Distributed Network Synchronization: The Internet And Electric Power Grids
Synchronization is a fundamental requirement of most networked engineering applications. It enables the necessary coordination among agents required to implement several communication systems as well as network protocols. Despite the great recent advances in understanding synchronization, a complete synchronization theory is yet to be developed. This thesis presents a systematic study of synchronization on distributed systems that covers theoretical guarantees for synchronization, performance analysis and optimization, as well as design and implementation of algorithms. We first present several theoretical results that deepen the understanding of how coupling, delay and topology affect the behavior of a system of coupled oscillators. We obtain a sufficient condition that can be used to check limit cycle stability, and use it to characterize a family of coupling functions guaranteeing convergence to in-phase synchronization (phase consensus). The effect of heterogeneous delay is then investigated by developing a new framework that unveils the dependence of the orbit's stability on the delay distribution. Finally, we consider the effect of frequency heterogeneity. While coupled oscillators with heterogeneous frequency cannot achieve phase consensus, we show that a second order version of the system can achieve synchronization for arbitrary natural frequencies and we relate the limiting frequency of the system to the harmonic mean of the natural frequencies. Based on the insight provided by our theoretical results, we then focus on more practical aspects of synchronization in two particular areas: information networks and power networks. Within information networks, we examine the synchronization of computer clocks connected via a data network and propose a discrete algorithm to synchronize them. Unlike current solutions, which either estimate and compensate the frequency difference (skew) among clocks or introduce offset corrections that can generate jitter and possibly even backward jumps, this algorithm achieves synchronization without any of these problems. We present a detailed convergence analysis together with a characterization of the parameter values that guarantee convergence. We then study and optimize the effect of noisy measurements and clock wander on the system performance using a parameter dependent H2 norm. In particular, we show that the frequency of the system drifts away from its theoretical value in the absence of a leader. We implement the algorithm on a cluster of IBM BladeCenter servers running Linux and we experimentally verify that our algorithm outperforms the well-established solution. We also show that the optimal parameter values depend on the network conditions and topology. Finally, we study synchronization on power networks. By relating the dynamics of power networks to the dynamics of coupled oscillators, we can gain insight into how different network parameters affect performance. We show that the rate of convergence of networks is related to the algebraic connectivity of a state dependent Laplacian which varies with the network power scheduling and line impedances. This provides a novel method to change the voltage stability margins by updating the power scheduling or line impedances. Unfortunately, there exists a decoupling between the market clearing procedure used to dispatch power and the security analysis of the network, that prevents the direct use of this solution. Furthermore, focusing on voltage stability may generate other types of instabilities such as larger transient oscillations. This motivates the use of a unifying stability measure that can minimize oscillations or maximize voltage stability margins, and can be readily combined with current dispatch mechanisms generating a dynamics-aware optimal power flow formulation.
Chiang, Hsiao-Dong; Tong, Lang; Strogatz, Steven H
Ph. D., Electrical Engineering
Doctor of Philosophy
dissertation or thesis