Nodes In Power Grid Research Articles

TrendRank method for evaluating the importance of power grid nodes considering information network

To ensure the stable operation of power systems, critical nodes need to be identified for key protection. The LeaderRank algorithm is a fast and accurate algorithm for identifying key nodes, but it has obvious inappropriateness when targeting the power system. For this reason, this paper considers the scheduling function of the information network and the power flow betweenness of the power grid. A TrendRank algorithm is proposed to identify key nodes in complex power grids. TrendRank values can be computed iteratively by a weighted distribution strategy of internally linked nodes and then ranked. The performance of the TrendRank method has been fully tested and benchmarked on IEEE39 and IEEE118. The comparison of four performance metrics fully validates the effectiveness and superiority of the method. The TrendRank algorithm provides an idea in protecting the power system, which makes the economic cost of protecting the power system lower.

Power-grid stability predictions using transferable machine learning.

Complex network analyses have provided clues to improve power-grid stability with the help of numerical models. The high computational cost of numerical simulations, however, has inhibited the approach, especially when it deals with the dynamic properties of power grids such as frequency synchronization. In this study, we investigate machine learning techniques to estimate the stability of power-grid synchronization. We test three different machine learning algorithms-random forest, support vector machine, and artificial neural network-training them with two different types of synthetic power grids consisting of homogeneous and heterogeneous input-power distribution, respectively. We find that the three machine learning models better predict the synchronization stability of power-grid nodes when they are trained with the heterogeneous input-power distribution rather than the homogeneous one. With the real-world power grids of Great Britain, Spain, France, and Germany, we also demonstrate that the machine learning algorithms trained on synthetic power grids are transferable to the stability prediction of the real-world power grids, which implies the prospective applicability of machine learning techniques on power-grid studies.

An Algorithm for Calculation and Extraction of the Grid Voltage Component

Calculating the values of the parameters of distorted periodic signals in real-time is important for the control of many processes. In particular, this information is necessary for the proper operation of power electronics devices that cooperate with the power grid. In such cases, it is necessary to determine the phase, frequency, and amplitude of the fundamental component of the voltage in the power grid node. Also, in many cases, the control process needs a signal which is synchronised with the power grid voltage. Both processes should be realised in real-time. A number of solutions to the problem of calculating the values of the voltage parameters have been described in the literature. However, these methods generally introduce significant time delays and have several restrictions regarding the variability in the values of these parameters. They also often require the significant computational power of a unit that performs the task of identification. The algorithm presented in this work is based on the properties of a pair of orthogonal signals, generated by a two-dimensional finite impulse response filter, which has a certain transfer function resulting from the needs of the algorithm, what is the innovation of the algorithm. These signals are then used in the program module, which both, calculates, in the time domain, the instantaneous values of the frequency and the amplitude of the fundamental component of the power grid voltage, and generates a signal, being in-phase with this component. The presented algorithm is fast, accurate, and relatively simple; therefore, it does not require a high computational power processor. This algorithm was experimentally verified by implementation in microcomputer-based units, which were then applied in the control systems of the power electronic devices, as well as in analysers of the energy quality.

Cascading-failure-resilient interconnection for interdependent power grid - Optical network

The interdependence between communication networks, e.g., an optical backbone network, and power grids is a critical issue to take into account when designing and operating both systems. In fact, failures in one network may cause further failures in the other network and vice versa. This is because nodes in power grids (i.e., power generators, loads or interchange nodes) are controlled and managed by telecommunication equipment, which, in turn, rely on the electricity grid for their power supply. Therefore, failures occurring on a limited portion of one network can cascade multiple times between these two networks, and a robust “interdependency network” (i.e., consisting of the interconnections between nodes in the two networks) is needed. This paper investigates the problem of designing a resilient interconnection against interdependent cascading-failures in interdependent power grid - optical networks. We formalize, using an Integer Linear Program, the new problem of Power Grid - Optical Network Interconnection (PGON-I), which consists in designing an interconnection between the power grid and the optical network that is resilient to cascading failures, i.e., avoids/reduces cascade. For this problem, we derive analytically upper and lower bounds on the number of interconnection links which ensure resilience against cascading failures initiated from a single node-failure. Starting from the analytical model, we develop a heuristic algorithm to solve large instances of the problem. Our results show that the higher the difference between the number of nodes in the two networks, the more interconnection links are needed to ensure resilience against failures cascade.

How modular structure determines operational resilience of power grids

The synchronization stability has been analyzed as one of the important dynamical characteristics of power grids. In this study, we bring the operational perspective to the synchronization stability analysis by counting not only full but also partial synchronization between nodes. To do so, we introduce two distinct measures that estimate the operational resilience of power-grid nodes: functional secureness centrality and functional robustness centrality. We demonstrate the practical applicability of the measures in a model network motif and an IEEE test power grid. As a case study of German power grid, we reveal that the modular structure of a power grid and particular unidirectional current flow determine the distribution of the operational resilience of power-grid nodes. Reproducing our finding on clustered benchmark networks, we validate the modular effect on power grid stability and confirm that our measures can be the insightful tools to understand the power grids’ synchronization dynamics.

Decentralized blockchain-based consensus for Optimal Power Flow solutions

We design, implement and analyze a decentralized consensus algorithm based on the blockchain technology for the solution of the Optimal Power Flow problem. The proposed algorithm enables independent power grid nodes, without prior trust on each other, to reach an agreement on the Optimal Power Flow solution. We decompose the Optimal Power Flow problem using a blockchain-based Alternating Direction Method of Multipliers and we comment on efficiency, trust, security and transparency issues. The successive iterants of the solution of the power flow problem are securely stored on the blockchain, removing the need for a central operating authority, while allowing network nodes to verify the validity and optimality of the solution. We illustrate the effectiveness of the consensus algorithm presented through simulation experiments on the 39-bus New England transmission system, and IEEE-57 and IEEE-118 benchmark systems. We systematically compare the effectiveness of the proposed algorithm with well established blockchain consensus algorithms. The results show that our method maintains the convergence characteristics of the Alternating Direction Method of Multipliers iterative scheme and enables independent network nodes to reach consensus.

Vulnerability in dynamically driven oscillatory networks and power grids.

Vulnerability of networks has so far been quantified mainly for structural properties. In driven systems, however, vulnerability intrinsically relies on the collective response dynamics. As shown recently, dynamic response patterns emerging in driven oscillator networks and AC power grid models are highly heterogeneous and nontrivial, depending jointly on the driving frequency, the interaction topology of the network, and the node or nodes driven. Identifying which nodes are most susceptible to dynamic driving and may thus make the system as a whole vulnerable to external input signals, however, remains a challenge. Here, we propose an easy-to-compute Dynamic Vulnerability Index (DVI) for identifying those nodes that exhibit largest amplitude responses to dynamic driving signals with given power spectra and thus are most vulnerable. The DVI is based on linear response theory, as such generic, and enables robust predictions. It thus shows potential for a wide range of applications across dynamically driven networks, for instance, for identifying the vulnerable nodes in power grids driven by fluctuating inputs from renewable energy sources and fluctuating power output to consumers.

Key Line Identification of Power Grid Based on Entropy Weight Method of Pearson Coefficient Index Selection

As one of the important infrastructure of the country, it is very important to identify the key links of the power network and protect them to prevent the blackout. Based on the theory of complex network, this paper proposes a comprehensive multi-attribute identification method for key nodes of power grid. Firstly, the Pearson correlation coefficient is used to select the evaluation index according to the topological characteristics of the power grid, then the entropy weight method is used to get the final decision matrix, and finally adopt the comprehensive method to calculate the order of the important lines in the power grid. In order to compare the advantages and disadvantages of different recognition methods, we compare the evaluation results of electrical method, and further verify the effectiveness of the proposed method in IEEE39 system.

Iterative learning control in prosumer-based microgrids with hierarchical control

Power systems are subject to fundamental changes due to the increasing infeed of renewable energy sources. Taking the accompanying decentralization of power generation into account, the concept of prosumer-based microgrids gives the opportunity to rethink structuring and operation of power systems from scratch. In a prosumer-based microgrid, each power grid node can feed energy into the grid and draw energy from the grid. The concept allows for spatial aggregation such that also an interaction between microgrids can be represented as a prosumer-based microgrid. The contribution of this work is threefold: (i) we propose a decentralized hierarchical control approach in a network including different time scales, (ii) we use iterative learning control to compensate periodic demand patterns and save lower-layer control energy and (iii) we assure asymptotic stability and monotonic convergence in the iteration domain for the linearized dynamics and validate the performance by simulating the nonlinear dynamics.

On structural and dynamical factors determining the integrated basin instability of power-grid nodes.

In electric power systems delivering alternating current, it is essential to maintain its synchrony of the phase with the rated frequency. The synchronization stability that quantifies how well the power-grid system recovers its synchrony against perturbation depends on various factors. As an intrinsic factor that we can design and control, the transmission capacity of the power grid affects the synchronization stability. Therefore, the transition pattern of the synchronization stability with the different levels of transmission capacity against external perturbation provides the stereoscopic perspective to understand the synchronization behavior of power grids. In this study, we extensively investigate the factors affecting the synchronization stability transition by using the concept of basin stability as a function of the transmission capacity. For a systematic approach, we introduce the integrated basin instability, which literally adds up the instability values as the transmission capacity increases. We first take simple 5-node motifs as a case study of building blocks of power grids, and a more realistic IEEE 24-bus model to highlight the complexity of decisive factors. We find that both structural properties such as gate keepers in network topology and dynamical properties such as large power input/output at nodes cause synchronization instability. The results suggest that evenly distributed power generation and avoidance of bottlenecks can improve the overall synchronization stability of power-grid systems.

An artificial intelligence based method for evaluating power grid node importance using network embedding and support vector regression

The identification of important nodes in a power grid has considerable benefits for safety. Power networks vary in many aspects, such as scale and structure. An index system can hardly cover all the information in various situations. Therefore, the efficiency of traditional methods using an index system is case-dependent and not universal. To solve this problem, an artificial intelligence based method is proposed for evaluating power grid node importance. First, using a network embedding approach, a feature extraction method is designed for power grid nodes, considering their structural and electrical information. Then, for a specific power network, steady-state and node fault transient simulations under various operation modes are performed to establish the sample set. The sample set can reflect the relationship between the node features and the corresponding importance. Finally, a support vector regression model is trained based on the optimized sample set for the later online use of importance evaluation. A case study demonstrates that the proposed method can effectively evaluate node importance for a power grid based on the information learned from the samples. Compared with traditional methods using an index system, the proposed method can avoid some possible bias. In addition, a particular sample set for each specific power network can be established under this artificial intelligence based framework, meeting the demand of universality.

Power Grid Partitioning Based on Functional Community Structure

Network partitioning is a popular research topic. Not all available partitioning methods are equally suitable for power grids. Community detection is a critical issue in complex network theory, and power grid is a typical type of complex network. This paper proposes a functional community structure based on an extended weighted network model. An extended adjacency matrix is used to represent an extended weighted complex network model based on coupling strength rather than the conventional adjacency matrix. Meanwhile, we upgraded the Newman fast algorithm of community detection for establishing a novel power grid partitioning algorithm. The electrical coupling strength (ECS) is defined to better reflect electrical characteristics between any two nodes in power grid. Modularity is also redefined as electrical modularity based on ECS. The Newman fast algorithm is upgraded with electrical modularity maximization as the objective to detect functional communities in power grids. A case study on IEEE test systems with 30, 39, 118, 300 buses and one Italian power network demonstrates the rationality of the extended weighted network model and partitioning algorithm.

Multistability and variations in basin of attraction in power-grid systems

Power grids sustain modern society by supplying electricity and thus their stability is a crucial factor for our civilization. The dynamic stability of a power grid is usually quantified by the probability of its nodes’ recovery to phase synchronization of the alternating current it carries, in response to external perturbation. Intuitively, the stability of nodes in power grids is supposed to become more robust as the coupling strength between the nodes increases. However, we find a counterintuitive range of coupling strength values where the synchronization stability suddenly droops as the coupling strength increases, on a number of simple graph structures. Since power grids are designed to fulfill both local and long-range power demands, such simple graph structures or graphlets for local power transmission are indeed relevant in reality. We show that the observed nonmonotonic behavior is a consequence of transitions in multistability, which are related to changes in stability of the unsynchronized states. Therefore, our findings suggest that a comprehensive understanding of changes in multistability are necessary to prevent the unexpected catastrophic instability in the building blocks of power grids.

Electrical LeaderRank method for node importance evaluation of power grids considering uncertainties of renewable energy

Node importance evaluation of power grids plays an important role in the safe operation and planning of power systems. This paper proposes an electrical LeaderRank (ELR) method to identify the important nodes in complex power grids, considering the renewable energy uncertainties, system topological structure, transmission power flow and the loss of loads caused by cascading failures. The proposed method uses an ELR value function to represent the importance of a system node, which can be derived iteratively from the weighted distribution strategy of its in-linked nodes. Furthermore, the uncertainties of wind and solar energy generation are modelled as interval numbers, and the interval power flow calculation is employed to obtain the interval power in transmission lines, direct adjacent matrix, and finally the interval ELR values. The performance of ELR method has been fully tested and benchmarked on the IEEE 118-bus power system and the Western Liaoning Power Grid of China. Comparative results on four performance criteria have not only demonstrated the validity and superiority of the proposed method, but also confirmed its capability to cope with the node importance evaluation of practical power grids.

Recognition and Vulnerability Analysis of Key Nodes in Power Grid Based on Complex Network Centrality

The analysis of blackouts, which can inevitably lead to catastrophic damage to power grids, helps to explore the nature of complex power grids but becomes difficult using conventional methods. This brief studies the vulnerability analysis and recognition of key nodes in power grids from a complex network perspective. Based on the ac power flow model and the network topology weighted with admittance, the cascading failure model is established first. The node electrical centrality is further pointed out, using complex network centrality theory, to identify the key nodes in power grids. To effectively analyze the behavior and verify the correctness of node electrical centrality, the net-ability and vulnerability index are introduced to describe the transfer ability and performance under normal operation and assess the vulnerability of the power system under cascading failures, respectively. Simulation results of IEEE 30-bus and IEEE 57-bus test cases show that the key nodes can be effectively identified with high electrical centrality, the resultant cascading failures that eventually lead to a severe decrease in net-ability, verifying the correctness and effectiveness of the analysis.

Voltage stability assessment and identification of important nodes in power transmission network through network response structural characteristics

Electrical power grids are often susceptible to voltage instability and have been a growing concern. In this study, the authors propose techniques based on network response structural characteristics for voltage stability assessment and for the identification of important nodes in electrical power grids. First, the network response structural characteristic indices (NRSCIs) which are inherent in the conventional power grids in terms of the Kirchhoff matrix is formulated. The eigenvalue decomposition (ED) technique is then applied to a submatrix of the Kirchhoff matrix to determine the topological strength of the electrical network graph. The vertex (node) that has a minimum eigenvalue is taken as the critical mode, from which its contributions to the entire graph is identified using the proposed network response structural characteristics theory participation factor (NRSCTPF). To demonstrate the magnitude of the concept formulated, the known degree centrality is modified in terms of the established NRSCI, which are then used to determine the important nodes of the network graph. The results obtained show that the proposed NRSCTPF and the degree centrality based on the NRSCI can be used for voltage stability assessment and identification of important nodes. The proposed approach is also less computationally intensive compared with the traditional approach.

Deciphering the imprint of topology on nonlinear dynamical network stability

Coupled oscillator networks show complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these relations by incorporating sampling-based measures of the transient behaviour of the system, its survivability, as well as its asymptotic behaviour, its basin stability. By combining basin stability and survivability we uncover novel, previously unknown asymptotic states with solitary, desynchronized oscillators which are rotating with a frequency different from their natural one. They occur almost exclusively after perturbations at nodes with specific topological properties. More generally we confirm and significantly refine the results on the distinguished role tree-shaped appendices play for nonlinear stability. We find a topological classification scheme for nodes located in such appendices, that exactly separates them according to their stability properties, thus establishing a strong link between topology and dynamics. Hence, the results can be used for the identification of vulnerable nodes in power grids or other coupled oscillator networks. From this classification we can derive general design principles for resilient power grids. We find that striving for homogeneous network topologies facilitates a better performance in terms of nonlinear dynamical network stability. While the employed second-order Kuramoto-like model is parametrised to be representative for power grids, we expect these insights to transfer to other critical infrastructure systems or complex network dynamics appearing in various other fields.

Using interdependency matrices to mitigate targeted attacks on interdependent networks: A case study involving a power grid and backbone telecommunications networks

Analysis of the interdependencies between interconnected critical infrastructures can help enhance the robustness of the individual infrastructures as well as the overall interconnected infrastructures. One of the most studied interdependent critical infrastructure network scenarios is a power grid connected to a backbone telecommunications network. In this interdependent infrastructure scenario, the robustness of the entire system is usually analyzed in the context of cascading failure models in the power grid. However, this paper focuses on targeted attacks, where an attack on a telecommunications network node directly affects a connected power grid node, and vice versa. Cascading failures are outside the scope of this paper because the objective is to enhance the robustness of the interconnections between the infrastructures. In order to mitigate the impacts of targeted attacks on the interdependent infrastructures, three interdependency matrices for connecting the infrastructures are specified and analyzed. The analysis identifies the interdependency matrix that best reduces the impacts of targeted attacks and the propagation of failures between the infrastructures. Additionally, the impacts of interconnecting a power grid to different telecommunications networks, each with different susceptibilities to targeted attacks, is evaluated.

Evaluation method of node importance for power grid considering inflow and outflow power

The effective identifications of important nodes in power grid are foundations of differentiated management and stable operation of power grid. However, the current studies on this field are not thorough enough. This paper applies the model based on co-citation (MBCC)-hypertext induced topic selection (HITS) algorithm used in web page ranking to power grid and proposes an index to determine node importance of power grid from the perspectives of inflow and outflow power. MBCC-HITS algorithm is modified considering load, power source, and line flow comprehensively for the differences between Internet and power grid in this paper. Then a method for evaluating node importance is proposed using the modified algorithm. Lastly, the rationality and validity of the proposed method are verified by comparisons with other methods in case studies of IEEE 14-bus and 118-bus systems.

Effect of Power Grid Interaction Disaster on Identifying Critical Lines and Nodes of Power Grid

Effect of Power Grid Interaction Disaster on Identifying Critical Lines and Nodes of Power Grid