Failure Localization in Power Systems via Tree Partitions

Cascading failures in power systems propagate non-locally, making the control and mitigation of outages extremely hard. In this work, we use the emerging concept of the tree partition of transmission networks to provide an analytical characterization of line failure localizability in transmission systems. Our results rigorously establish the well perceived intuition in power community that failures cannot cross bridges, and reveal a finer-grained concept that encodes more precise information on failure propagations within tree-partition regions. Specifically, when a non-bridge line is tripped, the impact of this failure only propagates within well-defined components, which we refer to as cells, of the tree partition defined by the bridges. In contrast, when a bridge line is tripped, the impact of this failure propagates globally across the network, affecting the power flow on all remaining transmission lines. This characterization suggests that it is possible to improve the system robustness by temporarily switching off certain transmission lines, so as to create more, smaller components in the tree partition; thus spatially localizing line failures and making the grid less vulnerable to large-scale outages. We illustrate this approach using the IEEE 118-bus test system and demonstrate that switching off a negligible portion of transmission lines allows the impact of line failures to be significantly more localized without substantial changes in line congestion

Geodesic vulnerability approach for identification of critical buses in power systems

One of the most critical issues in the evaluation of power systems is the identification of critical buses. For this purpose, this paper proposes a new methodology that evaluates the substitution of the power flow technique by the geodesic vulnerability index to identify critical nodes in power grids. Both methods are applied comparatively to demonstrate the scope of the proposed approach. The applicability of the methodology is illustrated using the IEEE 118-bus test system as a case study. To identify the critical components, a node is initially disconnected, and the performance of the resulting topology is evaluated in the face of simulations for multiple cascading faults. Cascading events are simulated by randomly removing assets on a system that continually changes its structure with the elimination of each component. Thus, the classification of the critical nodes is determined by evaluating the resulting performance of 118 different topologies and calculating the damage area for each of the disintegration curves of cascading failures. In summary, the feasibility and suitability of complex network theory are justified to identify critical nodes in power systems

Can Competition Outperform Collaboration? The Role of Misbehaving Agents

We investigate a novel approach to resilient distributed optimization with quadratic costs in a multi-agent system prone to unexpected events that make some agents misbehave. In contrast to commonly adopted filtering strategies, we draw inspiration from phenomena modeled through the Friedkin-Johnsen dynamics and argue that adding competition to the mix can improve resilience in the presence of misbehaving agents. Our intuition is corroborated by analytical and numerical results showing that (i) there exists a nontrivial trade-off between full collaboration and full competition and (ii) our competition-based approach can outperform state-of-the-art algorithms based on Weighted Mean Subsequence Reduced. We also study impact of communication topology and connectivity on resilience, pointing out insights to robust network design.Comment: Submitted to IEEE TAC - first revisio

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

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