Modelling and vulnerability analysis of cyber-physical power systems based on interdependent networks

The strong coupling between the power grid and communication systems may contribute to failure propagation, which may easily lead to cascading failures or blackouts. In this paper, in order to quantitatively analyse the impact of interdependency on power system vulnerability, we put forward a “degree–electrical degree” independent model of cyber-physical power systems (CPPS), a new type of assortative link, through identifying the important nodes in a power grid based on the proposed index–electrical degree, and coupling them with the nodes in a communication system with a high degree, based on one-to-one correspondence. Using the double-star communication system and the IEEE 118-bus power grid to form an artificial interdependent network, we evaluated and compare the holistic vulnerability of CPPS under random attack and malicious attack, separately based on three kinds of interdependent models: “degree–betweenness”, “degree–electrical degree” and “random link”. The simulation results demonstrated that different link patterns, coupling degrees and attack types all can influence the vulnerability of CPPS. The CPPS with a “degree–electrical degree” interdependent model proposed in this paper presented a higher robustness in the face of random attack, and moreover performed better than the degree–betweenness interdependent model in the face of malicious attack

Mitigation and recovery from cascading failures in interdependent networks under uncertainty

The interdependency of multiple networks makes today's infrastructures more vulnerable to failures. Prior works mainly focused on robust network design and recovery strategies after failures, given complete knowledge of failure location. Nevertheless, in real-world scenarios, the location of failures might be unknown or only partially known. In this work, we focus on cascading failures involving the power grid and its communication network with imprecision in failure assessment. We consider a model where functionality of the power grid and its failure assessment rely on the operation of a monitoring system and vice versa. We address ongoing cascading failures with a twofold approach: 1) Once a cascading failure is detected, we limit further propagation by re-dispatching generation and shedding loads, 2) We formulate a recovery plan to maximize the total amount of load served during the recovery intervention. We performed extensive simulations on real network topologies showing the effectiveness of the proposed approach in terms of number of disrupted power lines and total served load

Optimal Control Strategies for Complex Biological Systems

To better understand and to improve therapies for complex diseases such as cancer or diabetes, it is not sufficient to identify and characterize the interactions between molecules and pathways in complex biological systems, such as cells, tissues, and the human body. It also is necessary to characterize the response of a biological system to externally supplied agents (e.g., drugs, insulin), including a proper scheduling of these drugs, and drug combinations in multi drugs therapies. This obviously becomes important in applications which involve control of physiological processes, such as controlling the number of autophagosome vesicles in a cell, or regulating the blood glucose level in patients affected by diabetes. A critical consideration when controlling physiological processes in biological systems is to reduce the amount of drugs used, as in some therapies drugs may become toxic when they are overused. All of the above aspects can be addressed by using tools provided by the theory of optimal control, where the externally supplied drugs or hormones are the inputs to the system. Another important aspect of using optimal control theory in biological systems is to identify the drug or the combination of drugs that are effective in regulating a given therapeutic target, i.e., a biological target of the externally supplied stimuli. The dynamics of the key features of a biological system can be modeled and described as a set of nonlinear differential equations. For the implementation of optimal control theory in complex biological systems, in what follows we extract \textit{a network} from the dynamics. Namely, to each state variable $x_i$ we will assign a network node $v_i$ ($i=1,...,N$) and a network directed edge from node $v_i$ to another node $v_j$ will be assigned every time $x_j$ is present in the time derivative of $x_i$. The node which directly receives an external stimulus is called a \emph{driver nodes} in a network. The node which directly connected to an output sensor is called a \emph{target node}. %, and it has a prescribed final state that we wish to achieve in finite time. From the control point of view, the idea of controllability of a system describes the ability to steer the system in a certain time interval towards thea desired state with a suitable choice of control inputs. However, defining controllability of large complex networks is quite challenging, primarily because of the large size of the network, its complex structure, and poor knowledge of the precise network dynamics. A network can be controllable in theory but not in practice when a very large control effort is required to steer the system in the desired direction. This thesis considers several approaches to address some of these challenges. Our first approach is to reduce the control effort is to reduce the number of target nodes. We see that by controlling the states of a subset of the network nodes, rather than the state of every node, while holding the number of control signals constant, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs as long as the target set is appropriately sized. We call this strategy \emph{target control}. As our second approach is based on reducing the control efforts by allowing the prescribed final states are satisfied approximately rather than strictly. We introduce a new control strategy called \textit{balanced control} for which we set our objective function as a convex combination of two competitive terms: (i) the distance between the output final states at a given final time and given prescribed states and (ii) the total control efforts expenditure over the given time period. Based on the above two approaches, we propose an algorithm which provides a locally optimal control technique for a network with nonlinear dynamics. We also apply pseudo-spectral optimal control, together with the target and balance control strategies previously described, to complex networks with nonlinear dynamics. These optimal control techniques empower us to implement the theoretical control techniques to biological systems evolving with very large, complex and nonlinear dynamics. We use these techniques to derive the optimal amounts of several drugs in a combination and their optimal dosages. First, we provide a prediction of optimal drug schedules and combined drug therapies for controlling the cell signaling network that regulates autophagy in a cell. Second, we compute an optimal dual drug therapy based on administration of both insulin and glucagon to control the blood glucose level in type I diabetes. Finally, we also implement the combined control strategies to investigate the emergence of cascading failures in the power grid networks

Power network and smart grids analysis from a graph theoretic perspective

The growing size and complexity of power systems has given raise to the use of complex network theory in their modelling, analysis, and synthesis. Though most of the previous studies in this area have focused on distributed control through well established protocols like synchronization and consensus, recently, a few fundamental concepts from graph theory have also been applied, for example in symmetry-based cluster synchronization. Among the existing notions of graph theory, graph symmetry is the focus of this proposal. However, there are other development around some concepts from complex network theory such as graph clustering in the study. In spite of the widespread applications of symmetry concepts in many real world complex networks, one can rarely find an article exploiting the symmetry in power systems. In addition, no study has been conducted in analysing controllability and robustness for a power network employing graph symmetry. It has been verified that graph symmetry promotes robustness but impedes controllability. A largely absent work, even in other fields outside power systems, is the simultaneous investigation of the symmetry effect on controllability and robustness. The thesis can be divided into two section. The first section, including Chapters 2-3, establishes the major theoretical development around the applications of graph symmetry in power networks. A few important topics in power systems and smart grids such as controllability and robustness are addressed using the symmetry concept. These topics are directed toward solving specific problems in complex power networks. The controllability analysis will lead to new algorithms elaborating current controllability benchmarks such as the maximum matching and the minimum dominant set. The resulting algorithms will optimize the number of required driver nodes indicated as FACTS devices in power networks. The second topic, robustness, will be tackled by the symmetry analysis of the network to investigate three aspects of network robustness: robustness of controllability, disturbance decoupling, and fault tolerance against failure in a network element. In the second section, including Chapters 4-8, in addition to theoretical development, a few novel applications are proposed for the theoretical development proposed in both sections one and two. In Chapter 4, an application for the proposed approaches is introduced and developed. The placement of flexible AC transmission systems (FACTS) is investigated where the cybersecurity of the associated data exchange under the wide area power networks is also considered. A new notion of security, i.e. moderated-k-symmetry, is introduced to leverage on the symmetry characteristics of the network to obscure the network data from the adversary perspective. In chapters 5-8, the use of graph theory, and in particular, graph symmetry and centrality, are adapted for the complex network of charging stations. In Chapter 5, the placement and sizing of charging stations (CSs) of the network of electric vehicles are addressed by proposing a novel complex network model of the charging stations. The problems of placement and sizing are then reformulated in a control framework and the impact of symmetry on the number and locations of charging stations is also investigated. These results are developed in Chapters 6-7 to robust placement and sizing of charging stations for the Tesla network of Sydney where the problem of extending the capacity having a set of pre-existing CSs are addressed. The role of centrality in placement of CSs is investigated in Chapter 8. Finally, concluding remarks and future works are presented in Chapter 9

Disaster risk management of interdependent infrastructure systems for community resilience planning

This research focuses on developing methodologies to model the damage and recovery of interdependent infrastructure systems under disruptive events for community resilience planning. The overall research can be broadly divided into two parts: developing a model to simulate the post-disaster performance of interdependent infrastructure systems and developing decision frameworks to support pre-disaster risk mitigation and post-disaster recovery planning of the interdependent infrastructure systems towards higher resilience. The Dynamic Integrated Network (DIN) model is proposed in this study to simulate the performance of interdependent infrastructure systems over time following disruptive events. It can consider three different levels of interdependent relationships between different infrastructure systems: system-to-system level, system-to-facility level and facility-to-facility level. The uncertainties in some of the modeling parameters are modeled. The DIN model first assesses the inoperability of the network nodes and links over time to simulate the damage and recovery of the interdependent infrastructure facilities, and then assesses the recovery and resilience of the individual infrastructure systems and the integrated network utilizing some network performance metrics. The recovery simulation result from the proposed model is compared to two conventional models, one with no interdependency considered, and the other one with only system-level interdependencies considered. The comparison results suggest that ignoring the interdependencies between facilities in different infrastructure systems would lead to poorly informed decision making. The DIN model is validated through simulating the recovery of the interdependent power, water and cellular systems of Galveston City, Texas after Hurricane Ike (2008). Implementing strategic pre-disaster risk mitigation plan to improve the resilience of the interdependent infrastructure systems is essential for enhancing the social security and economic prosperity of a community. Majority of the existing infrastructure risk mitigation studies or projects focus on a single infrastructure system, which may not be the most efficient and effective way to mitigate the loss and enhance the overall community disaster resilience. This research proposes a risk-informed decision framework which could support the pre-disaster risk mitigation planning of several interdependent infrastructure systems. The characteristics of the Interdependent Infrastructure Risk Mitigation (IIRM) decision problem, such as objective, decision makers, constraints, etc., are clearly identified. A four-stage decision framework to solve the IIRM problem is also presented. The application of the proposed IIRM decision framework is illustrated using a case study on pre-disaster risk mitigation planning for the interdependent critical infrastructure systems in Jamaica. The outcome of the IIRM problem is useful for the decision makers to allocate limited risk mitigation budget or resources to the most critical infrastructure facilities in different systems to achieve greater community disaster resilience. Optimizing the post-disaster recovery of damaged infrastructure systems is essential to alleviate the adverse impacts of natural disasters to communities and enhance their disaster resilience. As a result of infrastructure interdependencies, the complete functional restoration of a facility in one infrastructure system relies on not only the physical recovery of itself, but also the recovery of the facilities in other systems that it depends on. This study introduces the Interdependent Infrastructure Recovery Planning (IIRP) problem, which aims at optimizing the assignment and scheduling of the repair teams for an infrastructure system with considering the repair plan of the other infrastructure systems during the post-disaster recovery phase. Key characteristics of the IIRP problem are identified and a game theory-based IIRP decision framework is presented. Two recovery time-based performance metrics are introduced and applied to evaluate the efficiency and effectiveness of the post-disaster recovery plan. The IIRP decision framework is illustrated using the interdependent power and water systems of the Centerville virtual community subjected to seismic hazard