•A fast assessment scheme of power angle and voltage is proposed: Firstly, the critical clearing time (CCT) was solved by the variable step size dichotomy method, and the safety boundary of power ...angle & voltage was constructed from the time dimension. Secondly, the results of system stability and the corresponding margin are given by the boundary of model fitting. The scheme is no need to know the fault clearing time, and only three sampling points are needed to achieve advance assessment.•A new MRSE-CNN model for assessment is proposed: The model integrates power angle and voltage through a multi task framework. At the same time, multi-scale convolution, residual module and squeeze excitation (SE) mechanism are used to improve the basic CNN, so as to maximize the assessment accuracy of the model.•An improved Huber loss function is proposed to solve the problem of different costs of being wrong in online assessment: The improved Huber loss function uses dynamic weight coefficient, so that the model can reduce the number of missing judgments and avoid the increase of misjudgments, further improving the stability of the model.•Solves the problem of accuracy degradation when the model faces unlearned scenarios, and significantly reduces the update cycle: Transfer learning is introduced into the integrated assessment of power angle and voltage for the first time. On this basis, an updated method active transfer learning (ATL) which integrating active learning and transfer learning is proposed. The adaptive update of the model in three dimensions of load, energy and topology is realized by using ATL, which greatly shortens the empty window period caused by the decline of model accuracy.
Transient voltage and transient power angle are in the same time scale, both of which are the basis of safety operation of the power system. However, there are few studies on the integration of power angle and voltage at present. How to quickly realize the integrated assessment of voltage & power angle and how to shorten the update period when the model accuracy drops are the problems that need to be solved urgently. Therefore, this paper proposes a fast assessment scheme that considers both transient voltage and transient power angle. In this study, the stable boundary between the transient power angle and the transient voltage is first constructed from the time dimension by the variable step dichotomy. And then, a convolutional neural network with multiscale residual squeeze excitation (MRSE-CNN) is proposed, which can assess the voltage and power angle without post-fault-clearance data. It only takes three sampling points to accurately learn the mapping between the input feature and the stable boundary. At the same time, the results of whether the transient voltage and the transient power angle are stable, and the corresponding margin are output. By introducing the improved Huber loss function to dynamically adjust the cost of misjudgment and missing judgment, the reliability of the model is further enhanced. In the online application, a pool-based active transfer learning is proposed for the unlearned scenarios under load, topology, and renewable energy, which greatly reduces the adaptive update time of the model in unlearned scenarios. The model is verified in the improved IEEE 39 bus system and provincial interconnection system. It shows that the proposed method can quickly and accurately realize the integrated adaptive assessment of transient power angle and voltage in any scenarios.
•Supervisory control of CIRs improves transient stability of synchronous generators.•CIRs are allowed to participate in dynamic grid support during abnormal conditions.•Control of CIRs can be ...performed during fault and post-fault periods.•The increasing penetration of CIRs can help improve the transient stability margins.
Power-electronic converters are increasingly utilized to integrate renewable and distributed energy resources (DERs) with conventional power grids. The increasing penetration of converter-interfaced resources (CIRs) could, in turn, influence the transient stability of traditional synchronous generators (SGs) in power systems due to their fast response and low inertia nature. This paper evaluates the transient stability of power systems containing SGs and grid-following CIRs under various control schemes and penetration of CIRs. The critical clearing time (CCT) of the SGs is used as the criterion for assessing transient stability following a fault. It is demonstrated that stability margins can be improved by actively controlling the grid-following CIRs during fault and post-fault periods. The proposed method is shown to increase the CCT compared to the conventional/alternative approaches, particularly the common practice that requires CIRs to inject only reactive power to support/regulate voltage during the fault period. It is also shown that with increased penetration of CIRs, if controlled appropriately, the transient stability of SGs can be improved, which is not commonly expected in low-inertia systems.
This paper addresses a novel deep learning (DL) approach for online estimating the transient stability margin (TSM) in power grids. The TSM is characterized by a functional relationship between power ...system variables and the critical clearing time (CCT). To enhance the accuracy of TSM estimation, an improved DL ensemble (iDLE) model, which incorporates the dynamic error correction (DEC) and the multi-objective ensemble learning (MOEL), is proposed. The iDLE model is formulated as an evolutionary multi-objective framework and optimized using the non-dominated sorting genetic algorithm (NSGA-II) along with fuzzy decision analysis to derive the optimal solution. The proposed model is applied to a classical test system and a practical power system, followed by a discussion of the results.
With continuous increase of penetration of renewable energies and power electronic equipment, power grid stability incidents are emerging frequently worldwide. In this paper, the transient stability ...assessment of renewable dominated power systems with multiple PLL-based voltage source converters (VSCs) is studied by calculating critical clearing time (CCT). A tangent hyperplane method is developed, which approximates the boundary of basin of attraction near unstable equilibrium point by linear system theory. The detailed algorithm is presented, accompanying with four typical case studies, including a single machine infinite system, two parallel VSCs, modified IEEE 9- bus, and modified 39- bus systems. Broad EMT simulations are performed to verify the accuracy and computational effectiveness of the algorithm. In all these tests, we find that the hyperplane method can give accurate estimations of CCTs. Hence it is expected to be an efficient method. In addition, we find that generally the CCT in renewable dominated power systems is around tens of milliseconds, which is much shorter than that in traditional power systems around hundreds of milliseconds. Therefore, it might be imperative to adopt faster controls and protections for renewable dominated power systems.
Machine learning (ML) for transient stability assessment has gained traction due to the significant increase in computational requirements as renewables connect to power systems. To achieve a high ...degree of accuracy; black-box ML models are often required - inhibiting interpretation of predictions and consequently reducing confidence in the use of such methods. This paper proposes the use of SHapley Additive exPlanations (SHAP) - a unifying interpretability framework based on Shapley values from cooperative game theory - to provide insights into ML models that are trained to predict critical clearing time (CCT). We use SHAP to obtain explanations of location-specific ML models trained to predict CCT at each busbar on the network. This can provide unique insights into power system variables influencing the entire stability boundary under increasing system complexity and uncertainty. Subsequently, the covariance between a variable of interest and the corresponding SHAP values from each location-specific ML model - can reveal how a change in that variable impacts the stability boundary throughout the network. Such insights can inform planning and/or operational decisions. The case study provided demonstrates the method using a highly accurate opaque ML algorithm in the IEEE 39-bus test network with Type IV wind generation.
One of the most important features of a reliable power system is its capability to supply the demand continuously. This continuous supply has been maintained by the transient stability of the system ...against large disturbances. The study of this type of stability is examined through different indicators. One of the common indicators to evaluate the transient stability of the power system is the well-known Critical Clearing Time (CCT) index. Conventional methods for calculating CCT have presented good accuracy, however, their computational cost is very high which makes them not suitable for real-time applications and real large-scale networks. Considering their ability to feature extraction of big data, deep neural networks can be utilized as reliable tools to cover these deficiencies. In this regard, to cover the shortcomings of the conventional methods, this paper proposes a method based on deep Convolutional Neural Networks (CNN) to estimate the CCT index in real-time power system applications. Moreover, to analyze a realistic case, nonlinear limiters of the excitation systems which have a considerable effect on transient stability index are considered in this study. Thanks to the using of several deep layers and the comprehensive established database, the accuracy of proposed method is appropriately high. Numerical studies on IEEE standard networks as well as a real case in Iran Power Grid (IPG) represents the advantages of the proposed method.
•A deep-learning-based convolutional neural network is designed to estimate CCT index of power system.•Nonlinear limiters of the excitation system are taken into account.•A real case study in Iran grid is considered for simulation.•As a result, the transient stability of system is accurately determined in on-line manner.
In this paper, we approach the problem of stability in nonlinear systems through a new perspective that views them as a combination of individual artificial systems carefully chosen to simplify the ...complex structure of nonlinear systems. This is achieved by recasting nonlinear vector fields as an algebraic sum of individual vector fields for which artificial systems with known invariant sets or at least in forms that allow for tractable approximation of their invariant sets. This attempt to restructure nonlinear systems stands out in comparison to other previous attempts like Lure' systems or network based models as a purely mathematical structuring technique that transcends the physical constraints and dependencies within dynamical models and allows the user to creatively construct artificial systems with the sole focus on the overall stability. The theoretical foundation is provided for a theorem about individual invariance to relate the invariant sets of individual artificial systems to the invariant set of their original system in a way that significantly simplifies the task of approximating regions of attraction. Several examples are used to demonstrate this theorem and we also evaluate the use this theorem for the challenging power system stability problems in both AC and DC grids. The proposed method is successfully applied to the IEEE 39- bus New England system, and a DC converter with constant power load giving accurate and realistic estimations of the critical clearing time and stability regions in comparison to state of the art approaches.
•Transient stability assessment with increasing the wind power penetration.•Using the Gershgorin theorem to tune the control parameters of the converter.•Neglecting the stator transients in ...closed-loop DFIG.•For power system stability studies, the 3rd order model of DFIG can be used.
In the power systems where a significant part of the total generated power is supplied by wind energy, the transient stability of the grid should be analyzed properly. This paper discusses the influence of the closed-loop control system of doubly-fed induction generator (DFIG) on transient stability. In this process, the stator and rotor electrical dynamics are considered during tuning the controllers. Accordingly, the DFIG with power electronics converters in the closed-loop control mode with generic PI controllers is considered. For this study, the dynamic model of the rotor side converter with more detail of the control system is used, because it has a direct effect on the dynamics of the generator speed/torque and hence on the system stability. Also, to tune the control parameters of the power electronics converters, the Gershgorin theorem is applied. Once an appropriate set of control parameters is obtained, the DFIG model is simplified and time-domain simulation is performed. For validation of the influence of modeling adequacy on closed-loop controlled DFIG, transient stability study under the different operating conditions is investigated. According to the simulation results, it is observed that for the closed-loop DFIG, neglecting the stator transients does not remove the high-frequency mode. Thus, the high-frequency mode is due to the rotor electrical dynamics. Additionally, the power system stability studies for closed-loop DFIG are not model order dependent. Accordingly, for the closed-loop controlled DFIG in the transient stability studies where fast electrical transients are not of interest, a simplified model, whereby both stator and rotor dynamics are neglected, is adequate.
Transient stability analysis is a crucial tool for evaluating stability and ensuring safe operation of power systems. Among existing methodologies for transient stability analysis, direct methods ...show merits in performing fast contingency screening and providing quantitative information for the degree of stability. However, the inherent conservatism of direct methods and their restriction on power system models still pose significant challenges for practical applications. This paper is devoted to further developing direct methods by proposing a novel adaptive Lyapunov function method , which enables estimation of critical clearing time with drastically reduced conservatism. The novelties of the proposed method lie in three aspects. First, we propose an adaptive sector condition which bounds the nonlinearity of the power system model in an adjustable neighborhood of a given equilibrium point. Second, we introduce an improved bounding technique for the time derivative of the Lyapunov function. Third, by exploiting the freedom of the adaptive sector condition and the adjustable neighborhood , the construction of Lyapunov functions along with the choice of the parameters in the sector conditions can be co-optimized to achieve the tightest possible estimation of the critical clearing time. The effectiveness of the proposed method is validated on four benchmark systems.
Contingency screening for transient stability of large-scale, strongly nonlinear, interconnected power systems is one of the most computationally challenging parts of Dynamic Security Assessment and ...requires huge resources to perform time-domain simulations-based assessment. To reduce computational cost of time-domain simulations, direct energy methods have been extensively developed. However, these methods, as well as other existing methods, still rely on time-consuming numerical integration of the fault-on dynamics. This task is computationally hard, since possibly thousands of contingencies need to be scanned and thousands of accompanied fault-on dynamics simulations need to be performed and stored on a regular basis. In this paper, we introduce a novel framework to eliminate the need for fault-on dynamics simulations in contingency screening. This simulation-free framework is based on bounding the fault-on dynamics and extending the recently introduced Lyapunov Function Family approach for transient stability analysis of structure-preserving model. In turn, a lower bound of the critical clearing time is obtained by solving convex optimization problems without relying on any time-domain simulations. A comprehensive analysis is carried out to validate this novel technique on a number of IEEE test cases.
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