Comprehensive Assessment of Transient Stability for Grid-Forming Converters Considering Current Limitations, Inertia and Damping Effects

A numerical solution for evaluating the effects of foundation embedment on the effective period and damping and the response of soil–structure systems is presented. A simple system similar to that used in practice to account for inertial interaction effects is investigated, with the inclusion of kinematic interaction effects for the important special case of vertically incident shear waves. The effective period and damping are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free-field ground motion. In this way, the use of standard free-field response spectra applicable to the effective period and damping of the system is permitted. Also, an approximate solution for total soil–structure interaction is presented, which indicates that the system period is insensitive to kinematic interaction and the system damping may be expressed as that for inertial interaction but modified by a factor due to kinematic interaction. Results involving both kinematic and inertial effects are compared with those obtained for no soil–structure interaction and inertial interaction only. The more important parameters involved are identified and their influences are examined over practical ranges of interest. © 1998 John Wiley & Sons, Ltd.

Inerter is the mechanical dual of the capacitor via the force-current analogy. It has the property that the force across the terminals is proportional to their relative acceleration. Compared with flywheel-based inerters, fluid-based forms have advantages of improved durability, inherent damping and simplicity of design. In order to improve the understanding of the physical behaviour of this fluid-based device, especially caused by the hydraulic resistance and inertial effects in the external tube, this work proposes a comprehensive model identification methodology. Firstly, a modelling procedure is established, which allows the topological arrangement of the mechanical networks to be obtained by mapping the damping, inertance and stiffness effects directly to their respective hydraulic counterparts. Secondly, an experimental sequence is followed, which separates the identification of friction, stiffness and various damping effects. Furthermore, an experimental set-up is introduced, where two pressure gauges are used to accurately measure the pressure drop across the external tube. The theoretical models with improved confidence are obtained using the proposed methodology for a helical-tube fluid inerter prototype. The sources of remaining discrepancies are further analysed.

Grid-forming (GFM) converters face significant challenges in low-voltage ride-through (LVRT) due to their limited overcurrent capacity. Various transient current-limiting methods have been proposed to address this issue. However, simple current-limiting settings during grid faults can severely compromise the transient stability and reactive power output of GFM, thereby affecting compliance with grid codes. To align with the global push for sustainable energy systems, this study proposes a virtual impedance tuning method (CL-TS VI) that simultaneously considers current-limiting and transient stability requirements, addressing the dual demands of high efficiency and reliable integration of renewable energy. By combining this method with an inner-loop control design based on balanced currents, an enhanced low-voltage ride-through (E-LVRT) scheme is developed. The proposed scheme achieves the coordinated fulfillment of both current-limiting and transient stability requirements by quantitatively analyzing the applicable range of virtual impedance parameters. Specifically, under the constraint of current-limiting conditions, fault scenarios are classified into two categories, with and without equilibrium points, depending on the severity of voltage sag. Then, based on the Lyapunov stability theory, separate virtual impedance design criteria are proposed for these two scenarios, ensuring that the GFM maintains both current-limiting capability and transient stability during fault ride-through while minimizing active power losses. Additionally, the proposed scheme enhances reactive power support capability in the post-fault phase, ensuring compliance with grid code requirements while promoting sustainable grid operation. The proposed strategy is validated through time-domain simulations and hardware experiments. The results demonstrate that the proposed scheme significantly improves the transient stability of GFM and provides a reliable solution for its efficient operation under complex grid conditions.

With the large-scale grid connection of Renewable energy sources as well as modern power electronics devices, the accuracy and rapidity of transient stability evaluation in power grids are increasingly stringent.The data-driven power system transient stability assessment can achieve online real-time prediction by learning the temporal characteristics before and after faults, but its application is limited by its inherent black-box nature. In this paper, an extreme gradient boosting (XGBoost) model-based transient stability assessment method is proposed for power systems, which can optimize the prediction accuracy while ensuring immediate response. To improve the interpretability of the evaluation results, the Yellowbrick algorithm is used to interpret the evaluation model prediction results from the perspective of feature importance, and the correctness of the interpretation results is verified by making predictive attribution analysis on a single sample based on Local Interpretable Model-agnostic Explanations (LIME) algorithm, which provides a reliable basis for online assessment of grid transient stability.

Transient voltage stability assessment of renewable energy grid based on residual SDE-Net

This paper investigates the transient synchronization stability mechanisms and technological advancements associated with grid-following (GFL) converters, providing a systematic review of the current research landscape and future directions in this field. The current literature lacks a comprehensive understanding of how outer-loop control dynamics and grid-converter interactions critically influence transient stability mechanisms. This oversight often leads to incomplete or overly simplistic stability assessments, particularly under high penetration of renewable energy sources. Furthermore, existing stability criteria and analytical methodologies do not adequately address the compounded challenges arising from multi-control-loop coupling effects and systems with multiple parallel converters. These limitations underscore the inability of conventional methodologies to holistically model the transient synchronization behavior of GFL converters in modern power-electronics-dominated grids. To address these gaps, this work synthesizes a comprehensive review of modeling frameworks, analytical methodologies, transient stability mechanisms, and influence factors specific to GFL converters. First, based on the fundamental differences between synchronous generators and GFL, this paper summarizes the second-order equivalent model derived from phase-locked loop (PLL) dynamic. It conducts a comparative analysis of the applicability and limitations of conventional stability assessment methods, such as the equal-area criterion, phase portrait method, and Lyapunov functions, within power-electronics-dominated systems. It highlights potential mechanistic misinterpretations arising from neglecting outer-loop control and grid interactions. Second, the paper delineates the principal challenges inherent in the transient synchronization stability analysis of GFL converters. These challenges encompass the dynamic influences of multi-control-loop coupling effects and the imperative for advancing stability criterion research in systems with multiple parallel converters. Building on existing studies, the paper further explores innovative applications of artificial intelligence (AI) in transient stability assessment, including stability prediction based on deep learning, data-physics hybrid modeling, and human–machine collaborative optimization strategies. It emphasizes that enhancing model interpretability and dynamic generalization capabilities will be critical future directions. Finally, by addressing these gaps, this work provides theoretical foundations and technical references for transient synchronization stability analysis and control in high-penetration inverter-based resources (IBRs) grids.

The topological configuration of a bulk power grid is often altered by network investment upgrades, forecasted disasters and random faults, as well as planned operator-triggered transmission line maintenance and controlled switching actions. Such topological variations can drastically change the measurement data distribution from phasor measurement units (PMUs), which may in turn compromise the accuracy of the artificial intelligence (AI)-aided monitoring and control applications using the measurements. For instance, data-driven transient stability assessment (TSA) models that were trained with static network topologies may no longer be accurate for monitoring power grid stability as the network topology changes. Not only would the number of possible topology changes be too vast to train all possible scenarios, but also the training process will render computationally intensive. This paper proposes a model-based transfer learning (TL) approach that integrates a convolutional neural network and a long short-term memory network (ConvLSTM), to efficiently train a new stability prediction model that predicts the system operating states (SOSs) and identify critical generators (CGs) in case of instability when the system undergoes enduring topological changes. Numerical analyses on three test cases including the IEEE 39-bus test system, the IEEE 118-bus test system, and the large-scale 2000-bus synthetic power grid in the state of Texas verify the efficiency of the proposed approach and highlight benefits in training time and accuracy, when compared to the state-of-the-art alternatives. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —As the national power grid goes through transitions towards digitalization and modernization with emerging technologies, maintaining its reliability and resiliency against environmental stressors and cyber attacks remains an urgent need. The power system topology is expected to change more frequently, sometimes to accommodate the proliferation of heterogeneous distributed energy resources and tackle their intermittence, sometimes event-driven due to disruptive events (e.g., faults), and sometimes operator-triggered for maintenance activities and responsive control to return the system back to its normal operating condition. This article is motivated by the need for an efficient and computationally-attractive approach for online situational awareness and real-time transient stability monitoring and assessment of the power grid under an enduring topological change, where the main goal is to identify the power system operating states (SOSs) and critical generators (CGs) in case of instability. Instead of training a new model for each topological change, this paper proposes an adaptive power system transient stability assessment (TSA) method that uses transfer learning (TL) which in return reduces the training time yet with less data than a newly-trained model for each topology change scenario.

Key feature selection is of great significance for intelligent assessment of transient power angle stability of power system. This paper proposes a key feature selection method for improved Relief. Through analyzing and comparing the applicability of correlation coefficient, mutual information and Relief, three representative key feature selection methods, in the intelligent assessment of transient angle stability of power system, the applicability of Relief is better. The Relief index reflects the strength of the feature to classify transient power angle stability and instability. By eliminating redundancy and increasing the weight of unstable samples, the accuracy of index calculation and the ability to adapt to sample imbalance are improved. Based on improved Relief, feature is selected by iterative optimization, which can automatically screen out the optimal key feature set. The effectiveness of the method is verified by an example of power grid.

Since the wide application of virtual synchronous generators (VSGs), the power grid faces great challenges in the safe and stable operation due to their limited thermal capacity and weak anti-disturbance ability. During transient period, for example, a fault occurs in the transmission line, the VSG may lose the transient angle stability and provoke the current hard limit. Even if the fault is cleared by tripping of line, it still faces the problem of instability and voltage dips. To address this problem, in this paper, the post-fault large-signal model of VSG is derived first via the travelling waves based fault information acquisition. Subsequently, with the effect of both active and reactive power loops taken into account, a two-stage simultaneous control scheme is proposed for improving the transient stability of VSG, while considering the current limitation during fault state and voltage support after fault clearance. This method is fulfilled by mode switching and an additional feedback control based on the fault signal. Finally, the effectiveness of the proposed method under both symmetrical and asymmetrical faults is verified. Moreover, the application of the proposed method in a multiple VSGs system is also verified. Besides, the robustness to parameter mismatch and the feasible operating region for the method are discussed.

The dynamic stability of an elastic prismatic slender column with semirigid connections at both ends of identical stiffness and with sidesway between the two ends totally inhibited, subject to parametric axial loads including the combined effects of rotary inertia and external damping is investigated in a classical manner. Closed-form expressions that can be used to predict the dynamic instability regions of slender columns are developed by making use of Floquet’s theory. The proposed solution is capable of capturing the phenomena of stability of columns under periodic axial loads using a single column element. The proposed method and corresponding equations can be used to investigate the effects of damping, rotary inertia and semirigid connections on the stability analysis of slender columns under periodically varying axial loads. The effects produced by shear deformations along the span of the column as well as those produced by the axial inertia, the coupling between longitudinal and transverse deflections and the curvature are not taken into account. Sensitivity studies are presented in a companion paper that show the effects of rotary inertia, damping and semirigid connections on the dynamic stability of columns under parametric axial loads.

The dynamic stability of an elastic prismatic slender column with semirigid connections at both ends of identical stiffness and with sidesway between the two ends totally inhibited, subject to parametric axial loads including the combined effects of rotary inertia and external damping was presented in a companion paper. Closed-form expressions that predict the dynamic instability regions of slender columns were developed by making use of Floquet’s theory. The proposed equations are straightforward and simple to apply. The proposed solution is capable of capturing the phenomena of stability of columns under periodic axial loads using a single column element. The proposed method and corresponding equations can be used to investigate the effects of damping, rotary inertia and semirigid connections on the stability analysis of slender columns under periodically varying axial loads. Sensitivity studies are presented herein that show the effects of rotary inertia, damping and semirigid connections on the dynamic stability of columns under parametric axial loads. Analytical studies indicate that the dynamic behavior of columns under periodic loading is strongly affected by the flexural stiffness of the end connections and the external damping, but not so much by the rotary inertia. Three examples are presented in detail and the calculated results are compared with those reported by other researchers.

The failure of power system transient stability is one of the main factors causing catastrophic accidents of power systems. Therefore, it is of great significance to evaluate the transient stability of a power system. This paper first introduces the evaluation methods of power system transient stability, including the assessment methods based on time domain simulation, direct method, artificial intelligence-based methods and the probabilistic assessment method. The key challenges in power system transient stability assessment are reviewed and analyzed, including the stability evaluation of power-electronized power system and the main elements of artificial intelligence method used in transient stability assessment. Last, the future research directions and conclusions are discussed.

A pattern recognition methodology is presented which utilizes spectral monitoring of electromechanical oscillations to assess the transient stability of interconnected power systems. The proposed frequency-domain approach permits definitive recognition of unstable dynamic modes. This is used to design an adaptive linear classifier which, in the developmental implementation, virtually eliminates both false dismissals and false alarms. The result is an accurate and reliable decision-making system which performs transient stability monitoring and assessment in real time.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Renewable energy sources interfaced with the grid through power-electronic converters may lose stability and capability to perform as desired when exposed to severe grid faults. As a result of this, transient stability analysis and assessment are particularly important for power system studies. Usually, synchronization stability and transient stability analysis are performed by simulation studies containing a large amount of details, which makes this process highly time-consuming for large-scale systems. To circumvent this issue, a nonlinear second-order model is developed to capture the essential effects of the synchronization process of grid-tied converters during faults. Due to this low-order model, the stability assessment can be approached using phase-plane analysis with a low computational burden - more than 4000 times faster than the full-order switching model. The simplified model is verified against a detailed switching model and laboratory setup of the entire converter system indicating a high accuracy (>96%). Accordingly, the simplified reduced-order model can be used for accurate transient stability studies when a low availability of computational power is present, if large-scale systems are considered, or for detailed uncertainty and sensitivity analysis.

Grid-forming (GFM) converters are regarded as the most promising solution for grid-connected converters of renewable energy due to their robustness against weak grids. However, attributable to their voltage source characteristics, GFM converters may experience overcurrent issues during large disturbances. The virtual impedance (VI) method is an effective method to solve this problem. Nevertheless, there exists a contradiction between the demands for VI posed by current limitations and transient stability. Firstly, the analytical equations of virtual impedance for limiting the fault steady-state current of a GFM converter with different depths of grid voltage sag are solved. On that basis, an adaptive method based on virtual impedance is proposed to limit the fault current. Moreover, the analytical equation of the output active power of the converter when using adaptive virtual impedance to limit the fault current is solved. On this basis, the effect of the virtual impedance ratio on the transient stability is investigated. Finally, an adaptive virtual-impedance-based current-limiting method with the functionality of transient stability enhancement for a grid-forming converter is innovatively proposed. The enhancement effect of the method is verified by the equal area criterion method and phase portrait method. Finally, the efficacy of the proposed method in limiting fault currents and enhancing transient stability is validated through hardware-in-the-loop (HIL) experiments.