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This paper presents a QV-based approach called Critical Voltage-Reactive Power Ratio (CVQR) index to assess the voltage instability tendencies of power system buses with increase in renewable energy (RE) penetration within the power system. The buses are thus ranked according to the order in which they are impacted by increase in renewable energy penetration. Simulations were performed using DIgSILENT PowerFactory and result analyses were done with MATLAB. The developed CVQR index has been employed to assess the effect of increasing RE generation on grid voltage stability. This index provides information on the voltage instability tendencies of all non-slack buses of the RE-integrated grid and the buses are ranked from the weakest to the strongest. The rankings obtained from the developed CVQR has been compared with five commonly-used indices and the result of the comparison verifies the accuracy of the proposed index. IEEE 14-bus and IEEE 39-bus New England systems have been used to evaluate the proposed CVQR index and various scenarios of RE system combinations and placements have been considered. Voltage collapse condition is indicated whenever the CVQR index associated with any bus becomes positive (CVQR > 0). This index can as well be applied to other power system networks. The overall ranking of the buses based on the CVQR index can provide insights on the most appropriate location for large inductive loads or compensating devices, which can either absorb or inject reactive power into the power system, thereby influencing the system's voltage stability. [ABSTRACT FROM AUTHOR]

With the intensive commissioning of high voltage direct current, transient voltage problems have become increasingly prominent, which seriously threatens the safe and stable operation of the power system. On the basis of cascaded CatBoost (CasCatBoost) and sparrow search algorithm (SSA), a novel temporal‐adaptive data‐driven method for short‐term voltage stability (STVS) assessment is proposed in this paper. First, normalized mutual information feature selection is employed for important feature selection to reduce the computational burden. Taking the important features as inputs, the CasCatBoost model is constructed to mine STVS informatization. On the basis of CatBoost and cascaded structure, CasCatBoost can enhance the assessment accuracy without sacrificing the assessment earliness. Furthermore, the SSA is embedded into the offline phases of CasCatBoost to determine the optimal confidence threshold. Extensive numerical tests are conducted on the improved New England 39‐bus system, and the simulation results demonstrate that the proposed method outperforms other representative machine learning algorithms and exhibits excellent reliability, rapidity, and applicability. [ABSTRACT FROM AUTHOR]

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Three static techniques (i.e. Power flow, Continuation Power Flow (CPF) and the Q–V curve) are used to assess the voltage stability of the power grid with a Solar Photovoltaic Generator (SPVG) and FACTS devices under nominal and heavy loading conditions. A static model is proposed for the power system that includes conventional power generation units and SPVGs with FACTS devices. Two models of SPVG were used (i.e., PV-model and PQ-model) to elucidate the effect of the SPVGs on the stability of the voltage under various operating conditions. The best location for FACTS devices was obtained under nominal and heavy load conditions using static techniques. A comparison between series and shunt FACTS devices under nominal and heavy loading conditions was carried out using the three static techniques. The interaction between SPVGs and FACTS devices was detailed in this paper. The proposed approach was tested on the New England 39-bus standard test system, and the results confirmed the effectiveness of the proposed approach under various operating conditions. [ABSTRACT FROM AUTHOR]

Transient stability (TS) and short-term voltage stability (STVS) assessment are of fundamental importance for the operation security of power systems. Both phenomena can be mutually influenced in weak power systems due to the proliferation of power electronic interface devices and the phase-out of conventional heavy machines (e.g., thermal power plants). There is little research on the assessment of both types of stability together, despite the fact that they develop over the same short-term period, and that they can have a major influence on the overall transient performance driven by large electrical disturbances (e.g., short circuits). This work addresses this open research challenge by proposing a methodology for the joint assessment of TS and STVS. The methodology aims at estimating the resulting short-term stability state (STSS) in stable, or unstable conditions, following critical events, such as the synchronism loss of synchronous generators (SG) or the stalling of induction motors (IM). The estimations capture the mechanisms responsible for the degradations of TS and STVS, respectively. The paper overviews the off-line design of the data-driven STSS classification methodology, which supports the design and training of a hybrid deep neural network RCNN (recurrent convolutional neural network). The RCNN can automatically capture spatial and temporal features from the power system through a time series of selected physical variables, which results in a high estimation degree for STSS in real-time applications. The methodology is tested on the New England 39-bus system, where the results demonstrate the superiority of the proposed methodology over other traditional and deep learning-based methodologies. For reference purposes, the numerical tests also illustrate the classification performance in special situations, when the training is performed by exclusively using measurements from generation and motor load buses, which constitute locations where the investigated stability can be observed. [ABSTRACT FROM AUTHOR]

The dc voltage and frequency $ (PVF)$ or modified dc voltage and frequency $ (PV^{2}F)$ double droop control is commended for its ability to regulate both the dc voltage and the frequency in a decentralized approach. However, a convincing response is not achieved due to an interaction between the droop characteristics of dc voltage and frequency. This interaction affects the dc voltage and frequency support of the ac-system-surrounded multiterminal HVdc (AC-MTdc) grid. To overcome this effect, a Duo control strategy is proposed in this article, which takes advantage of a bipolar voltage-source converter topology in the MTdc grid. The virtue of the proposed control technique is emphasized by comparing it with the existing $ PV^{2}F$ double droop control along with three case studies and two test systems. The validation of the interactionless Duo control strategy is carried out on a five-terminal CIGRE dc grid benchmark model integrated into a two-area power system (AC-MTdc grid-1) and a New England IEEE 39-bus system (AC-MTdc grid-2). These test systems are simulated in PSCAD/EMTdc software. [ABSTRACT FROM AUTHOR]

This research presents a new method based on a combined temporal convolutional neural network and long-short term memory neural network for the real-time assessment of short-term voltage stability to keep the electric grid in a secure state. The assessment includes both the voltage instability (stable state or unstable state) and the fault-induced delayed voltage recovery phenomenon subjected to disturbance. The trained model uses the time series post-disturbance bus voltage trajectories as the input in order to predict the stability state of the power system in a computationally efficient manner. The proposed method also utilizes a transfer learning approach that acclimates to the pre-trained model using only a few labeled samples, which assesses voltage instability under unseen network topology change conditions. Finally, the performance evaluated on the IEEE 9 Bus and New England 39 Bus test systems shows that the proposed method gives superior accuracy with higher efficacy and thus is suitable for online application. [ABSTRACT FROM AUTHOR]

Underfrequency load shedding is a common technique for maintaining the stability of the power system by removing the overload in a certain part of the system after a disturbance. The purpose of underfrequency load shedding is to balance output and load when a particular event causes a significant frequency drop in the power system. In conventional underfrequency load shedding schemes, the frequency thresholds of frequency relays are constant, this way it is difficult and sometimes impossible to control the frequency in various disturbances in the system. In this paper, an adaptive underfrequency load shedding (AUFLS) algorithm that is independent of communication between relays is presented. The relays are tuned to reduce loads taking into account local parameters such as voltage and frequency to prevent the occurrence of a cascade failure that can ultimately lead to the breakdown of the entire power system. In this paper, the rate of change of frequency (ROCOF) is obtained by applying the Hilbert-Huang transformation. Numerical simulations conducted on the New England 39 bus test system in the DIgSILENT PowerFactory and MATLAB software packages confirm the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

• A precise measurement-dependent real-time wide area loading margin-sensitivity study is presented. • This task is specific to a wind farm integrated WAMS-based large power system with GPS-aided PMU technology. • The study is based on the computation of a real-time sensitivity index while increasing static load levels linearly. • The sensitivity index can identify the weakest buses for load shedding and provides situational awareness to the grid operator to avoid any power outages. • This study also investigates the effects of increasing DFIG-based wind energy penetration to determine the optimum wind-power penetration level. Increase in integration of fluctuating and unpredictable renewable energy to the power grid, raise the complexity of real-time assessment of voltage stability. A precise measurement-dependent real-time wide area loading-margin-sensitivity study is a novel solution to this problem. This is a challenging task for a wind farm integrated WAMS-based large power system with GPS-aided PMU technology. The study here shows the computation of a real-time sensitivity index while increasing static load levels linearly. The index will be utilized for identifying the weakest buses for load shedding and provides situational awareness to the grid operator for load voltage control to avoid any power outages. Moreover, it assists in determining the fittest bus for load adjustment during scheduled maintenance and the auxiliary bus for instant load increment decisions based on demand. This study also investigates the effects of increasing DFIG-based wind energy penetration to determine the best wind-power penetration level. The proposed analysis was found to be accurate for voltage assessment on the WSCC three-machine nine-bus network and the New England sixteen-machine sixty-eight bus large power networks. An experimental study, to validate the results, is performed using a three-phase industrial category load on the SEL-based hardware test-bed using actual PMU recordings. [ABSTRACT FROM AUTHOR]

• A novel hybrid model and data-driven voltage stability online assessment approach is proposed. • The parameters in the model-driven method are modified based on the response data. • To improve accuracy, impedance difference is included in the data-driven input data. • The proposed method combines the clear mechanism of the model-driven and high accuracy of the data-driven. With the continuously increasing integration of renewable energy sources into power grids, the dynamic response of a power system is becoming more complex. For example, the interaction between the dynamic loads and low-voltage ride-through of renewable energy generators makes the voltage response more rapid and unpredictable. Ensuring the accuracy and speed of traditional voltage stability assessment methods is difficult. This study developed a novel hybrid model and data-driven voltage stability assessment approach. First, the equivalent parameters of a power system were calculated based on the measured data, and the parameters were constantly modified based on the response data. To further improve the accuracy of the approach, a data-driven method was introduced to correct the assessment results using a Thevenin equivalent-based assessment. The difference between the Thevenin and system impedances, which better reflects the system stability, was included in the data-driven input data. Finally, by combining the clear physical mechanism of the model-driven method and high accuracy of the data-driven method, the final the assessment process was a serial combination of the model- and data-driven methods. The effectiveness of the method was verified using an IEEE New England 10-generator 39-bus test system and a 100-bus actual system in China. The results showed that the method developed was more accurate and had higher robustness under data loss and noise conditions than other methods. [ABSTRACT FROM AUTHOR]

Facing the problem of workforce and time costs caused by the rescheduling of large‐scale power grids with renewable energy penetration, and the lack of parallel control research on rotor angle instability and transient voltage instability, a rescheduling method based on trajectory sensitivity and deep reinforcement learning (DRL) is proposed to meet the requirements of rotor angle stability and transient voltage stability at the same time. By introducing the process of rescheduling to meet the transient stability constraint, the Markov decision‐making process of rescheduling is first constructed. Then, a simple dominant instability type identification method is proposed according to the occurrence time, location, voltage pattern, and position of the oscillation centre. Moreover, a rescheduling strategy is formulated based on the dominant instability mode identification, trajectory sensitivity calculation, actionable device selection, action amount computation, and action of the device. Next, according to the improved distributed distributive deep deterministic policy gradients (D4PG), a DRL model is established to map the action to actionable generator pairs and capacitors/reactors, so as to realize parallel rescheduling of rotor angle instability and transient voltage instability. Finally, the improved New England 39‐bus system and an actual power grid are used to verify the effectiveness and advantages of the method. [ABSTRACT FROM AUTHOR]

From the power systems security point of view, determining the voltage stability margin is essential for the operation of systems. An inaccurate determination of the maximum loading factor or voltage collapse point in a power system may cause voltage instability and blackout of the system. So, applying a proper method with high accuracy and high speed is vital in analysing voltage stability in power systems. This article presents a novel method based on Thevenin equivalent of power systems to accurately determine load‐ability margin using phasor measurement units (PMUs) data. The proposed method is based on the fact that at the voltage collapse point, the characteristic curves of 'the reactive power at the receiving end' and 'the reactive power of the load' in the weakest bus are tangential to each other. Furthermore, online application of the proposed method requires accurate estimation of the 'ZIP load model' and 'Thevenin equivalent' of the system. The proposed method is designed to determine the load‐ability margin, ZIP load model and Thevenin equivalent of the power system, simultaneously. This characteristic of the method makes it possible to be applied for online voltage stability assessments. To demonstrate the effectiveness of the proposed method, the simulation results for IEEE 14‐bus, 39‐bus New England and IEEE 300‐bus are presented and analysed. [ABSTRACT FROM AUTHOR]

Aim. A novel technique for detecting imminent voltage instability is proposed in this paper, accompanied by a novel load shedding approach to protect the system from voltage instability. Methodology. The proposed methodology utilizes the computation of nodal reactive power loss to voltage sensitivities with load increments in the system. Originality. The nodal reactive power loss to voltage sensitivity is a novel computation and is explored to detect the likelihood of voltage instability in this work. Results. If the system is experiencing an unprecedented load growth and if all the measures reach their limits, then load shedding is the last resort to safeguard the system against instability. The sudden change in nodal reactive power loss to voltage sensitivities is utilized to devise the quantity of load to be cut in the system. Practical value. The time-based simulations performed in New England 39 bus test system (NE-39 bus), the simulated results show that nodal reactive power loss to voltage sensitivities can be used as a trusted indicator for early diagnosing of menacing voltage instability and the timely implementation of load shedding developed from nodal reactive power loss to voltage sensitivities on the system ensures voltage stability. References 29, tables 1, figures 9. [ABSTRACT FROM AUTHOR]

Voltage instability and voltage collapse are the serious problems that can occur due to reactive power deficits caused by increased load or contingencies. Detecting potential voltage collapse in power systems is essential to maintain voltage stability during high demand. The stability of power systems is an important issue in the planning and operation of these systems. This paper determined the optimal location and size of a FACT STATCOM device for improving the static voltage stability margin of a transmission system. The study network is the IEE New-England transmission network. The problem has been formulated as a multi-criteria optimisation with the objectives of maximising load margin, minimising power losses and minimising voltage deviation. The objective function of the problem is adjusted using the analysis and optimisation method (CPF). The appropriate values and placement for STATCOMs are found using the CPF method based on the objectives below. The proposed method is verified using a simulation test on the IEEE-100 kV network which is part of the IEEE- 39 bus New England power system. The simulation results showed the efficiency of the CPF for the nominal values and the optimal location of the STATCOM. The results showed that the improvement of the voltage stability margin, the voltage profile of IEEE-100 kV is increased and the power losses are reduced. Finally, STATCOM ensures the overall stability of the transport network. [ABSTRACT FROM AUTHOR]

One of the most effective corrective control strategies to prevent voltage collapse and instability is load shedding. In this paper, a multiple-deme parallel genetic algorithm is used for a suitable design of load shedding. The load shedding algorithm is implemented when the voltage stability margin index of the power system is lower than a predefined value. In order to increase the computational speed, the voltage stability margin index is estimated by a modular neural network method in a fraction of a second. In addition, in order to use the exact values of the voltage stability margin index for neural network training, a simultaneous equilibrium tracing technique has been employed considering the detailed model of the components of the generating units such as the governor and the excitation system. In the proposed algorithm, the entire population is partitioned into several isolated subpopulations (demes) in which demes distributed in different processors and individuals may migrate occasionally from one subpopulation to another. The proposed technique has been tested on New England-39 bus test system, and the obtained results indicate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Growing integration of wind power and increasing use of induction motor loads dramatically affect a power system's dynamic performance. To address the challenges, this paper proposes a robust dynamic VAR planning method to enhance the voltage stability of wind energy power systems under uncertainty. Firstly, two indices are developed to evaluate the steady-state and the short-term voltage stability of the system. Then, a robustness index is proposed to quantitatively evaluate the robust optimality of the solutions, considering the uncertainties from wind power output and STATCOMs initial state before a contingency. Four objectives are optimized simultaneously: 1) total planning cost, 2) short-term voltage stability index, 3) steady-state voltage stability index, and 4) robustness of the solutions. Finally, an Adaptive Non-dominated Sorting Genetic Algorithm-III based on Latin Hypercube Sampling (A-NSGA-III-LHS)is designed to solve this many-objective optimization problem with 3 improvements over the standard NSGA-III: 1) adaptive mutation rate, 2) Differential Evolution operator, 3) Latin Hypercube Sampling based initial population generation. The proposed method is tested on the New England 39-bus system with an industry-standard complex load model, showing high robust optimality and computational efficiency over conventional methods. [ABSTRACT FROM AUTHOR]

• The vulnerable branches which affect the transient voltage security are identified. • Image-form samples combine grid structure and power flow information visually. • Knowledge visualization makes CNN-based transient voltage stability assessment model more understandable and reliable. • A comprehensive vulnerability indicator integrates the knowledge in CNN, grid topology and branch state. • The proposed method is demonstrated on a real-life provincial grid with renewable energy integration. Because of the increasing proportion of grid-connected converters, the transient voltage problem has increased the risk of the secure and stable operation of power systems. As the extension of transient voltage stability assessment (TVSA), transient voltage vulnerability assessment is the key technique to detect the crucial elements which can cause the insecurity risk of power system transient voltage. Although deep learning-based TVSA models have demonstrated the high accuracy, it is more important to display the knowledge learnt by the models and utilize it to recognize the weakness of transient voltage. This paper presents a transient voltage vulnerability assessment method by knowledge visualization of convolutional neural network (CNN). First, the image-form sample construction method is proposed to characterize the power system operating condition, which prepares for training CNN-based TVSA model. Then, the knowledge in TVSA model is visualized based on Gradient-weighted Class Activation Mapping (Grad-CAM) and Activation Maximization (AM) algorithms, which is analyzed from the perspective of power system stability. Finally, a comprehensive vulnerability indicator is proposed for identify the weakness of transient voltage, which combines the knowledge inside the TVSA model and the indicators with clear physical meaning. Simulation results of the New England 39-bus test system and the real Shandong provincial power grid in China demonstrate that the visualization makes the model more reliable and the proposed method can accurately identify the vulnerable branches. [ABSTRACT FROM AUTHOR]

• The TVS&TAS integrated assessment scheme based on TSEL-MT-STGNN model is proposed. The scheme can not only assess both TVS&TAS status through adaptive time window, but also achieve high accuracy by fusing spatio-temporal features. • A TVS&TAS integrated margin assessment method is proposed. The method gives intuitive safety margin results based on the safety boundary. • In the training process, a multi-graph parallel training scheme is proposed to speed up the training process. By introducing time constrained loss function (TCLF) and dynamic weight training method, the response time is greatly reduced on the basis of maintaining the existing accuracy. • Based on the ensemble learning framework, STGNN with different structures is integrated. By comparison, the proposed two-stage integration method has higher accuracy and stability in the face of PMU data loss and industrial noise. Transient angle stability (TAS) and transient voltage stability (TVS) are important bases for safe operation of power system. With the replacement of a high percentage of new energy, the voltage and power angle problems are closely coupled, so an integrated assessment method that takes into account the rapidity, accuracy and stability is urgently needed to deal with the system risks. In order to solve this problem, firstly, we propose a multi-task spatio-temporal graph neural network model based on two-stage ensemble learning (TSEL-MT-STGNN) for integrated assessment of TAS&TVS. In the first stage of this model, the topological spatial features of the system are extracted through multi-type graph neural networks, and the obtained knowledge is input to the gated recurrent unit (GRU) for further temporal feature extraction, so as to achieve spatio-temporal information fusion. In this stage, TAS and TVS were combined through the multi-task framework to achieve integrated assessment under the shared features. In the second stage, meta -learner multi-layer perceptron (MLP) is used to fuse the output results of multi-type spatio-temporal graph neural network. Secondly, an integrated assessment method is proposed based on the model, which enables end-to-end assessment, and gives the stability result and safety margin of the system in the current state without knowing the fault clearing time. Thirdly, in order to ensure the timeliness of the assessment method, a multi-graph parallel training scheme is proposed to accelerate the training process. By introducing time constrained loss function and dynamic weight training, the response time is greatly reduced on the basis of maintaining the existing accuracy, thus achieving advance assessment. Finally, the improved New England 39-bus system is taken as an example for verification and analysis. The results show that the proposed method can achieve high-precision advance assessment of TAS&TVS, and has strong robustness and anti-noise capability. © 2017 Elsevier Inc. All rights reserved. [ABSTRACT FROM AUTHOR]

• Power system stability is discussed using the Game Theory. • Since voltage and frequency stability are strictly related together, simultaneous prediction of voltage stability and frequency stability are considered. • The combined method of measuring the weak bus and Game Theory is introduced. • The problem of possibility methods uncertainty has been solved in the stability prediction. Disturbances in the power system may lead to changes in the Voltage and Frequency Stability (VFS) status since they have a lot of parameters in common. Therefore, it is critical to predict these two aspects of power system stability simultaneously, while appropriate protection operations can be taken to improve VFS status. Furthermore, the VFS assessments can be more accurate and faster by eliminating improper statuses in prediction. This paper proposes a novel method for predicting the VFS status using the online measurements of the weak bus based on the theory of Mixed Strategy Games (MSGs). In MSG, the voltage and frequency represent the players, while the stability status is considered as the players' strategy. The Equilibrium Points (EPs), which are obtained from the strategies of the two players, are mapped once the system is subjected to the disturbances. Also, the strategies without EPs are excluded from the game. The probability of each of the players' strategies is evaluated by drawing a game tree. Finally, the EP of the game with the highest probabilities is determined for two players to predict VFS using the Nash Equilibrium (NE). This method involves high levels of accuracy and speeds up real-time prediction using online measurements since it considers the interdependencies effect of these two aspects on each other, elimination of impossible status, certainty in choosing the best solution. The simulations are carried out on IEEE 14-bus, New England 39-bus, and 118-bus systems using MATLAB and DIgSILENT software. The obtained results are compared with the findings of other methods. [ABSTRACT FROM AUTHOR]

• Propose a deep-learning intelligent system incorporating data augmentation for STVS assessment. • Build a BiGRU-attention-based assessment model to extract temporal dependencies. • Effectiveness and superiority of the approach is verified by the New England 39-bus system. • Statistical tests have been performed to examine the performance of the proposal. Facing the difficulty of expensive and trivial data collection and annotation, how to make a deep learning-based short-term voltage stability assessment (STVSA) model work well on a small training dataset is a challenging and urgent problem. Although a big enough dataset can be directly generated by contingency simulation, this data generation process is usually cumbersome and inefficient; while data augmentation provides a low-cost and efficient way to artificially inflate the representative and diversified training datasets with label preserving transformations. In this respect, this paper proposes a novel deep-learning intelligent system incorporating data augmentation for STVSA of power systems. First, due to the unavailability of reliable quantitative criteria to judge the stability status for a specific power system, semi-supervised cluster learning is leveraged to obtain labeled samples in an original small dataset. Second, to make deep learning applicable to the small dataset, conditional least squares generative adversarial networks (LSGAN)-based data augmentation is introduced to expand the original dataset via artificially creating additional valid samples. Third, to extract temporal dependencies from the post-disturbance dynamic trajectories of a system, a bi-directional gated recurrent unit with attention mechanism based assessment model is established, which bi-directionally learns the significant time dependencies and automatically allocates attention weights. The test results demonstrate the presented approach manages to achieve better accuracy and a faster response time with original small datasets. Besides classification accuracy, this work employs statistical measures to comprehensively examine the performance of the proposal. [ABSTRACT FROM AUTHOR]

• Multivariate power series voltage solution is derived by multidimensional holomorphic embedding method. • Analytical static voltage stability boundary is obtained offline based on Cauchy - Hadamard theorem. • The feasibility of online operating conditions is judged very quickly by the proposed method. This paper proposes a novel analytical method to calculate the Static Voltage Stability Boundary (SVSB) for power systems as a hypersurface in a high-dimensional space on power flow solutions. First, the proposed method derives the analytical voltage solution of AC power flows in the form of Multivariate Power Series (MPS) using the Multidimensional Holomorphic Embedding Method (MDHEM). Second, based on the Cauchy-Hadamard theorem , the proposed method is able to derive an analytical expression of the SVSB using the obtained voltage MPS. Besides, a theoretical proof is given in this paper to generalize the proposed method from unidimensional to multidimensional scenarios. In general, the SVSB is found to be analyzable and its analytical expression can be derived offline. Therefore, in the online stage, the proposed method can be used to judge the feasibility of operating conditions very quickly. IEEE 14-bus system, New England 39-bus system, and IEEE 118-bus system are adopted to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• Bus indices are reordered to strength the topology information. • Dynamic responses and topological information are strategically fused and converted into sequential state images. • The sliding 3D-CNN can handle varying degrees of disturbance and performs continuous online monitoring. • 3D-CNN is highly efficient with fewer parameters and can extract features independently of spatial locations. • The translation invariance characteristic makes 3D-CNN highly generic to unknown scenarios. A real-time continuous monitoring system (CMS) for long-term voltage stability assessment with sliding three-dimensional convolutional neural network (3D-CNN) is proposed in this paper. Given a power system, its dynamic responses and topological information are strategically fused and converted into sequential state images, which constitute the learning input of the sliding 3D-CNN. In this way, both spatial and temporal correlation are considered in the CMS. The bus indices are reordered to strengthen the topology information in these images. With the localized weight-shared convolution operations, 3D-CNN can be conducted more efficiently with fewer parameters, and extract features independently of spatial locations. The translation invariance characteristic makes 3D-CNN highly generic to unknown scenarios, which is further enhanced after bus indices reordering. The sliding window of the 3D-CNN enables the CMS to handle varying degrees of disturbance and performs continuous online monitoring. Numerical tests are carried out on the New England 10-generator-39-bus system to demonstrate the effectiveness. Test results also show the potential of the CMS in robustness to PMU measurement errors and information losses. [ABSTRACT FROM AUTHOR]

• A power network is decomposed into two-bus channels with vulnerability index. • A scalable holomorphic embedding method is proposed to solve vulnerability index. • A criterion is developed to identify the truly vulnerable buses. • The potential applications to integrated energy systems are elaborated. This paper proposes a novel method of identifying buses vulnerable to power system voltage instability. Unlike traditional sensitivity and modal analysis methods, the proposed method can preserve the nonlinearity of power flow equations, and visually pinpoint the vulnerable buses in advance for any possible load increasing scenarios. Based on the power flow equations on decomposed two-bus equivalent channels from the power network, a vulnerability index is introduced and visualized for each channel in the solvability region of its decoupled power flow equations bounded by a parabola. It is found that the arrival at the parabolic boundary indicates a potentially vulnerable bus but not necessarily results in voltage collapse. Thus, a criterion on the gradient of vulnerability index trajectory is proposed to discover and differentiate two types of potentially vulnerable buses: one type has trajectories that are tangent to the boundary but stay inside the solvability region; the other type has trajectories crossing the boundary to result in unsolvable power flow equations, which are identified as the vulnerable buses. The proposed method is validated on the IEEE 14-bus, IEEE 118-bus, and New England power systems with comparison to the traditional methods, and the test results show that the proposed method performs better than the traditional methods with satisfactory robustness under voltage fluctuation. In particular, the proposed method is 33.3% and 66.7% more accurate than the voltage sensitivity method in prospective operating conditions on the IEEE 14-bus and 118-bus systems, respectively. [ABSTRACT FROM AUTHOR]