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- Genre: Academic theses
- Creators: Vittal, Vijay
Description
Bacteriophage (phage) are viruses that infect bacteria. Typical laboratory experiments show that in a chemostat containing phage and susceptible bacteria species, a mutant bacteria species will evolve. This mutant species is usually resistant to the phage infection and less competitive compared to the susceptible bacteria species. In some experiments, both susceptible and resistant bacteria species, as well as phage, can coexist at an equilibrium for hundreds of hours. The current research is inspired by these observations, and the goal is to establish a mathematical model and explore sufficient and necessary conditions for the coexistence. In this dissertation a model with infinite distributed delay terms based on some existing work is established. A rigorous analysis of the well-posedness of this model is provided, and it is proved that the susceptible bacteria persist. To study the persistence of phage species, a "Phage Reproduction Number" (PRN) is defined. The mathematical analysis shows phage persist if PRN > 1 and vanish if PRN < 1. A sufficient condition and a necessary condition for persistence of resistant bacteria are given. The persistence of the phage is essential for the persistence of resistant bacteria. Also, the resistant bacteria persist if its fitness is the same as the susceptible bacteria and if PRN > 1. A special case of the general model leads to a system of ordinary differential equations, for which numerical simulation results are presented.
ContributorsHan, Zhun (Author) / Smith, Hal (Thesis advisor) / Armbruster, Dieter (Committee member) / Kawski, Matthias (Committee member) / Kuang, Yang (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2012
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
ABSTRACT
This dissertation introduces a real-time topology monitoring scheme for power systems intended to provide enhanced situational awareness during major system disturbances. The topology monitoring scheme requires accurate real-time topology information to be effective. This scheme is supported by advances in transmission line outage detection based on data-mining phasor measurement unit (PMU) measurements.
A network flow analysis scheme is proposed to track changes in user defined minimal cut sets within the system. This work introduces a new algorithm used to update a previous network flow solution after the loss of a single system branch. The proposed new algorithm provides a significantly decreased solution time that is desired in a real- time environment. This method of topology monitoring can provide system operators with visual indications of potential problems in the system caused by changes in topology.
This work also presents a method of determining all singleton cut sets within a given network topology called the one line remaining (OLR) algorithm. During operation, if a singleton cut set exists, then the system cannot withstand the loss of any one line and still remain connected. The OLR algorithm activates after the loss of a transmission line and determines if any singleton cut sets were created. These cut sets are found using properties of power transfer distribution factors and minimal cut sets.
The topology analysis algorithms proposed in this work are supported by line outage detection using PMU measurements aimed at providing accurate real-time topology information. This process uses a decision tree (DT) based data-mining approach to characterize a lost tie line in simulation. The trained DT is then used to analyze PMU measurements to detect line outages. The trained decision tree was applied to real PMU measurements to detect the loss of a 500 kV line and had no misclassifications.
The work presented has the objective of enhancing situational awareness during significant system disturbances in real time. This dissertation presents all parts of the proposed topology monitoring scheme and justifies and validates the methodology using a real system event.
This dissertation introduces a real-time topology monitoring scheme for power systems intended to provide enhanced situational awareness during major system disturbances. The topology monitoring scheme requires accurate real-time topology information to be effective. This scheme is supported by advances in transmission line outage detection based on data-mining phasor measurement unit (PMU) measurements.
A network flow analysis scheme is proposed to track changes in user defined minimal cut sets within the system. This work introduces a new algorithm used to update a previous network flow solution after the loss of a single system branch. The proposed new algorithm provides a significantly decreased solution time that is desired in a real- time environment. This method of topology monitoring can provide system operators with visual indications of potential problems in the system caused by changes in topology.
This work also presents a method of determining all singleton cut sets within a given network topology called the one line remaining (OLR) algorithm. During operation, if a singleton cut set exists, then the system cannot withstand the loss of any one line and still remain connected. The OLR algorithm activates after the loss of a transmission line and determines if any singleton cut sets were created. These cut sets are found using properties of power transfer distribution factors and minimal cut sets.
The topology analysis algorithms proposed in this work are supported by line outage detection using PMU measurements aimed at providing accurate real-time topology information. This process uses a decision tree (DT) based data-mining approach to characterize a lost tie line in simulation. The trained DT is then used to analyze PMU measurements to detect line outages. The trained decision tree was applied to real PMU measurements to detect the loss of a 500 kV line and had no misclassifications.
The work presented has the objective of enhancing situational awareness during significant system disturbances in real time. This dissertation presents all parts of the proposed topology monitoring scheme and justifies and validates the methodology using a real system event.
ContributorsWerho, Trevor Nelson (Author) / Vittal, Vijay (Thesis advisor) / Heydt, Gerald (Committee member) / Hedman, Kory (Committee member) / Karady, George G. (Committee member) / Arizona State University (Publisher)
Created2015
Description
Factory production is stochastic in nature with time varying input and output processes that are non-stationary stochastic processes. Hence, the principle quantities of interest are random variables. Typical modeling of such behavior involves numerical simulation and statistical analysis. A deterministic closure model leading to a second order model for the product density and product speed has previously been proposed. The resulting partial differential equations (PDE) are compared to discrete event simulations (DES) that simulate factory production as a time dependent M/M/1 queuing system. Three fundamental scenarios for the time dependent influx are studied: An instant step up/down of the mean arrival rate; an exponential step up/down of the mean arrival rate; and periodic variation of the mean arrival rate. It is shown that the second order model, in general, yields significant improvement over current first order models. Specifically, the agreement between the DES and the PDE for the step up and for periodic forcing that is not too rapid is very good. Adding diffusion to the PDE further improves the agreement. The analysis also points to fundamental open issues regarding the deterministic modeling of low signal-to-noise ratio for some stochastic processes and the possibility of resonance in deterministic models that is not present in the original stochastic process.
ContributorsWienke, Matthew (Author) / Armbruster, Dieter (Thesis advisor) / Jones, Donald (Committee member) / Platte, Rodrigo (Committee member) / Gardner, Carl (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2015
Description
Power flow calculation plays a significant role in power system studies and operation. To ensure the reliable prediction of system states during planning studies and in the operating environment, a reliable power flow algorithm is desired. However, the traditional power flow methods (such as the Gauss Seidel method and the Newton-Raphson method) are not guaranteed to obtain a converged solution when the system is heavily loaded.
This thesis describes a novel non-iterative holomorphic embedding (HE) method to solve the power flow problem that eliminates the convergence issues and the uncertainty of the existence of the solution. It is guaranteed to find a converged solution if the solution exists, and will signal by an oscillation of the result if there is no solution exists. Furthermore, it does not require a guess of the initial voltage solution.
By embedding the complex-valued parameter α into the voltage function, the power balance equations become holomorphic functions. Then the embedded voltage functions are expanded as a Maclaurin power series, V(α). The diagonal Padé approximant calculated from V(α) gives the maximal analytic continuation of V(α), and produces a reliable solution of voltages. The connection between mathematical theory and its application to power flow calculation is described in detail.
With the existing bus-type-switching routine, the models of phase shifters and three-winding transformers are proposed to enable the HE algorithm to solve practical large-scale systems. Additionally, sparsity techniques are used to store the sparse bus admittance matrix. The modified HE algorithm is programmed in MATLAB. A study parameter β is introduced in the embedding formula βα + (1- β)α^2. By varying the value of β, numerical tests of different embedding formulae are conducted on the three-bus, IEEE 14-bus, 118-bus, 300-bus, and the ERCOT systems, and the numerical performance as a function of β is analyzed to determine the “best” embedding formula. The obtained power-flow solutions are validated using MATPOWER.
This thesis describes a novel non-iterative holomorphic embedding (HE) method to solve the power flow problem that eliminates the convergence issues and the uncertainty of the existence of the solution. It is guaranteed to find a converged solution if the solution exists, and will signal by an oscillation of the result if there is no solution exists. Furthermore, it does not require a guess of the initial voltage solution.
By embedding the complex-valued parameter α into the voltage function, the power balance equations become holomorphic functions. Then the embedded voltage functions are expanded as a Maclaurin power series, V(α). The diagonal Padé approximant calculated from V(α) gives the maximal analytic continuation of V(α), and produces a reliable solution of voltages. The connection between mathematical theory and its application to power flow calculation is described in detail.
With the existing bus-type-switching routine, the models of phase shifters and three-winding transformers are proposed to enable the HE algorithm to solve practical large-scale systems. Additionally, sparsity techniques are used to store the sparse bus admittance matrix. The modified HE algorithm is programmed in MATLAB. A study parameter β is introduced in the embedding formula βα + (1- β)α^2. By varying the value of β, numerical tests of different embedding formulae are conducted on the three-bus, IEEE 14-bus, 118-bus, 300-bus, and the ERCOT systems, and the numerical performance as a function of β is analyzed to determine the “best” embedding formula. The obtained power-flow solutions are validated using MATPOWER.
ContributorsLi, Yuting (Author) / Tylavsky, Daniel J (Thesis advisor) / Undrill, John (Committee member) / Vittal, Vijay (Committee member) / Arizona State University (Publisher)
Created2015
Description
Understanding the graphical structure of the electric power system is important
in assessing reliability, robustness, and the risk of failure of operations of this criti-
cal infrastructure network. Statistical graph models of complex networks yield much
insight into the underlying processes that are supported by the network. Such gen-
erative graph models are also capable of generating synthetic graphs representative
of the real network. This is particularly important since the smaller number of tradi-
tionally available test systems, such as the IEEE systems, have been largely deemed
to be insucient for supporting large-scale simulation studies and commercial-grade
algorithm development. Thus, there is a need for statistical generative models of
electric power network that capture both topological and electrical properties of the
network and are scalable.
Generating synthetic network graphs that capture key topological and electrical
characteristics of real-world electric power systems is important in aiding widespread
and accurate analysis of these systems. Classical statistical models of graphs, such as
small-world networks or Erd}os-Renyi graphs, are unable to generate synthetic graphs
that accurately represent the topology of real electric power networks { networks
characterized by highly dense local connectivity and clustering and sparse long-haul
links.
This thesis presents a parametrized model that captures the above-mentioned
unique topological properties of electric power networks. Specically, a new Cluster-
and-Connect model is introduced to generate synthetic graphs using these parameters.
Using a uniform set of metrics proposed in the literature, the accuracy of the proposed
model is evaluated by comparing the synthetic models generated for specic real
electric network graphs. In addition to topological properties, the electrical properties
are captured via line impedances that have been shown to be modeled reliably by well-studied heavy tailed distributions. The details of the research, results obtained and
conclusions drawn are presented in this document.
in assessing reliability, robustness, and the risk of failure of operations of this criti-
cal infrastructure network. Statistical graph models of complex networks yield much
insight into the underlying processes that are supported by the network. Such gen-
erative graph models are also capable of generating synthetic graphs representative
of the real network. This is particularly important since the smaller number of tradi-
tionally available test systems, such as the IEEE systems, have been largely deemed
to be insucient for supporting large-scale simulation studies and commercial-grade
algorithm development. Thus, there is a need for statistical generative models of
electric power network that capture both topological and electrical properties of the
network and are scalable.
Generating synthetic network graphs that capture key topological and electrical
characteristics of real-world electric power systems is important in aiding widespread
and accurate analysis of these systems. Classical statistical models of graphs, such as
small-world networks or Erd}os-Renyi graphs, are unable to generate synthetic graphs
that accurately represent the topology of real electric power networks { networks
characterized by highly dense local connectivity and clustering and sparse long-haul
links.
This thesis presents a parametrized model that captures the above-mentioned
unique topological properties of electric power networks. Specically, a new Cluster-
and-Connect model is introduced to generate synthetic graphs using these parameters.
Using a uniform set of metrics proposed in the literature, the accuracy of the proposed
model is evaluated by comparing the synthetic models generated for specic real
electric network graphs. In addition to topological properties, the electrical properties
are captured via line impedances that have been shown to be modeled reliably by well-studied heavy tailed distributions. The details of the research, results obtained and
conclusions drawn are presented in this document.
ContributorsHu, Jiale (Author) / Sankar, Lalitha (Thesis advisor) / Vittal, Vijay (Committee member) / Scaglione, Anna (Committee member) / Arizona State University (Publisher)
Created2015
Description
The electric power system is monitored via an extensive network of sensors in tandem with data processing algorithms, i.e., an intelligent cyber layer, that enables continual observation and control of the physical system to ensure reliable operations. This data collection and processing system is vulnerable to cyber-attacks that impact the system operation status and lead to serious physical consequences, including systematic problems and failures.
This dissertation studies the physical consequences of unobservable false data injection (FDI) attacks wherein the attacker maliciously changes supervisory control and data acquisition (SCADA) or phasor measurement unit (PMU) measurements, on the electric power system. In this context, the dissertation is divided into three parts, in which the first two parts focus on FDI attacks on SCADA and the last part focuses on FDI attacks on PMUs.
The first part studies the physical consequences of FDI attacks on SCADA measurements designed with limited system information. The attacker is assumed to have perfect knowledge inside a sub-network of the entire system. Two classes of attacks with different assumptions on the attacker's knowledge outside of the sub-network are introduced. In particular, for the second class of attacks, the attacker is assumed to have no information outside of the attack sub-network, but can perform multiple linear regression to learn the relationship between the external network and the attack sub-network with historical data. To determine the worst possible consequences of both classes of attacks, a bi-level optimization problem wherein the first level models the attacker's goal and the second level models the system response is introduced.
The second part of the dissertation concentrates on analyzing the vulnerability of systems to FDI attacks from the perspective of the system. To this end, an off-line vulnerability analysis framework is proposed to identify the subsets of the test system that are more prone to FDI attacks.
The third part studies the vulnerability of PMUs to FDI attacks. Two classes of more sophisticated FDI attacks that capture the temporal correlation of PMU data are introduced. Such attacks are designed with a convex optimization problem and can always bypass both the bad data detector and the low-rank decomposition (LD) detector.
This dissertation studies the physical consequences of unobservable false data injection (FDI) attacks wherein the attacker maliciously changes supervisory control and data acquisition (SCADA) or phasor measurement unit (PMU) measurements, on the electric power system. In this context, the dissertation is divided into three parts, in which the first two parts focus on FDI attacks on SCADA and the last part focuses on FDI attacks on PMUs.
The first part studies the physical consequences of FDI attacks on SCADA measurements designed with limited system information. The attacker is assumed to have perfect knowledge inside a sub-network of the entire system. Two classes of attacks with different assumptions on the attacker's knowledge outside of the sub-network are introduced. In particular, for the second class of attacks, the attacker is assumed to have no information outside of the attack sub-network, but can perform multiple linear regression to learn the relationship between the external network and the attack sub-network with historical data. To determine the worst possible consequences of both classes of attacks, a bi-level optimization problem wherein the first level models the attacker's goal and the second level models the system response is introduced.
The second part of the dissertation concentrates on analyzing the vulnerability of systems to FDI attacks from the perspective of the system. To this end, an off-line vulnerability analysis framework is proposed to identify the subsets of the test system that are more prone to FDI attacks.
The third part studies the vulnerability of PMUs to FDI attacks. Two classes of more sophisticated FDI attacks that capture the temporal correlation of PMU data are introduced. Such attacks are designed with a convex optimization problem and can always bypass both the bad data detector and the low-rank decomposition (LD) detector.
ContributorsZhang, Jiazi (Author) / Sankar, Lalitha (Thesis advisor) / Kosut, Oliver (Committee member) / Hedman, Kory (Committee member) / Vittal, Vijay (Committee member) / Arizona State University (Publisher)
Created2017
Description
The uncertainty and variability associated with stochastic resources, such as wind and solar, coupled with the stringent reliability requirements and constantly changing system operating conditions (e.g., generator and transmission outages) introduce new challenges to power systems. Contemporary approaches to model reserve requirements within the conventional security-constrained unit commitment (SCUC) models may not be satisfactory with increasing penetration levels of stochastic resources; such conventional models pro-cure reserves in accordance with deterministic criteria whose deliverability, in the event of an uncertain realization, is not guaranteed. Smart, well-designed reserve policies are needed to assist system operators in maintaining reliability at least cost.
Contemporary market models do not satisfy the minimum stipulated N-1 mandate for generator contingencies adequately. This research enhances the traditional market practices to handle generator contingencies more appropriately. In addition, this research employs stochastic optimization that leverages statistical information of an ensemble of uncertain scenarios and data analytics-based algorithms to design and develop cohesive reserve policies. The proposed approaches modify the classical SCUC problem to include reserve policies that aim to preemptively anticipate post-contingency congestion patterns and account for resource uncertainty, simultaneously. The hypothesis is to integrate data-mining, reserve requirement determination, and stochastic optimization in a holistic manner without compromising on efficiency, performance, and scalability. The enhanced reserve procurement policies use contingency-based response sets and post-contingency transmission constraints to appropriately predict the influence of recourse actions, i.e., nodal reserve deployment, on critical transmission elements.
This research improves the conventional deterministic models, including reserve scheduling decisions, and facilitates the transition to stochastic models by addressing the reserve allocation issue. The performance of the enhanced SCUC model is compared against con-temporary deterministic models and a stochastic unit commitment model. Numerical results are based on the IEEE 118-bus and the 2383-bus Polish test systems. Test results illustrate that the proposed reserve models consistently outperform the benchmark reserve policies by improving the market efficiency and enhancing the reliability of the market solution at reduced costs while maintaining scalability and market transparency. The proposed approaches require fewer ISO discretionary adjustments and can be employed by present-day solvers with minimal disruption to existing market procedures.
Contemporary market models do not satisfy the minimum stipulated N-1 mandate for generator contingencies adequately. This research enhances the traditional market practices to handle generator contingencies more appropriately. In addition, this research employs stochastic optimization that leverages statistical information of an ensemble of uncertain scenarios and data analytics-based algorithms to design and develop cohesive reserve policies. The proposed approaches modify the classical SCUC problem to include reserve policies that aim to preemptively anticipate post-contingency congestion patterns and account for resource uncertainty, simultaneously. The hypothesis is to integrate data-mining, reserve requirement determination, and stochastic optimization in a holistic manner without compromising on efficiency, performance, and scalability. The enhanced reserve procurement policies use contingency-based response sets and post-contingency transmission constraints to appropriately predict the influence of recourse actions, i.e., nodal reserve deployment, on critical transmission elements.
This research improves the conventional deterministic models, including reserve scheduling decisions, and facilitates the transition to stochastic models by addressing the reserve allocation issue. The performance of the enhanced SCUC model is compared against con-temporary deterministic models and a stochastic unit commitment model. Numerical results are based on the IEEE 118-bus and the 2383-bus Polish test systems. Test results illustrate that the proposed reserve models consistently outperform the benchmark reserve policies by improving the market efficiency and enhancing the reliability of the market solution at reduced costs while maintaining scalability and market transparency. The proposed approaches require fewer ISO discretionary adjustments and can be employed by present-day solvers with minimal disruption to existing market procedures.
ContributorsSinghal, Nikita Ghanshyam (Author) / Hedman, Kory W (Thesis advisor) / Vittal, Vijay (Committee member) / Sankar, Lalitha (Committee member) / Pal, Anamitra (Committee member) / Arizona State University (Publisher)
Created2018
Description
The flexibility in power system networks is not fully modeled in existing real-time contingency analysis (RTCA) and real-time security-constrained economic dispatch (RT SCED) applications. Thus, corrective transmission switching (CTS) is proposed in this dissertation to enable RTCA and RT SCED to take advantage of the flexibility in the transmission system in a practical way.
RTCA is first conducted to identify critical contingencies that may cause violations. Then, for each critical contingency, CTS is performed to determine the beneficial switching actions that can reduce post-contingency violations. To reduce computational burden, fast heuristic algorithms are proposed to generate candidate switching lists. Numerical simulations performed on three large-scale realistic power systems (TVA, ERCOT, and PJM) demonstrate that CTS can significantly reduce post-contingency violations. Parallel computing can further reduce the solution time.
RT SCED is to eliminate the actual overloads and potential post-contingency overloads identified by RTCA. Procedure-A, which is consistent with existing industry practices, is proposed to connect RTCA and RT SCED. As CTS can reduce post-contingency violations, higher branch limits, referred to as pseudo limits, may be available for some contingency-case network constraints. Thus, Procedure-B is proposed to take advantage of the reliability benefits provided by CTS. With the proposed Procedure-B, CTS can be modeled in RT SCED implicitly through the proposed pseudo limits for contingency-case network constraints, which requires no change to existing RT SCED tools. Numerical simulations demonstrate that the proposed Procedure-A can effectively eliminate the flow violations reported by RTCA and that the proposed Procedure-B can reduce most of the congestion cost with consideration of CTS.
The system status may be inaccurately estimated due to false data injection (FDI) cyber-attacks, which may mislead operators to adjust the system improperly and cause network violations. Thus, a two-stage FDI detection (FDID) approach, along with several metrics and an alert system, is proposed in this dissertation to detect FDI attacks. The first stage is to determine whether the system is under attack and the second stage would identify the target branch. Numerical simulations demonstrate the effectiveness of the proposed two-stage FDID approach.
RTCA is first conducted to identify critical contingencies that may cause violations. Then, for each critical contingency, CTS is performed to determine the beneficial switching actions that can reduce post-contingency violations. To reduce computational burden, fast heuristic algorithms are proposed to generate candidate switching lists. Numerical simulations performed on three large-scale realistic power systems (TVA, ERCOT, and PJM) demonstrate that CTS can significantly reduce post-contingency violations. Parallel computing can further reduce the solution time.
RT SCED is to eliminate the actual overloads and potential post-contingency overloads identified by RTCA. Procedure-A, which is consistent with existing industry practices, is proposed to connect RTCA and RT SCED. As CTS can reduce post-contingency violations, higher branch limits, referred to as pseudo limits, may be available for some contingency-case network constraints. Thus, Procedure-B is proposed to take advantage of the reliability benefits provided by CTS. With the proposed Procedure-B, CTS can be modeled in RT SCED implicitly through the proposed pseudo limits for contingency-case network constraints, which requires no change to existing RT SCED tools. Numerical simulations demonstrate that the proposed Procedure-A can effectively eliminate the flow violations reported by RTCA and that the proposed Procedure-B can reduce most of the congestion cost with consideration of CTS.
The system status may be inaccurately estimated due to false data injection (FDI) cyber-attacks, which may mislead operators to adjust the system improperly and cause network violations. Thus, a two-stage FDI detection (FDID) approach, along with several metrics and an alert system, is proposed in this dissertation to detect FDI attacks. The first stage is to determine whether the system is under attack and the second stage would identify the target branch. Numerical simulations demonstrate the effectiveness of the proposed two-stage FDID approach.
ContributorsLi, Xingpeng (Author) / Hedman, Kory (Thesis advisor) / Heydt, Gerald (Committee member) / Vittal, Vijay (Committee member) / Qin, Jiangchao (Committee member) / Arizona State University (Publisher)
Created2017
Description
The Kuramoto model is an archetypal model for studying synchronization in groups
of nonidentical oscillators where oscillators are imbued with their own frequency and
coupled with other oscillators though a network of interactions. As the coupling
strength increases, there is a bifurcation to complete synchronization where all oscillators
move with the same frequency and show a collective rhythm. Kuramoto-like
dynamics are considered a relevant model for instabilities of the AC-power grid which
operates in synchrony under standard conditions but exhibits, in a state of failure,
segmentation of the grid into desynchronized clusters.
In this dissertation the minimum coupling strength required to ensure total frequency
synchronization in a Kuramoto system, called the critical coupling, is investigated.
For coupling strength below the critical coupling, clusters of oscillators form
where oscillators within a cluster are on average oscillating with the same long-term
frequency. A unified order parameter based approach is developed to create approximations
of the critical coupling. Some of the new approximations provide strict lower
bounds for the critical coupling. In addition, these approximations allow for predictions
of the partially synchronized clusters that emerge in the bifurcation from the
synchronized state.
Merging the order parameter approach with graph theoretical concepts leads to a
characterization of this bifurcation as a weighted graph partitioning problem on an
arbitrary networks which then leads to an optimization problem that can efficiently
estimate the partially synchronized clusters. Numerical experiments on random Kuramoto
systems show the high accuracy of these methods. An interpretation of the
methods in the context of power systems is provided.
of nonidentical oscillators where oscillators are imbued with their own frequency and
coupled with other oscillators though a network of interactions. As the coupling
strength increases, there is a bifurcation to complete synchronization where all oscillators
move with the same frequency and show a collective rhythm. Kuramoto-like
dynamics are considered a relevant model for instabilities of the AC-power grid which
operates in synchrony under standard conditions but exhibits, in a state of failure,
segmentation of the grid into desynchronized clusters.
In this dissertation the minimum coupling strength required to ensure total frequency
synchronization in a Kuramoto system, called the critical coupling, is investigated.
For coupling strength below the critical coupling, clusters of oscillators form
where oscillators within a cluster are on average oscillating with the same long-term
frequency. A unified order parameter based approach is developed to create approximations
of the critical coupling. Some of the new approximations provide strict lower
bounds for the critical coupling. In addition, these approximations allow for predictions
of the partially synchronized clusters that emerge in the bifurcation from the
synchronized state.
Merging the order parameter approach with graph theoretical concepts leads to a
characterization of this bifurcation as a weighted graph partitioning problem on an
arbitrary networks which then leads to an optimization problem that can efficiently
estimate the partially synchronized clusters. Numerical experiments on random Kuramoto
systems show the high accuracy of these methods. An interpretation of the
methods in the context of power systems is provided.
ContributorsGilg, Brady (Author) / Armbruster, Dieter (Thesis advisor) / Mittelmann, Hans (Committee member) / Scaglione, Anna (Committee member) / Strogatz, Steven (Committee member) / Welfert, Bruno (Committee member) / Arizona State University (Publisher)
Created2018