Synchronization of Multi-Agent Systems with Microgrid Applications

Many social and engineering systems in the real world can be effectively modeled as multi-agent systems (MASs). A graph representation is used where nodes represent the states of individual entities, and edges signify the interactions between them. Notable examples include power grids, transportation networks, and the Internet. With the rise of large-scale infrastructures and advancements in computational power, MASs have garnered significant scholarly interest over the past few decades. Among various network properties, synchronization is a critical dynamic behavior frequently observed in nature, such as in neuronal network interactions and animal migrations. Furthermore, synchronization controllers are increasingly utilized in microgrid management. Hence, this thesis aims to investigate the role of synchronization in MASs and its application in the regulation of real-world microgrids. The work in this thesis can be broadly divided into four parts, which are summarized below. Initially, this study investigates the pinning synchronization problem in MASs with periodic switching topologies. Unlike previous research, the findings in this work demonstrate that synchronization can be achieved without requiring each individual topology to contain a spanning tree, instead the only requirement is that their combined graph has a spanning tree. The synchronization conditions of MASs are examined through the construction of a Lyapunov function and the application of averaging theory. An unmanned aerial vehicle (UAV) system is utilized as a practical example to validate these findings. The numerical simulations are proposed to study the influence of switching topology on the stability threshold of the switching period through numerical simulations. Based on the simulations, two observation conclusions are obtained, which are beneficial for the pinning control design. The second part of this study addresses the synchronization of MASs with nonlinear state dynamics. In particular, the Van der Pol oscillator is taken as an example. Due to the existence of a limit cycle in the Van der Pol oscillator, the synchronization issue is transformed into a local stability analysis of the error dynamic system near the limit cycle. The necessary and sufficient conditions that guarantee convergence are derived by examining the state transition matrix over one period of the limit cycle. Simulations are then detailed that verify the theoretical finding. In the third part, the focus is on identifying the most influential driver nodes to ensure the fastest synchronization speed in pinning control of MASs. A methodology is developed to determine the most effective pinning nodes under time-varying topologies. Firstly, synchronization conditions for MASs under pinning control are provided. Then a method is proposed to identify the optimal driver node that achieves the fastest synchronization in periodic switching topologies, demonstrating that the selection of these nodes can be independent of the system matrix under certain conditions. A method is introduced to estimate the switching period threshold. This approach ensures that the best driver nodes remain consistent with the one in the averaged system. Numerical simulations validate the practicality of these approaches. In the final part, this study addresses the challenge of improving control performance in islanded microgrids with switching communication networks by identifying the most influential distributed generator set. A focus is given to improve frequency regulation and active power sharing performance by pinning a set of distributed generators (DGs). To enhance the microgrid’s dynamic response under limited control resources, a method is introduced to determine the pinning DG set that ensures the fastest synchronization speed. This study further evaluates the influence of the network switching period on the DGs set selection, proposing a threshold to maintain the overall system performance. The developed methodology is validated through hardware-in-the-loop simulations on a modified IEEE 34-bus system, confirming its effectiveness in improving microgrid control performance. The findings of this thesis offer theoretical insights and practical contributions to the synchronization control of MASs, particularly in addressing pinning control strategies under periodic switching topologies and nonlinear dynamics. By demonstrating that synchronization can be achieved without requiring individual topologies to contain a spanning tree, this research relaxes conventional constraints, broadening the applicability of synchronization strategies. Additionally, the identification of optimal driver nodes for synchronization and their application to microgrid regulation presents a novel approach to improving the control efficiency in real-world power systems. The developed methodologies enhance the performance of islanded microgrids and contribute to the advancement of resilient and adaptive energy networks.<p></p>