Control methods for network dynamics and criticality phenomena (original) (raw)
Related papers
Cascading Failures in Power Grids
arXiv (Cornell University), 2022
Critical infrastructures are defined as those physical and cyber-based systems that are essential to the minimum operations of the economy and the government [1, 2]. Since they provide crucial support for the delivery of basic services to almost all segments of society, they form the backbone of any nation's economy. As one of the most complex, largescale networked systems, electric power system has become increasingly automated in the past few decades. However, the increased automation has introduced new vulnerabilities to equipment failures, human errors [3, 4, 5, 6, 7], weather and other natural disasters [8, 9], and physical and cyber-attacks [2, 10]. The ever-increasing system scale and the strong reliance on automatic devices increase the likelihood of turning a local disturbance into a large-scale cascading failure [11, 12, 13, 14, 15, 16]. This kind of wide-area failure may have a catastrophic impact on the whole society. Reports of recent major power system blackouts [17, 18, 19, 20, 21, 22, 23, 24] have shown how several events ranging from minor equipment failure and operator errors to severe weather events (such as forest fires, hurricanes and winter storms) have triggered widespread system wide power disruption affecting millions of customers. This necessitates the development of a framework which would assess the vulnerability of the power grid subjected to any of these events, and thereby allowing energy policy makers to identify critical components in the grid and subsequently allocate budgets to harden them. Statistical analysis of more than 400 blackouts in USA from 1984 to 1999 indicates that a large blackout, though rare, is more likely to occur than expected (heavy tails of a power law distribution) [25]. Therefore, large blackouts require more attention not only due to their higher probability of occurrence, but also due to the enormous societal damage caused by such events. Following this observation, several works [12, 26, 27, 28, 29, 30, 31, 32, 33, 34] have proposed multiple failure models to represent the system dynamics leading to a cascading outage. They have studied cascading failures in power grids using quasi-steady state analysis with DC power flow. With any reactive power component being ignored and the assumption of a flat voltage profile, the DC power flow analysis may produce good approximations under some circumstances, e.g., when performing steady-state planning level studies. However, the increased penetration of converter-based generator technologies, loads and transmission devices have contributed to newly evolved dynamic stability behaviors of the power grid [35]. Major cascading outages are caused when transient rotor angle stability and voltage stability of the power grid are affected [22, 36, 37, 38]. Therefore, a simple cascading failure model based on DC power flow analysis is not a suitable tool to simulate such events. In this paper, we consider the AC power flow model to accurately simulate the actual operating point in the power system. Several physics-based models have been used to study cascading failures in power grid networks and interdependent power and communication networks [39, 40, 41, 42, 43, 44, 45, 46]. The authors have considered the effect of connectivity between layered networks on the cascade probability in each network, and used the sandpile dynamics [47] to represent the cascade tripping of loads in the power grids. These papers are useful in that one can often either obtain analytical results, or carry out large number of simulations to get a detailed understanding of cascade dynamics. The physics based models are simplified models capable of showcasing mechanistic possible behavior of complex network systems, rather than providing precise predictions which requires engineering models with a large number of parameters [46]. The models fail to replicate the actual system conditions in a power grid where a node (or bus) trips due to under-voltage or under-frequency and not due to overload. Further, stability of a power system subjected to cascading events is evaluated either from the network structure point of view (evaluating the degree distribution of nodes) [42, 39, 41, 43] or from the convergence of steady-state power flow solution [26, 27, 28, 29, 30, 31, 32]. Such measures do not necessarily cover all possibilities of grid instability [35], as non-linear mechanisms such as rotor angle stability or voltage collapse are not accurately captured in these methods [36]. In this work, dynamic transient analysis has been used to assess stability of the power system. The reports of certain major blackouts [23, 22] suggest that cascades need not propagate locally due to the complex non-linear nature of the power grid. Furthermore, [24] discusses the various reasons leading to the historic 1996 WSCC outage, the most important being the operation of relays. Based on the NERC data, in more than 70% of the major disturbances, failures in protective relays are found to be a contributing factor [30]. Among these failures, a failed protection system that remains dormant in normal operating conditions and becomes exposed when an abnormal condition in the system forms, is the most troublesome to tackle [48]. Such failures are termed as hidden failures and these are capable of causing widespread cascading failures in the power system network leading to a major blackout [49]. This is equivalent to the human immune system where an immune response following immunization might be more damaging
Abruptness of Cascade Failures in Power Grids
Scientific Reports, 2014
Electric power-systems are one of the most important critical infrastructures. In recent years, they have been exposed to extreme stress due to the increasing demand, the introduction of distributed renewable energy sources, and the development of extensive interconnections. We investigate the phenomenon of abrupt breakdown of an electric power-system under two scenarios: load growth (mimicking the ever-increasing customer demand) and power fluctuations (mimicking the effects of renewable sources). Our results on real, realistic and synthetic networks indicate that increasing the system size causes breakdowns to become more abrupt; in fact, mapping the system to a solvable statistical-physics model indicates the occurrence of a first order transition in the large size limit. Such an enhancement for the systemic risk failures (black-outs) with increasing network size is an effect that should be considered in the current projects aiming to integrate national power-grids into ''super-grids''.
Addressing vulnerability to cascading failure against intelligent adversaries in power networks
Energy Systems, 2014
The blackout of August 14, 2003, showed that electric power grids are vulnerable to cascading failure. Since then, numerous methods of vulnerability analysis have been developed to help the owners and operators of power networks and other infrastructure systems protect them against possible catastrophic events (including attacks by intelligent adversaries). With cascading failures, even small attacks can have a large impact. Cascading failures have historically been considered a major unsolved problem for complex networks such as electricity systems, but recent developments in probabilistic analysis of cascading failure are making it possible to take cascading failures into account in methods of vulnerability assessment. In particular, our game-theoretic model can be used to analyze how an intelligent adversary might seek to take advantage of a network's vulnerability to cascading failure. Specifically, our model provides a tool to simulate power flows within the network, and analyze how attackers can use their knowledge of cascading failure. Our model can also be used to compare the effectiveness of different types of investments to make systems more resilient, including both hardening components and also making the system less vulnerable to cascading failure (e.g., by increasing the capacities of transmission lines, or adding new lines).
2004
We consider the risk of cascading failure of electric power transmission systems as overall loading is increased. There is evidence from both abstract and power systems models of cascading failure that there is a critical loading at which the risk of cascading failure sharply increases. Moreover, as expected in a phase transition, at the critical loading there is a power tail in the probability distribution of blackout size. (This power tail is consistent with the empirical distribution of North American blackout sizes.) The importance of the critical loading is that it gives a reference point for determining the risk of cascading failure. Indeed the risk of cascading failure can be quantified and monitored by finding the closeness to the critical loading. This paper suggests and outlines ways of detecting the closeness to criticality from data produced from a generic blackout model. The increasing expected blackout size at criticality can be detected by computing expected blackout size at various loadings. Another approach uses branching process models of cascading failure to interpret the closeness to the critical loading in terms of a failure propagation parameter λ. We suggest a statistic for λ that could be applied before saturation occurs. The paper concludes with suggestions for a wider research agenda for measuring the closeness to criticality of a fixed power transmission network and for studying the complex dynamics governing the slow evolution of a transmission network.
Exploring Complex Systems Aspects of Blackout Risk and Mitigation
IEEE Transactions on Reliability, 2000
Electric power transmission systems are a key infrastructure, and blackouts of these systems have major consequences for the economy and national security. Analyses of blackout data suggest that blackout size distributions have a power law form over much of their range. This result is an indication that blackouts behave as a complex dynamical system. We use a simulation of an upgrading power transmission system to investigate how these complex system dynamics impact the assessment and mitigation of blackout risk. The mitigation of failures in complex systems needs to be approached with care. The mitigation efforts can move the system to a new dynamic equilibrium while remaining near criticality and preserving the power law region. Thus, while the absolute frequency of blackouts of all sizes may be reduced, the underlying forces can still cause the relative frequency of large blackouts to small blackouts to remain the same. Moreover, in some cases, efforts to mitigate small blackouts can even increase the frequency of large blackouts. This result occurs because the large and small blackouts are not mutually independent, but are strongly coupled by the complex dynamics.
2016 IFIP Networking Conference (IFIP Networking) and Workshops, 2016
The operations of many modern cyber-physical systems, such as smart grids, are based on increasingly interdependent networks. The impact of cascading failures on such networks has recently received significant attention due to the corresponding effect of these failures on the society. In this paper, we conduct an empirical study on the robustness of interdependent systems formed by the coupling of power grids and communication networks by putting real distribution power grids to the test. We focus on the assessment of the robustness of a large set of medium-voltage (MV) distribution grids, currently operating live in the Netherlands, against cascading failures initiated by different types of faults / attacks. We consider both unintentional random failures and malicious targeted attacks which gradually degrade the capability of the entire system and we evaluate their respective consequences. Our study shows that current MV grids are highly vulnerable to such cascades of failures. Furthermore, we discover that a small-world communication network structure lends itself to the robustness of the interdependent system. Also interestingly enough, we discover that the formation of hub hierarchies, which is known to enhance independent network robustness, actually has detrimental effects against cascading failures. Based on real MV grid topologies, our study yields realistic insights which can be employed as a set of practical guidelines for distribution system operators (DSOs) to design effective grid protection schemes.
Identifying Critical Risks of CascadingFailures in Power Systems
IET Generation, Transmission & Distribution
Potential critical risks of cascading failures in power systems can be identified by exposing those critical electrical elements on which certain initial disturbances may cause maximum disruption to power transmission networks. In this work, we investigate cascading failures in power systems described by the direct current (DC) power flow equations, while initial disturbances take the form of altering admittance of elements. The disruption is quantified with the remaining transmission power at the end of cascading process. In particular, identifying the critical elements and the corresponding initial disturbances causing the worst-case cascading blackout is formulated as a dynamic optimization problem (DOP) in the framework of optimal control theory, where the entire propagation process of cascading failures is put under consideration. An Identifying Critical Risk Algorithm (ICRA) based on the maximum principle is proposed to solve the DOP. Simulation results on the IEEE 9-Bus and the IEEE 14-Bus test systems are presented to demonstrate the effectiveness of the algorithm.
We give a comprehensive account of a complex systems approach to large blackouts caused by cascading failure. Instead of looking at the details of particular blackouts, we study the statistics, dynamics and risk of series of blackouts with approximate global models. North American blackout data suggests that the frequency of large blackouts is governed by a power law. This result is consistent with the power system being a complex system designed and operated near criticality. The power law makes the risk of large blackouts consequential and implies the need for nonstandard risk analysis.
Small vulnerable sets determine large network cascades in power grids
Science (New York, N.Y.), 2017
The understanding of cascading failures in complex systems has been hindered by the lack of realistic large-scale modeling and analysis that can account for variable system conditions. Using the North American power grid, we identified, quantified, and analyzed the set of network components that are vulnerable to cascading failures under any out of multiple conditions. We show that the vulnerable set consists of a small but topologically central portion of the network and that large cascades are disproportionately more likely to be triggered by initial failures close to this set. These results elucidate aspects of the origins and causes of cascading failures relevant for grid design and operation and demonstrate vulnerability analysis methods that are applicable to a wider class of cascade-prone networks.
Comparing dynamics of cascading failures between network-centric and power flow models
International Journal of Electrical Power and Energy Systems, 2013
Small initial failures in power grids can lead to large cascading failures, which have significant economic and social costs, and it is imperative to understand the dynamics of these systems and to mitigate risks of such failures. We directly compare two prominent models for cascading failures in power grids: a power flow model-ORNL-PSerc-Alaska (OPA) and a complex networks model-Crucitti-Latora-Marchiori (CLM). Quantitative comparison of these two models is not trivial and has not been previously performed, so we present a method to quantitatively compare the two using transmission capacity as a common variable. Primarily, we find that the two models exhibit similar phase transitions in average network damage (load shed/demand in OPA, path damage in CLM) with respect to transmission capacity, sharing a common critical region and similar transitions in probability distributions of network damage size. Furthermore , we find that both OPA and CLM reveal similar impacts of network topology, size and heterogeneity of transmission capacity, with respect to vulnerability to large cascades. Thus, our analysis indicates that the CLM model, despite neglecting realistic power flow assumptions and exhibiting differences in behaviour at the local scale, nonetheless exhibits ensemble properties which are consistent with the more realistic OPA fast-scale model. Given the advantages of simplicity and scalability of CLM, these results provide impetus for the use of complex networks models to study ensemble properties of cascading failures in larger power grid networks. Crown