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.

Voltage source converter (VSC)-interfaced renewable power plants are typically far from load centers, the weak grid condition presents significant stability risks. Extensive research has been conducted to analyze oscillations within the DC voltage control (DVC) timescale. However, most studies focus on scenarios where generators are connected to the grid through long transmission lines. More general scenarios, where loads are distributed along these transmission lines, have not received sufficient attention, potentially leaving undiscovered oscillation mechanisms. This paper finds a small-signal stability issue, which is an unexpected oscillation that may occur if local loads are connected near the VSC-based power plants. To comprehensively analyze this phenomenon, this paper takes the phase-locked loop (PLL) as the main object and analyzes the interaction between the terminal voltage control (TVC), DVC, and PLL. Initially, the complex coupling relationship is clarified by applying series expansion to the interaction paths between TVC and DVC. It is found that the load effect contributes to forming a crucial path that introduces the negative damping torque caused by TVC to PLL. Subsequently, analyses show that undamped oscillation risks exist under normal control parameters. A targeted control strategy is proposed for oscillation suppression. Verifications are conducted using MATLAB/Simulink and RT-LAB.

The high inertia energy storage synchronous condenser (HIESSC) can provide both grid voltage and frequency support, which is a promising new type of grid-supporting equipment. However, HIESSC needs to achieve multiple objectives including rotor current limitation, reactive power support, torque ripple limitation, and fast demagnetization under grid fault conditions, and the compatibility among these objectives remains unclear. To address this issue, this paper proposes a multi-objective coordinated control strategy for HIESSC during the low voltage ride-through (LVRT) process from the perspective of the rotor-port impedance characteristics. First, the transient inductance values required to meet different LVRT objectives are analyzed, and the compatibility between different objectives is clarified. Then, the LVRT process of HIESSC is divided into three stages, and the control objectives that need to be optimized in different stages are clarified. Subsequently, through the stage-bystage design of current control commands, coordinated multi-objective satisfaction throughout the entire LVRT process is achieved. Finally, the proposed method is verified through experiments.

During low voltage ride through, the DFIG-based wind turbine faces the risk of transient synchronization instability, due to the absence of equilibrium point. To cope with it, this letter analyzes the existence mechanism of equilibrium point from the perspective of active power transmission balance. Then, a power transmission balance control is proposed to enhance synchronization stability, which is independent of grid parameters. The proposed method can maintain synchronization stability during severe grid voltage dips and frequency deviations. Finally, the proposed method is validated by experiments.

Line commutated converter-based high voltage direct current (LCC-HVDC) systems are widely deployed but face significant broadband small-signal stability challenges. Due to their low switching frequency, LCC switching dynamics critically influence broadband oscillatory behavior. Conventional switch-function-based approaches partially capture these dynamics via series approximations. However, they require high-order expansions of switching functions and still struggle to accurately represent the commutation process. Given that LCCs are inherently piecewise smooth, nonlinear time-periodic systems, this paper proposes a piecewise small-signal model for LCC-HVDC systems. Filippov's method is employed to precisely capture the switching behavior, while Floquet theory is utilized to assess system stability. Furthermore, to trace the root causes of unstable or under-damped oscillations, the concept of participation factors is extended from smooth linear time-periodic systems to piecewise smooth time-periodic systems, enabling quantitative analysis of the interaction between system modes and state variables. Compared with existing models, the proposed approach achieves higher accuracy while maintaining relatively high computational efficiency. The validity of the stability analysis is confirmed through hardware-in-the-loop (HIL) experiments.

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.

Voltage source converters (VSCs) are essential for integrating renewable energy into the grid. Their small-signal dynamics under unbalanced grid conditions have garnered significant attention. A typical approach is negative sequence (NS) control using a proportional-integral (PI) controller in the double synchronous reference frame (DSRF), known as DSRF control. Alternatively, the same control objective can be achieved using a PIR controller in the positive SRF, where a resonant term is inserted to track the NS component at twice the fundamental frequency. While the small-signal modeling and stability analysis of grid-tied VSC with DSRF control have been extensively studied, research on PIR control remains limited, and a comparative analysis of the two approaches is still lacking. To fill this gap, this paper develops a linear time-periodic (LTP) model of a grid-tied VSC with PIR control and presents a comprehensive comparison of the two typical NS control schemes using Floquet theory.

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.

Abstract Understanding the inertial response capability of wind farms is of substantial importance for modern power systems. However, the supplementary inertia control of wind turbines exhibits high-order inertia characteristics that differ fundamentally from those of synchronous generators. When multiple wind turbines are aggregated into a wind farm, these inertia characteristics become even more intricate. Because the aggregated inertia may no longer follow the simple additive rule commonly assumed in synchronous-generator-dominated systems, this paper first develops a high-order inertial response model for individual wind turbines. Using a two-generator system as an illustrative example, we further demonstrate how to derive an equivalent inertia model suitable for frequency-domain dynamic analysis of multi-machine interactions.

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.

It is crucial for manufacturers to evaluate the low voltage ride-through (LVRT) control limit capability of doubly fed variable speed pumped storage (DFVSPS) unit, which can contribute to optimizing the unit parameters and LVRT strategy. However, existing methods simplify the voltage boundary, making it difficult to accurately evaluate the LVRT control limit capability of DFVSPS unit. To address this issue, this paper proposes an optimization-theory-based method to evaluate LVRT control limit capability and the feasibility region of DFVSPS unit. First, the transient characteristics of DFVSPS unit are analyzed to streamline the LVRT control limit capability evaluation issue into an optimization problem, the objective of which is to minimize the rotor current under rotor voltage constraint. Then, this optimization problem is converted into a standard form of quadratic programming and solved, which provides an accurate evaluation of LVRT control limit capability. Subsequently, the influence of unit parameters on the LVRT control limit capability of DFVSPS unit is analyzed, and LVRT feasibility regions of DFVSPS unit in both generation and pumping modes are established. Finally, the proposed method and analysis are validated by experiments.

This study implements and improves a planning model for large-scale renewable energy bases that systematically exploits the spatiotemporal complementarity among wind, solar, and battery storage. First, the complementary characteristics are quantified. Then, the Complementary Characteristics-based Optimization Model is formulated to co-optimize the siting and sizing of wind farms, photovoltaic plants, and battery energy storage systems. The model aims to minimize total costs while maximizing power output during peak-demand periods. The Nelder-Mead simplex algorithm is employed to solve this optimization problem. A case study in Qinghai, China, demonstrates that compared to a conventional resource maximization approach, the CCOM increases firm capacity by 60- 80% (reaching 5,255 – 5,333 MW versus a baseline of 2,910 - 3,566 MW), albeit at a 7.2% higher capital cost. These results offer a more balanced and cost-effective solution for large-scale renewable energy integration.

Accurately assessing the inertial response of renewable energy generation (REG) is critical for frequency stability. However, REG represented by doubly-fed induction generator (DFIG)-based wind turbine (WT) exhibits inherent time-varying inertia behavior, fundamentally distinct from synchronous generators (SGs). Prevailing inertia assessment methods predominantly rely on SG-derived time-domain inertia constants, which cannot capture this intrinsic variability. Consequently, the rationality of directly applying these conventional methods to DFIG-based WT lacks theoretical justification. To address this gap, this paper derives an expression for calculating time-varying inertia using the angular momentum theorem. Results demonstrate that inertia in the time domain dynamically varies with disturbances, highlighting the significant limitations of conventional inertia descriptions. Alternatively, a frequency-domain inertia characterization method is investigated to provide a disturbance-independent description of inertia, effectively capturing its intrinsic time-varying nature. Due to the duality between time and frequency domains, this paper mathematically describes the relationship between frequency-domain inertia and time-domain inertia, explicitly clarifying the physical meaning of inertia in the frequency domain. Simulations on an IEEE 39-bus system verify that the frequency-domain inertia method accurately captures inertia dynamics and is suitable for frequency stability analysis. These findings emphasize frequency-domain inertia characterization as an essential method for representing inertia in renewable-rich power systems.

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.

During grid faults, fast demagnetization is crucial for the safe operation and reactive power support of doubly-fed induction generator (DFIG). However, existing demagnetization methods employing fixed control parameters fail to unlock the potential for fast demagnetization. To cope with it, this letter proposes a time-varying inductance emulating control that makes the rotor side of DFIG emulate an inductance with a time-varying value. The proposed method significantly accelerates the decay of stator flux while ensuring safe demagnetization within current and voltage constraints. Finally, experimental results validate the proposed method.

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.

Modern power grid suffers from low short-circuit ratio and absence of mechanical inertia. Conventional synchronous condensers (SynCons) could not provide sufficient inertia (typically H< 5 s), and has a slow reactive power regulation speed (typically > 2 s). To address these issues, this article proposes a high-inertia asynchronous condenser (HIAC) system, which combines the advantages of SynCons, doubly-fed machines (DFMs), and flywheel energy storage. Adopting ac excitation enables HIAC to achieve wide-range speed regulation (up to +/- 30%) far exceeding that of traditional synchronous machines (+/- 2%), which results in the provision of high equivalent inertia. Furthermore, the high dc bus voltage of ac excitation significantly enhances power response speed. This article introduces the operational principles and characteristics of the HIAC, as well as its hierarchical control strategy and active frequency/voltage support strategy. Finally, the effectiveness of the HIAC in supporting the voltage and frequency of renewable energy stations is verified by simulations and experiments. Results proved that the HIAC could prove equivalent inertia that is more than 10 times greater than that of the conventional SynCon and achieved rapid power response of around 20 ms

As a pivotal transition in engine startup or restart, the voltage build-up (VBU) process is the core of building the overall MEA’s electrical system, particularly within dual-shaft (high/low-pressure, HP/LP) architectures. Currently, VBU analysis relies on static boundaries and neglects the influence of key parameters, including shaft speed n, winding resistance Rs, and DC link capacitance cdc. To address this gap, this paper proposes a novel multi-parameter dynamic boundary analysis framework that systematically analyzes the impact of critical parameters n, Rs, and cdc on the VBU rate ůdc and the system’s dynamic boundaries. Based on this dynamic boundary analysis, an optimal VBU control strategy is proposed. This strategy maximizes the VBU rate while maintaining the safety margin. Experimental validation by a permanent magnetassisted synchronous reluctance motor confirms the accuracy of the theoretical analysis and the effectiveness of the proposed control method, where the VBU time is compressed by over 56.82%. This study clarifies the parametric advantages of HP or LP shaft VBU under various conditions and shortens the VBU time, thereby enhancing the engine’s fast-start potential for ground startup and in-flight restart scenarios.

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).

With the increasing size of wind turbines, the impact of periodic aerodynamic loads caused by wind shear and tower shadow effects on the stable operation of the units has become increasingly significant. Traditional analysis methods based on linear time invariant (LTI) models struggle to accurately characterize such periodic time-varying characteristics. Thus, for the generator-side system of a semi-direct drive permanent magnet synchronous generator (PMSG) - based wind turbine, this paper establishes a linear time periodic (LTP) state-space model for its generator-side system, which can effectively characterize the electromechanical coupling dynamics under periodic loads. Then, based on Floquet-Lyapunov theory, the influence of the speed feedback delay time constant on system stability is analyzed. The increase in the delay time constant is proven to induce system instability. Finally, simulation results verify the validity of the proposed analysis method.