibits reduced computational complexity, thereby enhancing its applicability to large-scale LTP systems. Building on this foundation, the article develops a new PSC-based EOS, which is fundamentally distinct from virtual impedance (VI)-based EOSs designed within the linear time-invariant framework. The proposed PSC-based EOS is then applied to a real-world, large-scale power electronics-dominated power system (PEPS). Both theoretical analysis and electromagnetic transient simulations conducted in RT-LAB validate that, compared to a well-established VI-based EOS, the proposed PSC-based EOS achieves larger stability margins and superior control performance across multiple operating conditions in time-periodic PEPSs comprising numerous diverse devices.

This study examines whether power systems using 100% phase-locked loop (PLL)-synchronized voltage-source converters (VSCs) can operate independently. While grid-forming (GFM) technology lacks a unified definition, independent operation remains its core requirement. Current views incorrectly associate PLL synchronization solely with grid-following (GFL) control, assuming that PLL-based equipment requires support from synchronous generators or GFM devices. We challenge this by revealing three essential conditions for independent operation in fully PLL-synchronized systems: stable device synchronization, controllable node voltages, and adjustable system frequency. Through detailed analysis and tests, we prove these requirements can be met in 100% VSC systems using PLL synchronization. This discovery breaks the traditional link between operational independence and synchronization methods. Our findings offer new insights for developing renewable-dominated grids. The above three conditions have been proven to be achievable in a 100% PLL-synchronized VSC system.

Negative sequence control has been the grid core of renewable power generation (RPG) grid-tied system. As a commonly used control for positive and negative sequence separation process, the dynamic of the decoupled double synchronous reference frame phase-locked loop (DDSRF-PLL) has drawn much attention. As a core structure of DDSRF, low-pass filters (LPFs) introduce phase delays, reduce system response speed, and may even lead to system instability. Although existing studies have focused on the parameter optimization of LPFs, their structural impact remains underexplored. Therefore, this paper employs the trajectory linearization method to establish the linear time-periodic (LTP) small-signal model of the RPG grid-tied system considering DDSRF, addressing the challenges posed by nonlinearities and time-varying dynamic coupling in modeling. Then, we investigate the impact of the structure effect of DDSRF on system stability. Through comparative analysis, it reveals that eliminating a specific LPF can significantly enhance system stability. Finally, the analysis results are verified by time-domain simulation.

With the development of doubly fed induction generator (DFIG)-based wind turbines (WTs), the application of virtual synchronous generation (VSG) concepts in DFIG control has gained attention for enhancing grid stability. The VSG-controlled DFIG system, characterized by its multiple timescale energy storage elements and control loops, presents a complex dynamic behavior of multiple timescales and there are interactions between different timescales. However, existing research mostly focuses on modeling and stability analysis of a single timescale, neglecting the cross-timescale effects. This paper presents a dynamic modeling methodology for VSG-controlled DFIG-based WTs to analyze the cross-timescale impact of voltage control on electromechanical dynamics. Firstly, cross-timescale phenomena and laws of the impact are revealed. An excitation and response dynamical model of VSG-controlled DFIG is proposed, which can provide a physical comprehension of the formation mechanisms behind cross-timescale phenomena within DFIG. Additionally, the analysis of the impact of voltage control on electromechanical dynamics is performed using the damping torque. Finally, the analyses of cross-timescale mechanisms are validated through time-domain simulations.