This work studies the consequences of a human-initiated targeted attack on the electric power system by simulating the detonation of a bomb at one or more substations in and around Washington DC. An AC power flow based transient analysis on a realistic power grid model of Eastern Interconnection is considered to study the cascading events. A detailed model of control and protection system in the power grid is considered to ensure the accurate representation of cascading outages. Particularly, the problem of identifying a set of k critical nodes, whose failure/attack leads to the maximum adverse impact on the power system has been analyzed in detail. It is observed that a greedy approach yields node sets with higher criticality than a degree-based approach, which has been suggested in many prior works. Furthermore, it is seen that the impact of a targeted attack exhibits a nonmonotonic behavior as a function of the target set size k. The consideration of hidden failures in the protective relays has revealed that the outage of certain lines/buses in the course of cascading events can save the power grid from a system collapse. Finally, a comparison with the DC steady state analysis of cascading events shows that a transient stability assessment is necessary to obtain the complete picture of cascading events in the aftermath of a targeted attack on the power grid. / M.S. / The modern day power system has been identified as a critical infrastructure providing crucial support to the economy of a country. Prior experience has shown that a small failure of a component in the power grid can lead to widespread cascading events and eventually result in a blackout. Such failures can be triggered by devastating damage due to a natural calamity or because of a targeted adversarial attack on certain points in the power system. Given limited budget to avoid widespread cascading failures in the network, an important problem would be to identify critical components in the power system. In this research an attempt has been made to replicate the actual power system conditions as accurately as possible to study the impact of a targeted adversarial attack on different points in the network. Three heuristics have been proposed to identify critical nodes in the network and their performance has been discussed. The case studies of cascading events have been performed on a synthetic power system network of Washington DC to achieve the actual system conditions of an operating power grid.

Stochastic and deterministic approaches for modeling complex networks are presented. The methodology combines analysis of the structure formed by the interconnections among the elements of a network with an assessment of the vulnerability towards the propagation of cascading failures. The goal is to understand the mutual interplay between the structure of the network connections and the propagation of cascading failures. Two fundamental issues related to the optimal design and operation of complex networks are addressed. The first concerns the impact that cascading failures have on networks due to the connectivity pattern linking their components. If the state of load on the network components is high, the risk of cascade spreadings becomes significant. In this case, the needed reduction of the connectivity efficiency to prevent the propagation of failures affecting the entire system is quantified. The second issue concerns the realization of the most efficient connectivity in a network that minimizes the propagations of cascading failures. It is found that a system that routinely approaches the critical load for the onset of cascading failures during its operation should have a larger efficiency value. This allows for a smoother transition to the cascade region and for a reasonable reaction time to counteract the onset of significant cascading failures. The interplay between the structure of the network connections and the propagation of cascading failures is assessed also in interdependent networks. In these systems, the linking among several network infrastructures is necessary for their optimal and economical operation. Yet, the interdependencies introduce weaknesses due to the fact that failures may cascade from one system to other interdependent systems, possibly affecting their overall functioning. Inspired by the global efficiency, a measure of the communication capabilities among interdependent systems, i.e. the interdependency efficiency, is defined. The relations between the structural parameters, i.e. the system links and the interdependency links, and the interdependency efficiency, are also quantified, as well as the relations between the structural parameters and the vulnerability towards the propagation of cascading failures. Resorting to this knowledge, the optimal interdependency connectivity is identified. Similar to the spreading of failures, the formation of a giant component is a critical phenomenon emerging as a result of the connectivity pattern in a network. This structural transition is exploited to identify the formation of macrometastases in the developed model for metastatic colonization in tumor growth. The methods of network theory proves particularly suitable to reproduce the local interactions among tumor cells that lead to the emergent global behavior of the metastasis as a community. This model for intercellular sensing reproduces the stepwise behavior characteristic of metastatic colonization. Moreover, it prompts the consideration of a curative intervention that hinders intercellular communication, even in the presence of a significant tumor cell population. / Ph. D.

Doctor of Philosophy / Department of Electrical and Computer Engineering / Caterina Scoglio / The science of complex networks has significantly advanced in the last decade and has provided valuable insights into the properties of real world systems by evaluating their structure and construction. Several phenomena occurring in real technological and social systems can be studied, evaluated, quantified, and remedied with the help of network science. The electric power grid is one such real technological system that can be studied through the science of complex networks. The electric grid consists of three basic sub-systems: Generation, Transmission, and Distribution. The transmission sub-system is of particular interest in this work because its mesh-like structure offers challenging problems to complex networks researchers. Cascading dynamics of power grids is one of the problems that can be studied through complex networks. The North American Electric Reliability Corporation (NERC) defines a cascading failure as the uncontrolled successive loss of system elements triggered by an incident at any location. In this dissertation, we primarily discuss the dynamics of cascading failures in the power transmission grid, from a complex networks perspective, and propose possible solutions for mitigating their effects. We evaluate the grid dynamics for two specific scenarios, load growth and random fluctuations in the grid, to study the behavior of the grid under critical conditions. Further, we propose three mitigation strategies for reducing the damage caused by cascading failures. The first strategy is intentional islanding in the power transmission grid. The aim of this method is to intentionally split the grid into two or more separate self- sustaining components such that the initial failure is isolated and the separated components can function independently, with minimum load shedding. The second mitigation strategy involves controlled placement of distributed generation (DG) in the transmission system in order to enhance robustness of the grid. The third strategy requires the addition of a link in the transmission grid by reduction of the average spectral distance, utilizing the Ybus matrix of the grid and a novel algorithm. Through this dissertation, we aim to successfully cover the gap present in the complex networks domain, with respect to the vulnerability analysis of power grid networks.

One of the biggest threats to the power systems as critical infrastructures is large-scale blackouts resulting from cascading failures (CF) in the grid. The ongoing shift in energy portfolio due to ever-increasing penetration of renewable energy sources (RES) may drive the electric grid closer to its operational limits and introduce a large amount of uncertainty coming from their stochastic nature. One worrisome change is the increase in CFs. The CF simulation models in the literature do not allow consideration of RES penetration in studying the grid vulnerability. In this dissertation, we have developed tools and models to evaluate the impact of RE penetration on grid vulnerability to CF. We modeled uncertainty injected from different sources by analyzing actual high-resolution data from North American utilities. Next, we proposed two CF simulation models based on simplified DC power flow and full AC power flow to investigate system behavior under different operating conditions. Simulations show a dramatic improvement in the line flow uncertainty estimation based on the proposed model compared to the simplified DC OPF model. Furthermore, realistic assumptions on the integration of RE resources have been made to enhance our simulation technique. The proposed model is benchmarked against the historical blackout data and widely used models in the literature showing similar statistical patterns of blackout size.

No description available.

<p><a>Disruptive events during recent decades have highlighted the vulnerabilities of complex systems of systems to disruption propagation: </a>Disruptions that start in one part of a system and can propagate to other parts. Such examples include: Fire spreading in building complexes and forests; plant/crop diseases in agricultural production systems; propagating malware in computer networks and cyber-physical systems; and disruptions in supply networks. The impacts of disruption propagation are devastating, with fire causing annual US$23 billion loss in the US alone, plant diseases/crop reducing agricultural productivity 20% to 40% annually, and computer malware causing up to US$2.3 billion loss per event (as a conservative estimate). These problems, the response to disruption propagation (<a>RDP</a>) problems, are challenging due to the involvement of different problem aspects and their complex dynamics. To better design and control the responses to disruption propagation, a general framework and problem-solving guideline for the RDP problems is necessary.<br></p><p><br></p> <p> </p> <p>To address the aforementioned challenge, this research develops the Collaborative Response to Disruption Propagation (<a>CRDP</a>) unifying framework to classify, categorize, and characterize the different aspects of the RDP problems. The CRDP framework allows analogical reasoning across the different problem contexts, such as the examples mentioned above. Three main components applicable to the investigate RDP problems are identified and characterized: (1) The client system as the victims; (2) The response mechanisms as the rescuers/protectors; and (3) The disruption propagation as the aggressors/attackers. This allows further characterization of the complex interactions between the components, which augments the design and control decisions for the response mechanisms to better respond to the disruptions. The new Covering Lines of Collaboration (<a>CLOC</a>) principle, consisting of three guidelines, is developed to analyze the system state and guide the response decisions. The first CLOC guideline recommends the network modeling of potential disruption propagation directions, creating a complex network for better situation awareness and analysis. The second CLOC guideline recommends the analysis of the propagation-restraining effects due to the existence of the response mechanisms, and utilizing this interaction in optimizing response decisions. The third CLOC guideline recommends the development of collaboration protocols between the response decisions to maximize the coverage of response against disruption propagation.</p><p><br></p> <p> </p> <p>The CRDP framework and the CLOC principle are validated with three RDP case studies: (1) Detection of unknown disruptions; (2) Strategic prevention of unexpected disruptions; (3) Teaming and coordination of repair agents against recurring disruptions. Formulations, analytics, and protocols specific to each case are developed. TIE/CRDP, a new version of the Teamwork Integration Evaluator (<a>TIE</a>) software, is developed to simulate the complex interactions and dynamics of the CRDP components, the response decision protocols, and their performance. The evaluator is capable of simulating and evaluating the complex interactions and dynamics of the CRDP components and the response decision protocols. <a>Experiment results indicate that advanced CLOC-based decisions significantly outperform the baseline and less advanced protocols for all three cases, with performance superiority of 9.7-32.8% in case 1; 31.1%-56.6% in case 2; 2.1%-12.1% for teaming protocols, and at least 50% for team coordination protocols in case 3.</a></p>

Systems such as the power grid, world wide web (WWW), and internet are categorized as complex systems because of the presence of a large number of interacting elements. For example, the WWW is estimated to have a billion webpages and understanding the dynamics of such a large number of individual agents (whose individual interactions might not be fully known) is a challenging task. Complex network representations of these systems have proved to be of great utility. Statistical physics is the study of emergence of macroscopic properties of systems from the characteristics of the interactions between individual molecules. Hence, statistical physics of complex networks has been an effective approach to study these systems. In this dissertation, I have used statistical physics to study two distinct phenomena in complex systems: i) Cascading failures and ii) Shortest paths in complex networks. Understanding cascading failures is considered to be one of the “holy grails“ in the study of complex systems such as the power grid, transportation networks, and economic systems. Studying failures of these systems as percolation on complex networks has proved to be insightful. Previously, cascading failures have been studied extensively using two different models: k-core percolation and interdependent networks. The first part of this work combines the two models into a general model, solves it analytically, and validates the theoretical predictions through extensive computer simulations. The phase diagram of the percolation transition has been systematically studied as one varies the average local k-core threshold and the coupling between networks. The phase diagram of the combined processes is very rich and includes novel features that do not appear in the models which study each of the processes separately. For example, the phase diagram consists of first- and second-order transition regions separated by two tricritical lines that merge together and enclose a two-stage transition region. In the two-stage transition, the size of the giant component undergoes a first-order jump at a certain occupation probability followed by a continuous second-order transition at a smaller occupation probability. Furthermore, at certain fixed interdependencies, the percolation transition cycles from first-order to second-order to two-stage to first-order as the k-core threshold is increased. We setup the analytical equations describing the phase boundaries of the two-stage transition region and we derive the critical exponents for each type of transition. Understanding the shortest paths between individual elements in systems like communication networks and social media networks is important in the study of information cascades in these systems. Often, large heterogeneity can be present in the connections between nodes in these networks. Certain sets of nodes can be more highly connected among themselves than with the nodes from other sets. These sets of nodes are often referred to as ’communities’. The second part of this work studies the effect of the presence of communities on the distribution of shortest paths in a network using a modular Erdős-Rényi network model. In this model, the number of communities and the degree of modularity of the network can be tuned using the parameters of the model. We find that the model reaches a percolation threshold while tuning the degree of modularity of the network and the distribution of the shortest paths in the network can be used as an indicator of how the communities are connected.

Doctor of Philosophy / Department of Electrical and Computer Engineering / Caterina Scoglio / Critical infrastructures are repeatedly attacked by external triggers causing tremendous amount of damages. Any infrastructure can be studied using the powerful theory of complex networks. A complex network is composed of extremely large number of different elements that exchange commodities providing significant services. The main functions of complex networks can be damaged by different types of attacks and failures that degrade the network performance. These attacks and failures are considered as disturbing dynamics, such as the spread of viruses in computer networks, the spread of epidemics in social networks, and the cascading failures in power grids. Depending on the network structure and the attack strength, every network differently suffers damages and performance degradation. Hence, quantifying the robustness of complex networks becomes an essential task. In this dissertation, new metrics are introduced to measure the robustness of technological and social networks with respect to the spread of epidemics, and the robustness of power grids with respect to cascading failures. First, we introduce a new metric called the Viral Conductance ($VC_{SIS}$) to assess the robustness of networks with respect to the spread of epidemics that are modeled through the susceptible/infected/susceptible ($SIS$) epidemic approach. In contrast to assessing the robustness of networks based on a classical metric, the epidemic threshold, the new metric integrates the fraction of infected nodes at steady state for all possible effective infection strengths. Through examples, $VC_{SIS}$ provides more insights about the robustness of networks than the epidemic threshold. In addition, both the paradoxical robustness of Barab\'si-Albert preferential attachment networks and the effect of the topology on the steady state infection are studied, to show the importance of quantifying the robustness of networks. Second, a new metric $VC_$ is introduced to assess the robustness of networks with respect to the spread of susceptible/infected/recovered ($SIR$) epidemics. To compute $VC_$, we propose a novel individual-based approach to model the spread of $SIR$ epidemics in networks, which captures the infection size for a given effective infection rate. Thus, $VC_$ quantitatively integrates the infection strength with the corresponding infection size. To optimize the $VC_$ metric, a new mitigation strategy is proposed, based on a temporary reduction of contacts in social networks. The social contact network is modeled as a weighted graph that describes the frequency of contacts among the individuals. Thus, we consider the spread of an epidemic as a dynamical system, and the total number of infection cases as the state of the system, while the weight reduction in the social network is the controller variable leading to slow/reduce the spread of epidemics. Using optimal control theory, the obtained solution represents an optimal adaptive weighted network defined over a finite time interval. Moreover, given the high complexity of the optimization problem, we propose two heuristics to find the near optimal solutions by reducing the contacts among the individuals in a decentralized way. Finally, the cascading failures that can take place in power grids and have recently caused several blackouts are studied. We propose a new metric to assess the robustness of the power grid with respect to the cascading failures. The power grid topology is modeled as a network, which consists of nodes and links representing power substations and transmission lines, respectively. We also propose an optimal islanding strategy to protect the power grid when a cascading failure event takes place in the grid. The robustness metrics are numerically evaluated using real and synthetic networks to quantify their robustness with respect to disturbing dynamics. We show that the proposed metrics outperform the classical metrics in quantifying the robustness of networks and the efficiency of the mitigation strategies. In summary, our work advances the network science field in assessing the robustness of complex networks with respect to various disturbing dynamics.

Urban service networks have come under increased pressure due to expansion of urban population, decrease of capital investment, growing interdependence, and man-made and natural hazards. This thesis introduces a simulation-based methodology for the estimation of the fragility of urban networks subjected to earthquake perturbation. The proposed Interdependent Fragility Assessment (IFA) algorithm abstracts the steps required for perturbation-induced damage propagation within and between networks through internal and interdependent links, respectively. Damage propagation uncertainty is accounted by considering conditional probabilities of failure for components and interdependent strengths measuring the likelihood of intersystemic failure propagation. The IFA algorithm is used in four applications. The first application subjected two simplified models of real interdependent urban power and water networks to selected seismic scenarios. Test results showed that interdependence presence worsens systemic fragility, but that the features of interdependence effects were jointly influenced by local fragility properties and interdependence strengths. A second application examined the role of cascading failures caused by component overloading in systemic fragility. The results showed that cascading failures worsen interdependence fragility, and that mitigation actions improving local component capacity have limited effect on controlling interdependent-induced fragility. Two additional conceptual mitigation measures, component fragility reduction ( CFR ) and interdependence redundancy enhancement ( IRE ), were explored. CFR , decreases component seismic fragilities while IRE adds interdependence links to dependent nodes. Test results showed that CFR outperforms IRE ; however, their combination achieved comparable fragility reductions. This outcome highlights the potential of synergistic mitigation policies in controlling interdependent systemic fragility. Finally, the IFA methodology was adapted to use a probabilistic seismic description for the estimation of unconditional systemic fragilities. The hazard description was obtained following an existing approach that uses importance sampling for the generation of intensity maps. The value of the hybrid methodology rests on its capacity to generate unconditional fragility estimates for direct use in risk assessment. Topics for future work include the development of more sophisticated models of cascading failure, the analysis of optimal mitigation actions using mitigation cost-structures and life-cycle costs, the extension of the IFA methodology for perturbation such as hurricanes and flooding, and interdependent fragility studies of theoretical network models.

There is a growing interest in investigating the high order contingency events that may result in large blackouts, which have been a great concern for power grid secure operation. The actual number of high order contingency is too huge for operators and planner to apply a brute-force enumerative analysis. This thesis presents a heuristic searching method based on particle swarm optimization (PSO) and tabu search to select severe high order contingencies. The original PSO algorithm gives an intelligent strategy to search the feasible solution space, but tends to find the best solution only. The proposed method combines the original PSO with tabu search such that a number of top candidates will be identified. This fits the need of high order contingency screening, which can be eventually the input to many other more complicate security analyses. Reordering of branches of test system based on severity of N-1 contingencies is applied as a pre-processing to increase the convergence properties and efficiency of the algorithm. With this reordering approach, many critical high order contingencies are located in a small area in the whole searching space. Therefore, the proposed algorithm tends to concentrate in searching this area such that the number of critical branch combinations searched will increase. Therefore, the speedup ratio is found to increase significantly. The proposed algorithm is tested for N-2 and N-3 contingencies using two test systems modified from the IEEE 118-bus and 30-bus systems. Variation of inertia weight, learning factors, and number of particles is tested and the range of values more suitable for this specific algorithm is suggested. Although illustrated and tested with N-2 and N-3 contingency analysis, the proposed algorithm can be extended to even higher order contingencies but visualization will be difficult because of the increase in the problem dimensions corresponding to the order of contingencies.