9 research outputs found
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
A General Framework for Uncertainty Quantification via Neural SDE-RNN
Uncertainty quantification is a critical yet unsolved challenge for deep
learning, especially for the time series imputation with irregularly sampled
measurements. To tackle this problem, we propose a novel framework based on the
principles of recurrent neural networks and neural stochastic differential
equations for reconciling irregularly sampled measurements. We impute
measurements at any arbitrary timescale and quantify the uncertainty in the
imputations in a principled manner. Specifically, we derive analytical
expressions for quantifying and propagating the epistemic and aleatoric
uncertainty across time instants. Our experiments on the IEEE 37 bus test
distribution system reveal that our framework can outperform state-of-the-art
uncertainty quantification approaches for time-series data imputations.Comment: 7 pages, 3 figure
Latent Neural ODE for Integrating Multi-timescale measurements in Smart Distribution Grids
Under a smart grid paradigm, there has been an increase in sensor
installations to enhance situational awareness. The measurements from these
sensors can be leveraged for real-time monitoring, control, and protection.
However, these measurements are typically irregularly sampled. These
measurements may also be intermittent due to communication bandwidth
limitations. To tackle this problem, this paper proposes a novel latent neural
ordinary differential equations (LODE) approach to aggregate the unevenly
sampled multivariate time-series measurements. The proposed approach is
flexible in performing both imputations and predictions while being
computationally efficient. Simulation results on IEEE 37 bus test systems
illustrate the efficiency of the proposed approach
Spatio-Temporal Probabilistic Voltage Sensitivity Analysis - A Novel Framework for Hosting Capacity Analysis
Smart grids are envisioned to accommodate high penetration of distributed
photovoltaic (PV) generation, which may cause adverse grid impacts in terms of
voltage violations. Therefore, PV Hosting capacity (HC) is being used as a
planning tool to determine the maximum PV installation capacity that causes the
first voltage violation and above which would require infrastructure upgrades.
Traditional methods of HC analysis are computationally complex as they are
based on iterative load flow algorithms that require investigation of a large
number of scenarios for accurate assessment of PV impacts. This paper first
presents a computationally efficient analytical approach to compute the
probability distribution of voltage change at a particular node due to random
behavior of randomly located multiple distributed PVs. Next, the derived
distribution is used to identify voltage violations for various PV penetration
levels and subsequently determine the HC of the system without the need to
examine multiple scenarios. Results from the proposed spatio-temporal
probabilistic voltage sensitivity analysis and the HC are validated via
conventional load flow based simulation approach on the IEEE 37 and IEEE 123
node test systems.Comment: 8 pages, 2 figures, discussion adde
Bayesian Inductive Learner for Graph Resiliency under uncertainty
In the quest to improve efficiency, interdependence and complexity are
becoming defining characteristics of modern engineered systems. With increasing
vulnerability to cascading failures, it is imperative to understand and manage
the risk and uncertainty associated with such engineered systems. Graph theory
is a widely used framework for modeling interdependent systems and to evaluate
their resilience to disruptions. Most existing methods in resilience analysis
are based on an iterative approach that explores each node/link of a graph.
These methods suffer from high computational complexity and the resulting
analysis is network specific. Additionally, uncertainty associated with the
underlying graphical model further limits the potential value of these
traditional approaches. To overcome these challenges, we propose a Bayesian
graph neural network-based framework for quickly identifying critical nodes in
a large graph. while systematically incorporating uncertainties. Instead of
utilizing the observed graph for training the model, a MAP estimate of the
graph is computed based on the observed topology, and node target labels.
Further, a Monte-Carlo (MC) dropout algorithm is incorporated to account for
the epistemic uncertainty. The fidelity and the gain in computational
complexity offered by the Bayesian framework are illustrated using simulation
results.Comment: 7 pages, 3 figure
Graph neural network based approximation of Node Resiliency in complex networks
The emphasis on optimal operations and efficiency has led to increased
complexity in engineered systems. This in turn increases the vulnerability of
the system. However, with the increasing frequency of extreme events,
resilience has now become an important consideration. Resilience quantifies the
ability of the system to absorb and recover from extreme conditions. Graph
theory is a widely used framework for modeling complex engineered systems to
evaluate their resilience to attacks. Most existing methods in resilience
analysis are based on an iterative approach that explores each node/link of a
graph. These methods suffer from high computational complexity and the
resulting analysis is network specific. To address these challenges, we propose
a graph neural network (GNN) based framework for approximating node resilience
in large complex networks. The proposed framework defines a GNN model that
learns the node rank on a small representative subset of nodes. Then, the
trained model can be employed to predict the ranks of unseen nodes in similar
types of graphs. The scalability of the framework is demonstrated through the
prediction of node ranks in real-world graphs. The proposed approach is
accurate in approximating the node resilience scores and offers a significant
computational advantage over conventional approaches.Comment: 7 pages, 1 figur