The American Multi-modal Energy System: Model Development with Structural and Behavioral Analysis using Hetero-functional Graph Theory

In the 21st century, infrastructure is playing an ever greater role in our daily lives. Presidential Policy Directive 21 emphasizes that infrastructure is critical to public confidence, the nation\u27s safety, and its well-being. With global climate change demanding a host of changes across at least four critical energy infrastructures: the electric grid, the natural gas system, the oil system, and the coal system, it is imperative to study models of these infrastructures to guide future policies and infrastructure developments. Traditionally these energy systems have been studied independently, usually in their own fields of study. Therefore, infrastructure datasets often lack the structural and dynamic elements to describe the interdependencies with other infrastructures. This thesis refers to the integration of the aforementioned energy infrastructures into a singular system-of-systems within the context of the United States of America as the American Multi-modal Energy System (AMES). This work develops an open-source structural and behavioral model of the AMES using Hetero-functional Graph Theory (HFGT), a data-driven approach, and model-based systems engineering practices in the following steps. First, the HFGT toolbox code is made available on GitHub and advanced to produce HFGs of systems on the scale of the AMES using the languages Python and Julia. Second, the analytical insights that HFGs can provide relative to formal graphs are investigated through structural analysis of the American Electric Power System which demonstrates how HFGs are better equipped to describe changes in system behavior. Third, a reference architecture of the AMES is developed, providing a standardized foundation to develop future models of the AMES. Fourth, the AMES reference architecture is instantiated into a structural model from which structural properties are investigated. Finally, a physically informed Weighted Least Squares Error Hetero-functional Graph State Estimation analysis of the AMES\u27 socio-economic behavior is implemented to investigate the behavior of the AMES with asset level granularity. These steps provide a reproducible and reusable structural and behavioral model of the AMES for guiding future policies and infrastructural developments to critical energy infrastructures

A Tensor-Based Formulation of Hetero-functional Graph Theory

Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large flexible engineering systems. In that regard, it intellectually resembles a fusion of network science and model-based systems engineering. With respect to the former, it relies on multiple graphs as data structures so as to support matrix-based quantitative analysis. In the meantime, HFGT explicitly embodies the heterogeneity of conceptual and ontological constructs found in model-based systems engineering including system form, system function, and system concept. At their foundation, these disparate conceptual constructs suggest multi-dimensional rather than two-dimensional relationships. This paper provides the first tensor-based treatment of some of the most important parts of hetero-functional graph theory. In particular, it addresses the "system concept", the hetero-functional adjacency matrix, and the hetero-functional incidence tensor. The tensor-based formulation described in this work makes a stronger tie between HFGT and its ontological foundations in MBSE. Finally, the tensor-based formulation facilitates an understanding of the relationships between HFGT and multi-layer networks

A novel framework for scalable resilience analyses in complex networks

Doctor of PhilosophyDepartment of Electrical and Computer EngineeringBalasubramaniam NatarajanResilience has emerged as a crucial and desirable characteristic of complex systems due to the increasing frequency of cyber intrusions and natural disasters. In systems such as power grids and transportation networks, resilience analysis typically deals with the assessment of system robustness in terms of identifying and safeguarding key system attributes. Robustness evaluation methods can be broadly classified into two types, namely network-based and performance-based. Network-based methodologies involve topological properties of the system, whereas performance-based methods deal with specific performance attributes such as voltage fluctuations in a power distribution network. Existing approaches to evaluate robustness have limitations in terms of (1) inaccurate modeling of the underlying system; (2) high computational complexity; and (3) lack of scalability. This dissertation addresses these challenges by developing computationally efficient frameworks to identify key entities of the system. First, it develops a probabilistic framework for a performance-based robustness attribute. Specifically, using power grid as a case study, this work focuses on the performance measure of interest, i.e., voltage fluctuations. This work first derives an analytical approximation for voltage change at any node of the network due to a change in power at other nodes of a three-phase unbalanced radial distribution network. Next, the probability distribution of voltage changes at a certain node due to random power changes at multiple locations in the network is derived. Then, these distributions with information theoretic metrics are used to derive a novel voltage influencing score (VIS) that quantifies the voltage influencing capacity of nodes with distributed energy resources (DERs) and active loads. VIS is then employed to identify the dominant voltage influencer nodes. Results demonstrate the high efficacy and low computational complexity of the proposed approach, enabling various future applications (e.g., voltage control). In the second part, this dissertation emphasizes on network-based robustness measures. Particularly, it focuses on the task of identifying critical nodes in complex systems so that preemptive actions can be taken to improve the system's resilience. Critical nodes represent a set of sub-systems and/or their interconnections whose removal from the graph maximally disconnects the network, and thus severely disrupts the operation of the system. The majority of the critical node identification methods in literature are based on an iterative approach, and thus suffer from high computational complexity and are not scalable to larger networks. Therefore, this work proposes a scalable and generic graph neural network (GNN) based framework for identifying critical nodes in large complex networks. The proposed framework defines a GNN-based model that learns the node criticality score on a small representative subset of nodes and can identify critical nodes in larger networks. Furthermore, the problem of quantifying the uncertainty in GNN predictions is also considered. Essentially, Assumed Density Filtering is used to quantify aleatoric uncertainty and Monte-Carlo dropout captures uncertainty in model parameters. Finally, the two sources of uncertainty are aggregated to estimate the total uncertainty in predictions of a GNN. Results in real-world datasets demonstrate that the Bayesian model performs at par with a frequentist model. Furthermore, the combinatorial case of critical node identification is also addressed in this dissertation, where the node criticality scores would be associated with a set of nodes. This simulates a concurrent scenario where multiple nodes are being disrupted simultaneously. Essentially, this problem falls under the generic category of graph combinatorial problems. This problem is approached through a novel deep reinforcement learning (DRL) based framework. Specifically, GNNs are used for encoding the underlying graph structure and DRL for learning to identify the optimal node sequence. Moreover, the framework is first developed for Influence Maximization (IM), where one is interested in identifying a set of seed nodes, which when activated, will result in the activation of a maximal number of nodes in the graph. This generic framework can be used for various use-cases, including the identification of critical nodes set related to concurrent disruption. The results on real world networks demonstrate the scalability and generalizability of the proposed methodology. Thirdly, this dissertation presents a comparative study of different performance and network-based robustness metrics in terms of ranking critical nodes of a power distribution network. The efficacy of failure-based metrics in characterizing voltage fluctuations is also investigated. Results show that hybrid failure-based metrics can quantify voltage fluctuations to a reasonable extent. Additionally, several other challenges in existing robustness frameworks are highlighted, including the lack of mechanism to effectively incorporate various performance and network-based resilience factors. Then, a novel modeling framework, namely hetero-functional graph theory (HFGT) is leveraged to model both power distribution networks as well as other dependent infrastructure networks. Results demonstrate that HFGT can address key modeling limitations, and can be used to accurately assess system robustness to failures

Enhancing neural-network performance via assortativity

The performance of attractor neural networks has been shown to depend crucially on the heterogeneity of the underlying topology. We take this analysis a step further by examining the effect of degree-degree correlations -- or assortativity -- on neural-network behavior. We make use of a method recently put forward for studying correlated networks and dynamics thereon, both analytically and computationally, which is independent of how the topology may have evolved. We show how the robustness to noise is greatly enhanced in assortative (positively correlated) neural networks, especially if it is the hub neurons that store the information.Comment: 9 pages, 7 figure

A Hybrid Dynamic System Assessment Methodology for Multi-Modal Transportation-Electrification

In recent years, electrified transportation, be it in the form of buses, trains, or cars have become an emerging form of mobility. Electric vehicles (EVs), especially, are set to expand the amount of electric miles driven and energy consumed. Nevertheless, the question remains as to whether EVs will be technically feasible within infrastructure systems. Fundamentally, EVs interact with three interconnected systems: the (physical) transportation system, the electric power grid, and their supporting information systems. Coupling of the two physical systems essentially forms a nexus, the transportation-electricity nexus (TEN). This paper presents a hybrid dynamic system assessment methodology for multi-modal transportation-electrification. At its core, it utilizes a mathematical model which consists of a marked Petri-net model superimposed on the continuous time microscopic traffic dynamics and the electrical state evolution. The methodology consists of four steps: (1) establish the TEN structure; (2) establish the TEN behavior; (3) establish the TEN Intelligent Transportation-Energy System (ITES) decision-making; and (4) assess the TEN performance. In the presentation of the methodology, the Symmetrica test case is used throughout as an illustrative example. Consequently, values for several measures of performance are provided. This methodology is presented generically and may be used to assess the effects of transportation-electrification in any city or area; opening up possibilities for many future studies