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No description available.

No description available.

No description available.

When a power system is subjected to a disturbance, the power flow changes, leading to deviations in the synchronous generator rotor angles. The rotor angle deviations propagate as electromechanical waves (EMWs) throughout the power system. These waves became observable since the development of synchrophasor measurement instruments. The speed of EMW propagation is hundreds of miles per second, much less than the electromagnetic wave propagation speed, which is the speed of light. Recently, with the development of renewable energy resources and a growth in using HVDC and FACTS devices, these waves are propagating slower, and their impacts are more considerable and complicated. The protection system needs a control system that can take suitable action based on local measurements to overcome the results of power system faults. Therefore, the dynamic behavior of power systems should be properly observed. The EMW propagation in the literature was studied using assumptions such as constant voltage throughout the entire power system and zero resistances and equal series reactances for the transmission lines. Although these assumptions help simplify the power system study model, the model cannot capture the entire power system's dynamic behaviors, since these assumptions are unrealistic. This research will develop an accurate model for EMW propagation when the system is facing a disturbance using a continuum model. The model includes a novel inertia distribution. It also investigates the impacts of voltage changes in the power system on EMW behaviors and when these impacts are negligible. Furthermore, the impacts of the internal reactances of synchronous generators and the resistances of transmission lines on EMW propagation are explored. / Doctor of Philosophy / Power systems, essential for electricity supply, undergo disturbances causing changes in power flow and synchronous generator behavior. These disturbances create electromechanical waves (EMWs) that influence system dynamics. Recent advancements, including renewable energy integration and new technologies, alter EMW behavior, posing challenges for control and protection systems. Existing studies simplify models, limiting their accuracy. This research aims to develop a realistic EMW propagation model considering factors like novel inertia distribution, voltage changes, and internal generator properties. This work addresses the evolving power landscape, enhancing our understanding of power system dynamics for improved control and reliability.

We study the nonlinear Schrödinger (NLS) equation on star graphs with the Neumann- Kirchhoff (NK) boundary conditions at the vertex. We analyze the stability of standing wave solutions of the NLS equation by using different techniques. We consider a half-soliton state of the NLS equation, and by using normal forms, we prove it is nonlinearly unstable due to small perturbations that grow slowly in time. Moreover, under certain constraints on parameters of the generalized NK conditions, we show the existence of a family of shifted states, which are parametrized by a translational parameter. We obtain the spectral stability/instability result for shifted states by using the Sturm theory for counting the Morse indices of the shifted states. For the spectrally stable shifted states, we show that the momentum of the NLS equation is not conserved which results in the irreversible drift of the family of shifted states towards the vertex of the star graph. As a result, the spectrally stable shifted states are nonlinearly unstable. We also study the NLS equation on star graphs with a delta-interaction at the vertex. The presence of the interaction modifies the NK boundary conditions by adding an extra parameter. Depending on the value of the parameter, the NLS equation admits symmetric and asymmetric standing waves with either monotonic or non-monotonic structure on each edge. By using the Sturm theory approach, we prove the orbital instability of the standing waves. / Thesis / Doctor of Philosophy (PhD)

Turbulent swirling flows are important in many applications including gas turbines, furnaces and cyclone dust separators among others. Although the mean flow fields have been relatively well studied, a complete understanding of the flow field including its dynamics has not been achieved. The work contained in this dissertation attempts to shed further light on the behavior of turbulent swirling flows, especially focused on the dynamic behavior of a turbulent swirling flow encountering a sudden expansion. Experiments were performed in a new isothermal turbulent swirling flow test facility. Two geometrical nozzle configurations were studied. The \cb\ nozzle configuration exhibits a cylindrical \cb\ in the center of the nozzle. The free vortex nozzle configuration is obtained when the cylindrical \cb\ is removed. Detailed laser velocimeter measurements were performed to map out the flow field near the sudden expansion of the 2.9" (ID) nozzle leading to the 7.4" (ID) downstream section. In addition to presenting detailed flow profiles for both nozzle and downstream flow fields, representative frequency spectra of the flow dynamics are presented. Along with the flow time histories and histograms, the wide variety of dynamic behavior was thus described in great detail. The dynamics observed in the experiment can be classified into three main categories: coherent and large scale motion, intermittent motion and coherent periodic motion. Free vortex geometry flows, in the parameter space of the experiments (Swirl number = 0 - 0.21), exhibited mostly coherent and large scale motion. The spectra in these cases were broadband with very light concentration of spectral energy observed in some specific cases. Center--body geometry flows exhibited all three categories of flows as swirl strength was increased from zero. Flows with little or no swirl exhibited broad--band spectra similar to those for the free vortex geometry. Intermediate swirl levels resulted in a large amount of low frequency energy which, with the aid of the time histories, was identified as a large scale intermittence associated with radial movement of the annular jet as it enters the sudden expansion. Large swirl levels resulted in high magnitude coherent oscillations concentrated largely just downstream of the sudden expansion. Linear stability analysis was used to help in the interpretation of the observed dynamics. Although, as implemented here (using the parallel flow assumption), the analysis was not successful in quantitatively matching the experimentally observed dynamics, significant insight into the physical mechanisms of the observed dynamics was obtained from the analysis. Specifically, the coherent oscillations observed for larger swirl levels were able to be described in terms of the interaction between the inner and outer shear layers of the flow field. / Ph. D.

DNA microarray has become a powerful tool in genetics, molecular biology, and biomedical research. DNA microarray can be used for measuring the genotypes, structural changes, and gene expressions of human genomes. Detection and characterization of multilevel, high-throughput microarray genomic data pose new challenges to statistical pattern recognition and machine learning research. In this dissertation, we propose novel computational methods for analyzing DNA copy number changes and learning the trees of phenotypes using DNA microarray data. DNA copy number change is an important form of structural variations in human genomes. The copy number signals measured by high-density DNA microarrays usually have low signal-to-noise ratios and complex patterns due to inhomogeneous composition of tissue samples. We propose a robust detection method for extracting copy number changes in a single signal profile and consensus copy number changes in the signal profiles of a population. We adapt a solution-path algorithm to efficiently solve the optimization problems associated with the proposed method. We tested the proposed method on both simulation and real CGH and SNP microarray datasets, and observed competitively improved performance as compared to several widely-adopted copy number change detection methods. We also propose a chromosome instability measure to summarize the extracted copy number changes for assessing chromosomal instabilities of tumor genomes. The proposed measure demonstrates distinct patterns between different subtypes of ovarian serous carcinomas and normal samples. Among active research on complex human diseases using genomic data, little effort and progress have been made in discovering the relational structural information embedded in the molecular data. We propose two stability analysis based methods to learn stable and highly resolved trees of phenotypes using microarray gene expression data of heterogeneous diseases. In the first method, we use a hierarchical, divisive visualization approach to explore the tree of phenotypes and a leave-one-out cross validation to select stable tree structures. In the second method, we propose a node bandwidth constraint to construct stable trees that can balance the descriptive power and reproducibility of tree structures. Using a top-down merging procedure, we modify the binary tree structures learned by hierarchical group clustering methods to achieve a given node bandwidth. We use a bootstrap based stability analysis to select stable tree structures under different node bandwidth constraints. The experimental results on two microarray gene expression datasets of human diseases show that the proposed methods can discover stable trees of phenotypes that reveal the relationships between multiple diseases with biological plausibility. / Ph. D.

The advent of various types of high-throughput genomic data has enabled researchers to investigate complex biological systems in a systemic way and started to shed light on the underlying molecular mechanisms in cancers. To analyze huge amounts of genomic data, effective statistical and machine learning tools are clearly needed; more importantly, integrative approaches are especially needed to combine different types of genomic data for a network or pathway view of biological systems. Motivated by such needs, we make efforts in this dissertation to develop integrative framework for pathway analysis. Specifically, we dissect the molecular pathway into two parts: protein-DNA interaction network and protein-protein interaction network. Several novel approaches are proposed to integrate gene expression data with various forms of biological knowledge, such as protein-DNA interaction and protein-protein interaction for reliable molecular network identification. The first part of this dissertation seeks to infer condition-specific transcriptional regulatory network by integrating gene expression data and protein-DNA binding information. Protein-DNA binding information provides initial relationships between transcription factors (TFs) and their target genes, and this information is essential to derive biologically meaningful integrative algorithms. Based on the availability of this information, we discuss the inference task based on two different situations: (a) if protein-DNA binding information of multiple TFs is available: based on the protein-DNA data of multiple TFs, which are derived from sequence analysis between DNA motifs and gene promoter regions, we can construct initial connection matrix and solve the network inference using a constraint least-squares approach named motif-guided network component analysis (mNCA). However, connection matrix usually contains a considerable amount of false positives and false negatives that make inference results questionable. To circumvent this problem, we propose a knowledge based stability analysis (kSA) approach to test the conditional relevance of individual TFs, by checking the discrepancy of multiple estimations of transcription factor activity with respect to different perturbations on the connections. The rationale behind stability analysis is that the consistency of observed gene expression and true network connection shall remain stable after small perturbations are applied to initial connection matrix. With condition-specific TFs prioritized by kSA, we further propose to use multivariate regression to highlight condition-specific target genes. Through simulation studies comparing with several competing methods, we show that the proposed schemes are more sensitive to detect relevant TFs and target genes for network inference purpose. Experimentally, we have applied stability analysis to yeast cell cycle experiment and further to a series of anti-estrogen breast cancer studies. In both experiments not only biologically relevant regulators are highlighted, the condition-specific transcriptional regulatory networks are also constructed, which could provide further insights into the corresponding cellular mechanisms. (b) if only single TF's protein-DNA information is available: this happens when protein-DNA binding relationship of individual TF is measured through experiments. Since original mNCA requires a complete connection matrix to perform estimation, an incomplete knowledge of single TF is not applicable for such approach. Moreover, binding information derived from experiments could still be inconsistent with gene expression levels. To overcome these limitations, we propose a linear extraction scheme called regulatory component analysis (RCA), which can infer underlying regulation relationships, even with partial biological knowledge. Numerical simulations show significant improvement of RCA over other traditional methods to identify target genes, not only in low signal-to-noise-ratio situations and but also when the given biological knowledge is incomplete and inconsistent to data. Furthermore, biological experiments on Escherichia coli regulatory network inferences are performed to fairly compare traditional methods, where the effectiveness and superior performance of RCA are confirmed. The second part of the dissertation moves from protein-DNA interaction network up to protein-protein interaction network, to identify dys-regulated protein sub-networks by integrating gene expression data and protein-protein interaction information. Specifically, we propose a statistically principled method, namely Metropolis random walk on graph (MRWOG), to highlight condition-specific PPI sub-networks in a probabilistic way. The method is based on the Markov chain Monte Carlo (MCMC) theory to generate a series of samples that will eventually converge to some desired equilibrium distribution, and each sample indicates the selection of one particular sub-network during the process of Metropolis random walk. The central idea of MRWOG is built upon that the essentiality of one gene to be included in a sub-network depends on not only its expression but also its topological importance. Contrasted to most existing methods constructing sub-networks in a deterministic way and therefore lacking relevance score for each protein, MRWOG is capable of assessing the importance of each individual protein node in a global way, not only reflecting its individual association with clinical outcome but also indicating its topological role (hub, bridge) to connect other important proteins. Moreover, each protein node is associated with a sampling frequency score, which enables the statistical justification of each individual node and flexible scaling of sub-network results. Based on MRWOG approach, we further propose two strategies: one is bootstrapping used for assessing statistical confidence of detected sub-networks; the other is graphic division to separate a large sub-network to several smaller sub-networks for facilitating interpretations. MRWOG is easy to use with only two parameters need to be adjusted, one is beta value for performing random walk and another is Quantile level for calculating truncated posteriori mean. Through extensive simulations, we show that the proposed scheme is not sensitive to these two parameters in a relatively wide range. We also compare MRWOG with deterministic approaches for identifying sub-network and prioritizing topologically important proteins, in both cases MRWG outperforms existing methods in terms of both precision and recall. By utilizing MRWOG generated node/edge sampling frequency, which is actually posteriori mean of corresponding protein node/interaction edge, we illustrate that condition-specific nodes/interactions can be better prioritized than the schemes based on scores of individual node/interaction. Experimentally, we have applied MRWOG to study yeast knockout experiment for galactose utilization pathways to reveal important components of corresponding biological functions; we also applied MRWSOG to study breast cancer patient prognostics problems, where the sub-network analysis could lead to an understanding of the molecular mechanisms of antiestrogen resistance in breast cancer. Finally, we conclude this dissertation with a summary of the original contributions, and the future work for deepening the theoretical justification of the proposed methods and broadening their potential biological applications such as cancer studies. / Ph. D.

The widespread integration of power converters in applications such as microgrids and data centers has introduced significant stability challenges. This dissertation presents a novel approach to modeling and comprehensive stability analysis for both single-phase and three-phase converters, addressing vital gaps in the existing literature. The first part of the dissertation (Chapters 2 to 4) focuses on single-phase power supply units, proposing an impedance model and a loop gain model based on dq-frame analysis. These models have been validated through extensive experimental testing, demonstrating their effectiveness in stability analysis across a range of system configurations, including single-phase, three-phase three-wire, and three-phase four-wire systems. The second part (Chapters 5 and 6) examines three-phase converters used for integrating renewable energy into microgrids. It introduces a grid-forming control, followed by a detailed investigation into its impedance modeling and stability assessment. This part specifically tackles the challenges posed by the appearance of right-half-plane poles in stability analysis, proposing a new stability margin index to address these issues. The efficacy of these research findings is further substantiated by the development and implementation of a Power-Hardware-in-the-Loop testbed, providing practical validation. Overall, this dissertation has enhanced the modeling, understanding, and management of stability issues in power electronics systems, offering valuable insights and methodologies that are likely to influence future research and development in the field. / Doctor of Philosophy / Power electronics play a crucial role in many of today's advanced technologies, including Renewable Energy (like wind and solar power), Electric Vehicles, Cloud Computing, and Artificial Intelligence. In renewable energy, power electronics are key for converting energy sources for efficient grid integration. Electric vehicles rely on power converter systems for charging their batteries and driving their motors. Similarly, in Cloud Computing and Artificial Intelligence, power electronics ensure that the computers and servers in data centers have a steady and reliable power supply for operation. However, using these advanced power electronics on a large scale, like in wind farms or data centers, can lead to challenges, including many reported system instability issues. These issues highlight the importance of a thorough analysis and understanding of the behavior and interaction of power electronics systems. In addressing these challenges, power electronics converters, conceptualized as a blend of circuits and control systems, demand comprehensive modeling from the ground up. Such modeling is essential to understanding their behavior, ranging from individual components to the entire system. This is key to establishing a clear connection between intricate design details and overall system performance. With power electronics systems becoming more complex and the continual emergence of new technologies, there remains a significant array of unanswered questions, especially in the domain of stability analysis for AC power electronics systems. This dissertation delves into two prominent modeling methods for stability analysis: impedance modeling and loop gain modeling. By exploring and addressing specific gaps identified in prior research, this work aims to contribute to a more profound understanding and enhanced application of these critical methods. The research presented in this dissertation is methodically divided into two main sections. The first section, including Chapter 2 to Chapter 4 is dedicated to exploring single-phase converter power supply units (PSUs) systems. This section introduces innovative models for analyzing their stability, applicable to single-phase PSUs in various system configurations, including both single-phase and three-phase setups. This modeling approach is a significant step forward in understanding and enhancing the stability of single-phase PSU loads. The second section, including Chapter 5 and Chapter 6, delves into the analysis of three-phase converters used in integrating renewable energy sources into microgrids. A notable feature of these converters is their grid-forming control mechanism, which includes a new frequency and power droop control loop. This part also explores modeling the impact of these converters on microgrid stability. Moreover, the issue of right-half-plane (RHP) poles in impedance analysis- a complex problem that can affect stability analysis is addressed. It proposes innovative methods for measuring stability in such conditions. In conclusion, this research made advancements in the modeling for stability analysis of power converter systems. For single-phase converters, the developed impedance model and loop gain model, based on dq-frame analysis, have been proven to be accurate. These models are versatile for stability analysis in various AC systems with single-phase PSU loads. In the study of three-phase converters, the grid-forming converter was successfully designed to support the grid as a distributed energy resource interface. This design contributes positively to microgrid stability. Furthermore, to address the presence of RHP poles in stability analysis, a new stability margin index was defined to better understand and manage these challenges. These findings represent important steps forward in the field of power electronics and contribute valuable insights for future research and development.