Robust Power Grid Research Articles

Systemic Vulnerability of Swiss Power Grid to Natural Events

It is important to increase the security and robustness of power grids under a variety of events. In this case, “vulnerability analysis” is usually used to identify the most vulnerable elements of a power grid under different hazards. There are different kinds of methodology to identify vulnerability such as complex network, logical, functional methods and Monte Carlo simulation. In this work, the complex network, Swiss power grid, and seismic hazard are used as an approach, a test system, and a scenario, respectively. First, Swiss power grid is modeled using Gephi software and five different metrics of the complex network method are applied to the model. Then, TOPSIS as a multi-criteria decision method is used to combine the results of the previous step. Finally, to find out the most exposed nodes in the case of an earthquake, Swiss seismic hazard data is used and combined with TOPSIS outputs. The results show well the critical locations of power grid due to the seismic hazard.

Optimal Noise-Canceling Networks.

Natural and artificial networks, from the cerebral cortex to large-scale power grids, face the challenge of converting noisy inputs into robust signals. The input fluctuations often exhibit complex yet statistically reproducible correlations that reflect underlying internal or environmental processes such as synaptic noise or atmospheric turbulence. This raises the practically and biophysically relevant question of whether and how noise filtering can be hard wired directly into a network's architecture. By considering generic phase oscillator arrays under cost constraints, we explore here analytically and numerically the design, efficiency, and topology of noise-canceling networks. Specifically, we find that when the input fluctuations become more correlated in space or time, optimal network architectures become sparser and more hierarchically organized, resembling the vasculature in plants or animals. More broadly, our results provide concrete guiding principles for designing more robust and efficient power grids and sensor networks.

Algorithm for Analysis of Power Grid Vulnerability to Geomagnetic Disturbances

AbstractMultiple power system equipment damage from strong geomagnetic disturbance (GMD) can significantly disrupt power grid operation. This has happened twice: in 1989, in North America and the United Kingdom and, in 2003, in Scandinavia and South Africa. Modern bulk high‐voltage power grids were designed more than 60 years ago for achieving more economic benefits in power transfer. In turn, high‐voltage, and especially the lately designed ultrahigh‐voltage, grids are more vulnerable to GMD. It is anticipated that the demand of detailed study of power grid's vulnerability to GMD will expand with broader awareness of the negative effects. The common approach requires the knowledge of the data on geophysical parameters of the study region, which is not accessible to the specialists without relevant background. In this paper, an alternative algorithm for preliminary evaluation of power grid's robustness to GMD is proposed. It takes into account various critical factors and provides a useful tool for stakeholders to identify potentially weak power grids and develop mitigation procedures beforehand. The advantage is that this algorithm can be used by specialists who do not have a comprehensive understanding of the GMD effect on power grid operation.

Analysis of Dynamical Robustness to Noise in Power Grids

Resilience of power grids is a problem of tremendous practical and theoretical relevance. In this work, we model a power grid as a complex network of coupled oscillators. We investigate the robustness of synchronization, associated with the normal operating regime of the network, to partial malfunctioning of the nodes. Differently from previous efforts on power grid resilience, node malfunctioning is not modeled by removing a node from the network. Instead, we insert a continuous perturbation into the node dynamical equation, which reduces the degree of synchronization of the network. This framework enables an analytical treatment of the problem, ultimately leading to a detailed quantification of the criticality of each network node. The approach is applied to the UCTE European transmission network 1st synchronous area and to the IEEE 118-bus test case. The identification of nodes which are more critical to synchronization yields non-trivial hints at a complex interplay between topology and dynamics in shaping dynamical robustness of power grids.

Analysis of Failures in Power Grids

This paper focuses on line failures in the transmission system of power grids. Recent large-scale power outages demonstrated the limitations of percolation- and epidemic-based tools in modeling failures and cascades in power grids. Hence, we study failures and cascades by using computational tools and a linearized power-flow model. We first obtain results regarding the Moore-Penrose pseudoinverse of the power grid admittance matrix. Based on these results, we analytically study the impact of a single-line failure on the flows on other lines and introduce metrics to evaluate the robustness of grids to failures. We also illustrate via simulation the impact of the distance and resistance distance on the flow increase following a failure, and discuss the difference from the epidemic models. We use the pseudoinverse of admittance matrix to develop an efficient algorithm to identify the cascading failure evolution, which can be a building block for cascade mitigation. Finally, we show that finding the lines whose removal results in the minimum yield (the fraction of demand satisfied after the cascade) is NP-Hard and present a simple heuristic for finding such a set. Overall, the results demonstrate that using the resistance distance and the pseudoinverse of the admittance matrix provides important insights and can support the development of algorithms for designing robust power grids and controlling the evolution of a cascade upon failures.

Smoothing effect for spatially distributed renewable resources and its impact on power grid robustness.

In this paper, we show that spatial correlation of renewable energy outputs greatly influences the robustness of the power grids against large fluctuations of the effective power. First, we evaluate the spatial correlation among renewable energy outputs. We find that the spatial correlation of renewable energy outputs depends on the locations, while the influence of the spatial correlation of renewable energy outputs on power grids is not well known. Thus, second, by employing the topology of the power grid in eastern Japan, we analyze the robustness of the power grid with spatial correlation of renewable energy outputs. The analysis is performed by using a realistic differential-algebraic equations model. The results show that the spatial correlation of the energy resources strongly degrades the robustness of the power grid. Our results suggest that we should consider the spatial correlation of the renewable energy outputs when estimating the stability of power grids.

Network Hierarchy Evolution and System Vulnerability in Power Grids

The seldom addressed network hierarchy property and its relationship with vulnerability analysis for power transmission grids from a complex-systems point of view are given in this paper. We analyze and compare the evolution of network hierarchy for the dynamic vulnerability evaluation of four different power transmission grids of real cases. Several meaningful results suggest that the vulnerability of power grids can be assessed by means of a network hierarchy evolution analysis. First, the network hierarchy evolution may be used as a novel measurement to quantify the robustness of power grids. Second, an antipyramidal structure appears in the most robust network when quantifying cascading failures by the proposed hierarchy metric. Furthermore, the analysis results are also validated and proved by empirical reliability data. We show that our proposed hierarchy evolution analysis methodology could be used to assess the vulnerability of power grids or even other networks from a complex-systems point of view.

Feature combination analysis in smart grid based using SOM for Sudan national grid

In the investigation of power grid security, the cascading failure in multicontingency situations has been a test because of its topological unpredictability and computational expense. Both system investigations and burden positioning routines have their limits. In this project, in view of sorting toward Self Organizing Maps (SOM), incorporated methodology consolidating spatial feature (distance)-based grouping with electrical attributes (load) to evaluate the vulnerability and cascading impact of various part sets in the force lattice. Utilizing the grouping result from SOM, sets of overwhelming stacked beginning victimized people to perform assault conspires and asses the consequent falling impact of their failures, and this SOM-based approach viably distinguishes the more powerless sets of substations than those from the conventional burden positioning and other bunching strategies. The robustness of power grids is a central topic in the design of the so called "smart grid". In this paper, to analyze the measures of importance of the nodes in a power grid under cascading failure. With these efforts, we can distinguish the most vulnerable nodes and protect them, improving the safety of the power grid. Also we can measure if a structure is proper for power grids.

Vulnerability analysis of the US power grid based on local load-redistribution

In this paper, local load-redistribution is employed to study the vulnerability of the US power grid subjected to attacks, and the initial load of power node is assumed as the linear summation of its degree and the sum of its neighbors’ degrees. Based on the simulation results, we find that with the decrease of the initial load of power node, the critical threshold of tolerance parameter increases subjected to the highest load node-based attack, but the critical threshold decreases subjected to the lowest load node-based attacks. Meanwhile, we discover that the critical threshold subjected to the lowest load node-based attack is larger than that subjected to the highest load node-based attack when the tunable parameter α∈[0.1,0.9]. Moreover, this paper compares the new model with the other two existing models, and the results illustrate that there are many similarities between these two existing models, but they are different from the new model presented in this paper. Furthermore, the infimum of tolerance parameter is proposed to portray the minimum cost of power grid, which can give a method to construct more robust power grids in the future.

Extraction of primary and secondary frequency control from active power generation data of power plants

Abstract Frequency control is a vital component of a secure and robust power grid and it ought to be closely monitored. Frequency control consists of two main components; primary and secondary control and their contributions are usually aggregated in the active power generation data of a plant, which is acquired via Supervisory Control And Data Acquisition. In many cases, such as in Turkey, they are demanded to be evaluated separately due to different impacts on power system or different financial policies. However, this is not usually a straightforward process since primary and secondary response cannot be obtained distinctly. In this work, Extraction of Primary and Secondary Control (EPSCon) algorithm is introduced to extract primary and secondary response over active power generation data. Based on time and frequency domain characteristics of primary and secondary response, EPSCon is developed on a Expectation-Maximization type recursive scheme employing Generalized Cross Correlation and l 1 Trend Filtering techniques. Favorably, EPSCon uses a simple plant model built upon basic governor and plant load controller technical characteristics as an initial estimate of primary and secondary response.

Can the structural robustness of complex networks be enhanced by interconnection?

To improve the structural robustness of a large complex network, we propose to interconnect it with a smaller but more robust network. We demonstrate the validity of our method by employing the metric of natural connectivity. By this approach, one can enhance the robustness of a network without modifying its inner structure or reshuffling the original links. Our method will lead to build more robust distributed power grids.

A Flocking-Based Paradigm for Hierarchical Cyber-Physical Smart Grid Modeling and Control

It is well known that information will play an important role in enhancing emerging smart grid system operation. Therefore, questions naturally arise as to when the increased data-dependence may be considered excessive. Two practical considerations emerge: 1) communications and computational overhead, in which redundant and irrelevant information acquisition and use results in heavy computational burden with limited performance return; and 2) increasing risks of power system disruption due to information delay from communication congestion or cyber attack. One strategy to improve smart grid resilience is to determine the appropriate degree of dependence on cyber information to balance performance with overhead and risk. In this paper, we present a hierarchical cyber-physical multiagent model of smart grid system operation based on flocking theory in the context of the transient stability problem. Through this model, we study strategies that harness a selective degree of cyber technology by leveraging physical couplings. Our formulation enables the identification of large-scale distributed control strategies for robust and resilient power grid operation. We demonstrate the potential performance improvements of our findings on the New England 39-bus power system for case studies involving a variety of system faults and communication delays.

Node-wise robustness against fluctuations of power consumption in power grids

We propose a new concept of node-wise robustness of power grids under variation of effective power in one load node using a mathematical model that takes into account the change in voltage and reactive power of load nodes. We employ the topology of the power grid in eastern Japan. We define the robustness as the threshold value of the effective power, above which the steady state loses its stability. We show that the robustness is highly heterogeneous among the load nodes. We find that the shortest path length from generators is most highly correlated with the robustness of the load nodes. We numerically demonstrate that the supply of reactive power enhances the robustness.

An efficient method of robustness analysis for power grid under cascading failure

The robustness of power grids is a central topic in the design of the so called ”smart grid”. As the total amount of load in the power grid is becoming more and more each day, and the sizes of power grids are becoming larger and larger each year, it will result in larger damages to the society if the power grids broke down. For example, the Northeast blackout of 2003 in the US resulted in a loss of 61,800MW of electric load that served more than 50 million people ELCON (2003). In this paper we try to analyze the measures of importance of the nodes in a power grid under cascading failure. Moreover, we introduce the notion of degree correlation for the case where only the statistical information of a power grid is known. Mean field theory is used for our analysis. With these efforts, we can distinguish the most vulnerable nodes and protect them, improving the safety of the power grid. Also we can measure if a structure is proper for power grids. Above all, a new multi-loop structure for smart grid is shown to be better than the contemporary one.

Non-monotonic increase of robustness with capacity tolerance in power grids

The robustness of different scale power grids is analyzed based on complex network theory in terms of electrical betweenness and weighted efficiency. The robustness of a power grid does not always increase monotonically with the capacity. This property is different from the results obtained in previous studies, which have indicated that the robustness increases monotonically with capacity. To understand the non-monotonic phenomenon, the cascading failure is divided into several sub-stages, and we analyze the number of overloaded nodes and the average remaining load in each sub-stage. The results indicate that the increasing capacity is barely able to reduce the number of overloaded nodes at the beginning of malfunction, which may lead to more nodes being removed subsequently, including certain nodes with many connections or large load. More loads remain in the power grid such that certain nodes cannot take the load. This eventually causes overloading of more nodes and a decline in the robustness of the power grid. The conclusion may be useful for power grid planners seeking to design grids with cost-effective capacity.

An entropy-based metric to quantify the robustness of power grids against cascading failures

The cascading failure phenomenon in a power grid is related to both the structural aspects (number and types of buses, density of transmission lines and interconnection of components), and the operative state (flow distribution and demand level). Existing studies most often focus on structural aspects, and not on operative states. This paper proposes a new metric to assess power network robustness with respect to cascading failures, in particular for cascading effects due to line overloads under targeted attacks. The metric takes both the effect of structural aspects and the effect of the operative state on network robustness into account, using an entropy-based approach. IEEE test systems and real world UCTE networks are used to demonstrate the applicability of this robustness metric.

Balancing System Survivability and Cost of Smart Grid Via Modeling Cascading Failures

As a typical emerging application of cyber physical system, smart power grid is composed of interdependent power grid and communication/control networks. The latter one contains relay nodes for communication and operation centers to control power grid. Failure in one network might cause failures in the other. In addition, these failures may occur recursively between the two networks, leading to cascading failures. We propose a k-to- n interdependence model for smart grid. Each relay node and operation center is supported by only one power station, while each power station is monitored and controlled by k operation centers. Each operation center controls n power stations. We show that the system controlling cost is proportional to k. Through calculating the fraction of functioning parts (survival ratio) using percolation theory and generating functions, we reveal the nonlinear relation between controlling cost and system robustness, and use graphic solution to prove that a threshold exists for the proportion of faulty nodes, beyond which the system collapses. The extensive simulations validate our analysis, determine the percentage of survivals and the critical values for different system parameters. The mathematical and experimental results show that smart grid with higher controlling cost has a sharper transition, and thus is more robust. This is the first paper that focuses on on improving smart power grid robustness by changing monitoring strategies from an interdependent complex networks perspective.

Weakly explosive percolation in directed networks

Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness of power grids and information networks, the spreading of epidemics and forest fires, and the stability of gene regulatory networks. Recent studies have shown that if network edges are added "competitively" in undirected networks, the onset of percolation is abrupt or "explosive." The unusual qualitative features of this phase transition have been the subject of much recent attention. Here we generalize this previously studied network growth process from undirected networks to directed networks and use finite-size scaling theory to find several scaling exponents. We find that this process is also characterized by a very rapid growth in the giant component, but that this growth is not as sudden as in undirected networks.

Secure wireless communication system for smart grid with rechargeable electric vehicles

Current transportation systems are emitting a considerable amount of greenhouse gas into the atmosphere. The recent advances in the fuel cell battery is making the zero-carbon electric vehicle (EV) increasingly practical for the commercial market. However, mass use of EVs requires support from a powerful and robust power grid that can efficiently generate, aggregate, and distribute a large amount of energy in real time with low carbon emission. Such a system calls for the application of modern communication technologies that inherently suffer from various cyber attacks. Attacks against the communication system in smart grid can cause catastrophic damage to the highly interdependent smart grid users. In this article, we first propose a smart grid model for supporting mass EV use, then introduce some typical security issues in the communication system, especially for the wireless security in such a smart grid. We mainly introduce two types of security protocols: key agreement from wireless channel estimation and jamming-resilient communication.

Robust Parallel Preconditioned Power Grid Simulation on GPU With Adaptive Runtime Performance Modeling and Optimization

Leveraging the power of nowadays graphics processing units for robust power grid simulation remains a challenging task. Existing preconditioned iterative methods that require incomplete matrix factorizations cannot be effectively accelerated on graphics processing unit (GPU) due to its limited hardware resource as well as data parallel computing. This paper presents an efficient GPU-based multigrid preconditioning algorithm for robust power grid analysis. By combining the fast geometric multigrid solver with the robust Krylov-subspace iterative solver, power grid DC and transient analysis can be performed efficiently on GPU without loss of accuracy (largest errors <;0.5 mV). Unlike previous GPU-based algorithms that rely on good power grid regularities, the proposed algorithm can be applied for more general power grid structures. Additionally, we also propose an accuracy-aware GPU performance modeling and optimization framework to automatically obtain the best power grid simulation configurations. Experimental results show that the DC and transient analysis on GPU can achieve more than 25X speedups over the best available CPU-based solvers.