Transient Stability Boundary Research Articles

A multi-task transient stability assessment method adapted to topology changes using multi-graph sample and aggregate-attention network

Transient stability assessment (TSA) plays a pivotal role in guiding power grid risk control strategies. However, it faces challenges when dealing with complex multi-graph inputs generated by pre-fault, fault occurrence, and post-fault states. Meanwhile, most previous research studies neglected the assessment of the transient stability level. To address this, we propose a multi-task transient stability assessment (MTTSA) approach. In MTTSA, we introduce a multi-graph sample and aggregate-attention network (GraphSAGE-A) designed to capture stability features even amidst topology changes. A multi-head attention mechanism and local normalization method are adopted for a better extraction of the global and contextual information. Additionally, we introduce a quantified transient stability risk index considering the transient stability boundary and incorporate a multi-task dense structure to enhance MTTSA’s performance. Empirical tests, under changing operating conditions, conducted on the IEEE 39-bus system showcase a significant performance improvement with the proposed MTTSA method.

Approaching the Transient Stability Boundary of a Power System: Theory and Applications

Estimating the stability boundary is a fundamental and challenging problem in transient stability studies. It is known that a proper level set of a Lyapunov function or an energy function can provide an inner approximation of the stability boundary, and the estimation can be expanded by trajectory reversing methods. In this paper, we streamline the theoretical foundation of the expansion methodology, and generalize it by relaxing the request that the initial guess should be a subset of the stability region. We investigate topological characteristics of the expanded boundary, showing how an initial guess can approach the exact stability boundary locally or globally. We apply the theory to power system transient stability assessment, and propose expansion algorithms to improve the well-known Potential Energy Boundary Surface (PEBS) and Boundary of stability region based Controlling Unstable equilibrium point (BCU) methods. Case studies on the IEEE 39-bus system well verify our results and demonstrate that estimations of the stability boundary and the critical clearing time can be significantly improved with modest computational cost. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the problem of determining whether a power system can retain transient stability subject to large disturbances such as short-circuit fault and generator tripping. The most well-known approaches to such a problem are the direct methods that can avoid time-costly simulations and “directly” determine the transient stability by estimating the stability boundary. Nevertheless, such estimations are generally too conservative. This paper proposes a new expansion method to improve the direct methods, which allows the initial estimation to lie partially outside the real boundary and hence enables applications to both global and local direct methods. Our method can expand the initial estimation towards the real stability boundary, thus reducing the conservativeness and providing a more accurate stability assessment such as the critical clearing time (CCT) of a fault. In this paper, we first mathematically establish the expansion theory and then propose numerical algorithms for power system applications. Simulations on the IEEE 39-bus benchmark verify our approach and show that the conservativeness can be significantly reduced with modest computational cost. Our approach can be further extended to scenarios where a valid Lyapunov (energy) function is unavailable.

Reduced-Order Modeling and Transient Synchronization Stability Analysis of Multiple Heterogeneous Grid-Tied Inverters

This article outlines a generalized reduced-order modeling approach for assessing the transient synchronization stability of multiple grid-tied converter systems operating in grid-feeding mode and having heterogeneous characteristics. The analytical approach utilizes the nonlinear quasi-static dynamics of the phase-locked loop (PLL) for obtaining the reduced-order models (ROM) of multiple heterogeneous grid-feeding converters having same and different point of synchronization (POS). This is a significant contribution in contrast to the prior effort where reduced-order modeling has been carried out only for homogeneous grid-tied multi-converter systems. In addition to this, an innovative methodology has been proposed in this article for analyzing the transient synchronization stability of the multi-converter systems leveraging the Lyapunov's direct method. The Lyapunov functions are constructively synthesized by invoking an assumption that the reduced-order models are conservative in nature. Following this, the well-known Lyapunov's second theorem is applied for deriving the sufficient conditions required for obtaining the transient stability boundary of the heterogeneous grid-feeding converter systems. Numerical simulations are performed in MATLAB 2017a platform to demonstrate that the ROM are highly accurate and computationally efficient. Besides, the efficacy of the proposed methodology for analyzing the transient synchronization stability of heterogeneous grid-feeding multi-converter systems is verified numerically.

Design-Oriented Analysis and Transient Stability Enhancement Control for a Virtual Synchronous Generator

Under fault conditions, virtual synchronous generators (VSGs) are prone to lose transient stability, similar to synchronous generators. However, the existing studies on VSG transient stability are not comprehensive. The transient characteristics of VSGs are highly affected by control parameters, but the transient models of VSGs in existing studies are overly simplified. In addition, the critical clearing angle (CCA) and critical clearing time (CCT) are two indices used to measure the transient stability of a system, but there are few studies that consider both CCA and CCT. In this article, we analyze the CCA and CCT quantitatively to describe the transient stability boundary of a VSG under different control parameters and fault conditions. Then, an equal proportional area criterion is proposed to provide guidance for the control of virtual inertia in the VSG. Based on a theoretical analysis, a transient control method for a VSG is proposed, which can improve the transient stability of the VSG in terms of both CCA and CCT. Finally, simulation and experimental tests are performed to validate the correctness of the theoretical analysis and the proposed method.

Transient stability analysis of the standalone solar‐storage AC supply system based on grid‐forming and grid‐following converters during sudden load variation

AbstractThe standalone solar‐storage AC supply system is an efficient form of utilizing renewable energy. The solar‐storage supply system normally includes two types of converters, grid‐forming (GFM) and grid‐following (GFL) converters. Nevertheless, the incompatibility of the dynamic performance between the GFM and GFL converters due to different control schemes may introduce the transient instability risk to the solar‐storage supply system. To address this issue, it is extremely necessary to perform transient stability analysis and stability‐enhanced control for such a system. In this paper, a sixth‐order model of the dc‐link timescale for the solar‐storage supply system is developed, whose accuracy and applicability are verified by comparing with the detailed electromagnetic model. Based on the derived model, the analysis demonstrates that the solar‐storage supply system faces the potential risk of transient instability under large disturbances of sudden load variation, due to the mismatch of the transient response speeds between virtual excitation control of the GFM converter and dc voltage control of the GFL converter. The transient stability boundary of the system is quantitatively investigated, by depicting the basin of attraction of the post‐disturbance equilibrium point. Furthermore, from the perspective of improving the coordination of the transient behaviours between the GFM converter and the GFL converter, the parameters related to virtual excitation control and dc voltage control are designed to enhance the transient stability of the system. Time‐domain simulations and real‐time simulations are conducted to validate the theoretical analysis.DC–AC power convertors, microgrids, power system control, power system transient stability, renewable energy power conversion

Synchronization Stability of Grid-Following Converters Governed by Saturation Nonlinearities

Saturation nonlinearities caused by control limiters will be activated during large disturbances, complicating the stability of grid-tied voltage source converters (VSCs). This letter investigates the large-disturbance synchronization stability of the grid-tied VSC considering two typical control limiters, i.e., the hard limiter of the reference current and the circular limiter used to avoid overmodulation. A unified differential equation (UDE) model is proposed to quantify the transient responses and stability boundaries of the system under different saturation conditions. It is revealed that the VSC behaves as a current source when the hard limiter is activated; while the interaction between the two limiters drives the VSC to work as a voltage source, making it immune to synchronization instability.

Evaluating the significance of samples in deep learning-based transient stability assessment

Deep learning-based transient stability assessment has achieved big success in power system analyses. However, it is still unclear how much of the data is superfluous and which samples are important for training. In this work, we introduce the latest technique from the artificial intelligence community to evaluate the significance of the samples used in deep learning model for the transient stability assessment. From empirical experiments, it is found that nearly 50% of the low-significance samples can be pruned without affecting the testing performance at the early training stages, thus saving much computational time and effort. We also observe that the samples with the fault-clearing time close to the critical clearing time often have higher significance indexes, indicating that the decision boundary learned by the deep network is highly related to the transient stability boundary. This is intuitive, but to the best of our knowledge, this work is the first to analyze the connection from sample significance aspects. In addition, we combine the stability scores with the significance index to provide an auxiliary criterion for the degree of stability, indicating the distance between a sample and the stability boundary. The ultimate goal of the study is to create a tool to generate and evaluate some benchmark datasets for the power system transient stability assessment analysis, so that various algorithms can be tested in a unified and standard platform like computer vision or natural language-processing fields.

Impact of DC-Bus Voltage Control on Synchronization Stability of Grid-Tied Inverters

The impact of dc-bus voltage control (DVC) on transient synchronization stability of grid-tied inverters operating in grid-feeding mode has been assessed in this brief. A nonlinear quasi-static model magnifying the dynamics of phase-locked loop (PLL) and DVC of grid-tied inverter has been developed first. Following this, the steady-state and transient stability boundaries of the model are analytically characterized and numerically evaluated. The proposed model and the stability assessment method eliminates the inaccuracies associated with the previously developed model which considers the dynamics of PLL alone.

Transient stability assessment in large-scale power systems using sparse logistic classifiers

In this paper, the problem of transient stability assessment is formulated as a pattern recognition problem. The transient stability boundary (TSB) separates the region between the secure and unsecure operation conditions. In large-scale power networks, the TSB is a very high dimensional hyperplane. A modern machine learning method called the “sparse logistic classifier” is applied for finding the TSB. This approach combines the classical logistic classifier with a L1 penalty, and it inherently possesses the automatic feature reduction property desired for high-dimensional modeling. This methodology is demonstrated by a 470-bus power network, and compared with several competing methods recently applied in this field. These competing methods include the support vector machine (SVM) and the k-nearest neighbor (kNN) classifier, as well as the classical logistic classifier which is not equipped with the L1 design. Fit for high dimensional problems, our approach demonstrates superior predictive classification accuracy.

Calculation of the transient stability boundary of AC/DC inter‐connected system based on the stability margin of dynamic energy

Concerning the transient power angle stability problem in AC/DC inter-connected system caused by DC line grounding fault, a transient stability analysis method based on the stability margin of dynamic energy is proposed. First, the analytical expressions of the dynamic energy function before alpha retard, during alpha retard and after alpha retard are derived. According to the topologies of system and the integration intervals of energy function in different stages, the expressions of the acceleration energy, position energy and margin energy are obtained, which, respectively, reflect the rotating speed of system, the swing range of power angle and the system's ability of resisting in stability. Then, the surplus energy in the system is calculated by subtracting the sum of the acceleration energy and position energy from the margin energy, and the stability margin of the system is obtained. And then, the stability boundary of the system is derived. It is revealed that, if the stability margin is exactly right 0 at the end moment of alpha retard, the system is critical stable. Finally, hardware-in-the-loop tests are conducted in RT-LAB platform. The simulation results verify that, the stability margin reaches the minimal value at the end moment of alpha retard, and this value can clearly reflect the stability of system. Besides, the earlier the alpha retard starts or the longer the distance between the fault point and the rectifier outlet is, the better it is for the stability of system.

Data-Driven Transient Stability Boundary Generation for Online Security Monitoring

Transient stability boundary (TSB) is an important tool in power system online security monitoring, but practically it suffers from high computational burden using state-of-the-art methods, such as time-domain simulation (TDS), with numerous scenarios taken into account (e.g., operating points (OPs) and N-1 contingencies). The purpose of this work is to establish a data-driven framework to generate sufficient critical samples close to the boundary within a limited time, covering all critical scenarios in current OP. Therefore, accurate TSB can be periodically refreshed by tracking current OP in time. The idea is to develop a search strategy to obtain more data samples near the stability boundary, while traverse the rest part with fewer samples. To achieve this goal, a specially designed transient index sensitivity based search strategy and critical scenarios selection mechanism are proposed, in order to find out the most representative scenarios and periodically update TSB for online monitoring. Two case studies validate effectiveness of the proposed method.

Research on Applicability of the Practical Transient Voltage Stability Criterion Based on Voltage Magnitude and Sag Duration

Voltage sags threaten the transient voltage stability of power systems. To evaluate the transient voltage stability, practical criteria based on voltage magnitude and sag duration are widely used in practical engineering. However, the applicability of practical criteria needs to be studied. In this paper, in a single-load system, a theoretical derivation was first made to obtain the transient voltage stability boundary. Then, by studying the relationship between the practical criteria and the stability boundary, the application scope of the practical criteria was determined. The application scope described in this paper can guide operators to use the practical criteria correctly and avoid misjudgment of the transient voltage stability as much as possible. Finally, a case study based on PSCAD/EMTDC is presented, and the simulation results verified the conclusions proposed in this paper.

Construction of Multi-State Transient Stability Boundary Based on Broad Learning

This paper presents a novel methodology for the construction of a transient stability boundary (TSB) that overcomes the lack of TSB analytical description for multiple operating states and contingencies in power systems. The proposed approach models the TSB as a nonlinear mapping between the system parameters of interest and the corresponding critical clearing time (CCT). This compact mathematical expression is built based on an efficient discriminative network, broad learning system (BLS). While keeping a high accuracy and generalization ability, the newly introduced construction method provides an efficient update strategy that does not require an entire retraining cycle. These properties make this method suitable for online transient stability assessment (TSA). The prospects of the developed method are verified via case studies by employing the IEEE 9-bus, IEEE 39-bus (New England) test systems and a real system of China Southern Power Grid. In comparison with existing methods, the newly introduced algorithm has a higher prediction accuracy and improved robustness. The demonstrated characteristics indicate that the proposed method may serve as a valuable tool in the framework of online TSA.

Identification of transient stability boundaries for power systems with multidimensional uncertainties using index-specific parametric space

This paper introduces a method for the identification of transient stability boundaries in power systems with multidimensional uncertainties. This method uses a parametric space rather than the state-space to identify the critical operating states. First, different transient stability indices are used to map the state-space of system into the index-specific parametric spaces. Then, these index-specific parametric spaces are characterized to identify their practicality and effectiveness to reflect the system’s state-space information accurately and to quantify uncertainties. Finally, the transient stability boundaries are identified using the index-specific parametric spaces considering multidimensional uncertainties. The indices studied in this paper are on basis of rotor-angle difference, transient kinetic energy, and transient potential energy. This method is verified using a 16-machine, 68-bus computer model of the New England Test System and the New York Power System in MATLAB and DigSILENT environments. The uncertainty in this paper is represented in up to 4-dimensions and is modeled in form of loading conditions and generation dispatch uncertainties. This method is further applicable to higher dimensions and other forms of uncertainties and has the utility for probabilistic studies and predictive analytics.

Transient stability assessment in large-scale power systems based on the sparse single index model

We apply a class of nonlinear semiparametric models to the problem of transient stability analysis of a large-scale power system. The mapping between the pre-contingency state and the transient stability boundary (TSB) is modelled by a block-oriented structure known as the single-index model (SIM). In this model one has a single dimensional projection that enters the unknown nonlinearity nonparametrically. Such models form a rich class of nonlinear mappings that includes classical models, e.g., linear and logistic regression, as special cases. The generalized case of the SIM is utilized that is taking into account the sparsity of the projection vector. This yields a low-dimensional nonlinear model suitable for high-dimensional data emerging in modern power systems. The parametric part of the model is obtained by the properly modified sparsity sensitive LASSO algorithm. The nonlinear nonparametric part of the model is estimated by the monotonically corrected kernel regression estimate. The precision of our modeling is verified for two fault cases of the 470-bus power system. It is shown that for the examined faults, the proposed modeling methodology exhibits a stronger prediction accuracy compared to the existing competing methods recently applied in the field, namely, kernel ridge regression, as well as LASSO linear modeling.

Additive modeling and prediction of transient stability boundary in large-scale power systems using the Group Lasso algorithm

In this paper, the problem of prediction of the transient stability boundary (TSB) of large-scale power systems is analyzed. For any given fault in a power system, whether a pre-contingency condition is considered as a stable operating point can be characterized by the critical clearing time (CCT). The mapping between the pre-contingency steady state and the CCT is in this paper modelled as additive multivariate regression of nonlinear functions of individual input features. Each individual univariate nonlinear function is approximated by an orthogonal polynomials representation, and then the Group Lasso as well as the adaptive Group Lasso algorithms are employed to estimate the original multivariate regression function. Although the original nonlinear structure is highly dimensional, it is shown in this paper that the final model exhibits a simple parsimonious form composed of only a few input features. This is due to the ability of the employed algorithms to recover the inherent sparsity in additive components of the proposed additive representation. This methodology is demonstrated by being applied to multiple fault cases in the context of a 470-bus power network. This approach is also compared with two competing methods recently applied in the dynamic security assessment literature: kernel ridge regression, as well as the Lasso method applicable to linear sparse models.

Prediction of the Transient Stability Boundary Based on Nonparametric Additive Modeling

This paper applies modern statistical nonparametric methodology to the problem of prediction of the transient stability boundary of large-scale power engineering systems. The stability issue is characterized by the critical clearing time (CCT) that is employed to determine whether a precontingency steady-state condition is stable for a given fault in the power system. The multidimensional mapping between the precontingency steady-state conditions and the corresponding CCT is modeled as an additive structure of one-dimensional functions. Nonparametric kernel estimation methods are applied to the assumed additive model yielding the boundary prediction algorithm that is easily interpretable and avoids the curse of dimensionality. The precision of our additive nonlinear modeling is demonstrated in the context of fault prediction of the 470-bus power network. For the specified fault type, we demonstrate a stronger prediction accuracy compared to other large-scale machine learning methods that have been used for the transient stability boundary problem so far.

Prediction of the Transient Stability Boundary Using the Lasso

This paper utilizes a class of modern machine learning methods for estimating a transient stability boundary that is viewed as a function of power system variables. The simultaneous variable selection and estimation approach is employed yielding a substantially reduced complexity transient stability boundary model. The model is easily interpretable and yet possesses a stronger prediction power than techniques known in the power engineering literature so far. The accuracy of our methods is demonstrated using a 470-bus system.

Two approaches to transient stability-constrained optimal power flow

Formulation of transient stability-constrained optimal power flow (TSC-OPF) and finding a practical solution for the problem have gained much attention recently. In this paper, two approaches to include transient stability constraints in the OPF problem considering detailed dynamic models for generators and their controls are introduced. The first method is based on the maximum relative rotor angle deviation (MRRAD) of generators which suits systems that have specific requirements on MRRAD. The second method represents the transient stability margin of the system based on generators output power (GOP) and hence does not rely on MRRADs. The transient stability boundary can be represented by a nonlinear function of GOP. The Artificial Neural Network (ANN) curve-fitting tool is used to derive a mathematical formulation for the transient stability boundary (TSB). The closed form representation of the TSB is then inserted in the OPF problem as a new constraint. The proposed method is examined using the WSCC 9-bus, the New England 39-bus and the IEEE 300-bus test systems. The results indicate that the proposed methods lead to lower computational time in solving TSC-OPF which has been a serious challenge for this problem.

Derivation of an Accurate Polynomial Representation of the Transient Stability Boundary

This paper presents an efficient method to estimate a transient stability boundary (TSB) as a nonlinear function of power system variables. The proposed method exploits the computational efficiency of linear estimation methods to determine an accurate nonlinear function. The novelty of the proposed method is that a nonlinear transformation is applied to the original variables, voltage magnitudes, and phase angles, so that the TSB is approximately linear in terms of the transformed variables. The linear function obtained using the transformed variables is indeed nonlinear in terms of original variables. The attractiveness of this method is that the estimated function is not a linearized approximation, although a linear estimation method is used. The potential of the proposed method is demonstrated using the New England 39-bus system and a larger power system with 470 buses