Global Robustness vs. Local Vulnerabilities in Complex Synchronous Networks

In complex network-coupled dynamical systems, two questions of central importance are how to identify the most vulnerable components and how to devise a network making the overall system more robust to external perturbations. To address these two questions, we investigate the response of complex networks of coupled oscillators to local perturbations. We quantify the magnitude of the resulting excursion away from the unperturbed synchronous state through quadratic performance measures in the angle or frequency deviations. We find that the most fragile oscillators in a given network are identified by centralities constructed from network resistance distances. Further defining the global robustness of the system from the average response over ensembles of homogeneously distributed perturbations, we find that it is given by a family of topological indices known as generalized Kirchhoff indices. Both resistance centralities and Kirchhoff indices are obtained from a spectral decomposition of the stability matrix of the unperturbed dynamics and can be expressed in terms of resistance distances. We investigate the properties of these topological indices in small-world and regular networks. In the case of oscillators with homogeneous inertia and damping coefficients, we find that inertia only has small effects on robustness of coupled oscillators. Numerical results illustrate the validity of the theory.Comment: 11 pages, 9 figure

Performance Measures for Oscillator Networks

Oscillator networks consist of a set of simple subsystems, e.g. damped harmonic oscillators that interact with each other across a network with a specified structure. Such networks of coupled oscillators serve as a model for many systems such as power grids, vehicle platoons, and biological networks. Even though the dynamics of each oscillator are simple, the coupling between them can produce complex behavior. One possible behavior is synchronization, where all of the oscillators reach a state where their relative phase angles are constant and their frequencies are uniform. This work examines the synchronization performance of oscillator networks, i.e. how well the network maintains synchrony in the face of persistent disturbances. Specifically, we define a class of performance measures for oscillator networks as the H2-norm of particular input-output linear systems. This class of performance measures corresponds to measuring the average value of a quadratic form of the oscillator phases when stochastic disturbances are applied to some subset of the oscillators. Depending on the specific quadratic form that is chosen, this performance measure can correspond to a variety of physically meaningful and domain specific quantities. For example, it can be used to quantify the total interactions between oscillators during resynchronization after a disturbance. This quantity corresponds to the transient resistive losses in maintaining synchronous operation in a power network. Alternatively, one can instead measure the network coherence, which quantifies how closely the oscillator network acts like a single rigid body. Our results demonstrate a strong connection between the concept of effective resistance and our class of performance measures. For example, our results make precise the intuitive notion that more "tightly connected'' oscillator networks are more coherent by showing that the maximum effective resistance in the network is the correct notion of connectivity. We consider applications of the work to both power grids and vehicle platoons with local and absolute (global) velocity feedback. For power grids we use our effective resistance based results to obtain novel bounds on the resistive losses due to generators maintaining synchrony. For vehicle platoons we investigate the coherence in the platoon as a performance measure. We show that for large scale platoons local velocity feedback performs worse than absolute velocity feedback under certain conditions related to the asymptotic behavior of the maximum effective resistance in the underlying graph

Modeling and Monitoring of the Dynamic Response of Railroad Bridges using Wireless Smart Sensors

Railroad bridges form an integral part of railway infrastructure in the USA, carrying approximately 40 % of the ton-miles of freight. The US Department of Transportation (DOT) forecasts current rail tonnage to increase up to 88 % by 2035. Within the railway network, a bridge occurs every 1.4 miles of track, on average, making them critical elements. In an effort to accommodate safely the need for increased load carrying capacity, the Federal Railroad Association (FRA) announced a regulation in 2010 that the bridge owners must conduct and report annual inspection of all the bridges. The objective of this research is to develop appropriate modeling and monitoring techniques for railroad bridges toward understanding the dynamic responses under a moving train. To achieve the research objective, the following issues are considered specifically. For modeling, a simple, yet effective, model is developed to capture salient features of the bridge responses under a moving train. A new hybrid model is then proposed, which is a flexible and efficient tool for estimating bridge responses for arbitrary train configurations and speeds. For monitoring, measured field data is used to validate the performance of the numerical model. Further, interpretation of the proposed models showed that those models are efficient tools for predicting response of the bridge, such as fatigue and resonance. Finally, fundamental software, hardware, and algorithm components are developed for providing synchronized sensing for geographically distributed networks, as can be found in railroad bridges. The results of this research successfully demonstrate the potentials of using wirelessly measured data to perform model development and calibration that will lead to better understanding the dynamic responses of railroad bridges and to provide an effective tool for prediction of bridge response for arbitrary train configurations and speeds.National Science Foundation Grant No. CMS-0600433National Science Foundation Grant No. CMMI-0928886National Science Foundation Grant No. OISE-1107526National Science Foundation Grant No. CMMI- 0724172 (NEESR-SD)Federal Railroad Administration BAA 2010-1 projectOpe

The Impact of Renewable Power Generation and Extreme Weather Events on the Stability and Resilience of AC Power Grids

Der erste Teil dieser Arbeit beschäftigt sich mit der Frage, welchen Einfluss kurzzeitige Schwankungen der erneuerbaren Energiequellen auf die synchrone Netzfrequenz haben. Zu diesem Zweck wird eine lineare Antworttheorie für stochastische Störungen von dynamischen Systemen auf Netzwerken hergeleitet. Anschließend wird diese Theorie verwendet, um den Einfluss von kurzfristigen Wind- und Sonnenschwankungen auf die Netzdynamik zu analysieren. Hierbei wird gezeigt, dass die Frequenzantwort des Netzes weitestgehend homogen ist, aber die Anfälligkeit für Leistungsschwankungen aufgrund von Leitungsverlusten entlang des Leistungsflusses zunimmt. Der zweite Teil der Arbeit befasst sich mit der Modellierung von netzbildenden Wechselrichterregelungen. Bislang existiert kein universelles Modell zur Beschreibung der kollektiven Dynamik solcher Systeme. Um dies zu erreichen, wird unter Ausnutzung der inhärenten Symmetrie des synchronen Betriebszustandes eine Normalform für netzbildende Akteure abgeleitet. Anschließend wird gezeigt, dass dieses Modell eine gute Annäherung an typische Wechselrichter-Dynamiken bietet, aber auch für eine datengesteuerte Modellierung gut geeignet ist. Der letzte Teil der Arbeit befasst sich mit der Analyse des Risikos von Stromausfällen, welche durch Hurrikans verursacht werden. Hohe Windgeschwindigkeiten verursachen häufig Schäden an der Übertragungsinfrastruktur, welche wiederum zu Überlastungen anderer Komponenten führen und damit eine Kaskade von Ausfällen im gesamten Netz auslösen können. Simulationen solcher Szenarien werden durch die Kombination eines meteorologischen Windmodells sowie eines Modells für kaskadierende Leitungsausfälle durchgeführt. Durch Monte-Carlo-Simulationen in einer synthetischen Nachbildung des texanischen Übertragungsnetzes können einzelne kritische Leitungen identifiziert werden, welche zu großflächigen Stromausfällen führen.The first part of this thesis addresses the question which impact short-term renewable fluctuations have on the synchronous grid frequency. For this purpose, a linear response theory for stochastic perturbations of networked dynamical systems is derived. This theory is then used to analyze the impact of short-term wind and solar fluctuations on the grid frequency. It is shown that while the network frequency response is mainly homogenous, the susceptibility to power fluctuations is increasing along the power flow due to transmission line losses. The second part of the thesis is concerned with modeling grid-forming inverter controls. So far there exists no universal model for studying the collective dynamics of such systems. By utilizing the inherent symmetry of the synchronous operating state, a normal form for grid-forming actors is derived. It is shown that this model provides a useful approximation of certain inverter control dynamics but is also well-suited for a data-driven modeling approach. The last part of the thesis deals with analyzing the risk of hurricane-induced power outages. High wind speeds often cause damage to transmission infrastructure which can lead to overloads of other components and thereby induce a cascade of failures spreading through the entire grid. Simulations of such scenarios are implemented by combining a meteorological wind field model with a model for cascading line failures. Using Monte Carlo simulations in a synthetic test case resembling the Texas transmission system, it is possible to identify critical lines that trigger large-scale power outages

SPS phase control system performance via analytical simulation

A solar power satellite transmission system which incorporates automatic beam forming, steering, and phase control is discussed. The phase control concept centers around the notation of an active retrodirective phased array as a means of pointing the beam to the appropriate spot on Earth. The transmitting antenna (spacetenna) directs the high power beam so that it focuses on the ground-based receiving antenna (rectenna). A combination of analysis and computerized simulation was conducted to determine the far field performance of the reference distribution system, and the beam forming and microwave power generating systems