Distributed Mesh-to-Tree Graph Transformation for Managing Flows in Electrical Networks

This thesis introduces a graph-theoretic framework for a multi-layered transformation of a meshed electrical network into a spanning tree and its potential applications. The spanning tree representation simplifies the original network and contains the minimum information necessary for restoring physical laws when returning to the meshed network representation. The distributed, multi-layered nature of the framework provides a valuable mechanism for zooming in and zooming out in order to represent the desired level of detail.;The proposed applications of this framework can be categorized into algorithms for flow analysis and monitoring, and algorithms for the optimization of flows.;The applications of the proposed framework to linearized real power flow analysis include the modeling and tracing of bilateral transactions with specified contract paths; representation and management of the corresponding loop flows; and fast distributed flow computations and monitoring. Our distributed power flow algorithms can be used for efficient computation of the equipment failure (contingencies) effects in large electric power networks. Additionally, these distributed algorithms can be implemented to include secure information exchange protocols for protecting proprietary data.;The performance of our proposed algorithms strongly depends on the chosen network clustering into areas. Two aspects are considered in this thesis: computational complexity for improving the computational performance of our algorithms, and communication complexity regarding the amount of information that needs to be exchanged.;Furthermore, the spanning tree representation can be used to formulate more efficient optimization algorithms due to its simplified network topology. More efficient Linear Programming (LP) flow optimization algorithms can be applied directly to the spanning tree. Additionally, the spanning tree enables the application of graph (not LP) optimization algorithms to electric (power) networks directly on the tree representation. Additionally, tracing information as part of the flow analysis can be used for loop flow management through various loop flow pricing mechanisms and/or reduction of loop flows through flow control.;In short, the proposed Mesh-to-Tree transformation for electrical networks opens major possibilities for multi-layered computing and control design. In this thesis, only some applications are explored. Many others would be good topics for future work. Particularly challenging would be the generalization of the proposed transformation to AC electric power networks.