A Distributed Linear Programming Model in a Smart Grid

Advances in computing and communication have resulted in large-scale distributed environments in recent years. They are capable of storing large volumes of data and, often, have multiple compute nodes. However, the inherent heterogeneity of data components, the dynamic nature of distributed systems, the need for information synchronization and data fusion over a network, and security and access-control issues makes the problem of resource management and monitoring a tremendous challenge in the context of a Smart grid. Unfortunately, the concept of cloud computing and the deployment of distributed algorithms have been overlooked in the electric grid sector. In particular, centralized methods for managing resources and data may not be sufficient to monitor a complex electric grid. Most of the electric grid management that includes generation, transmission, and distribution is, by and large, managed at a centralized control. In this dissertation, I present a distributed algorithm for resource management which builds on the traditional simplex algorithm used for solving large-scale linear optimization problems. The distributed algorithm is exact, meaning its results are identical if run in a centralized setting. More specifically in this dissertation, I discuss a distributed decision model, where a large-scale electric grid is decomposed into many sub models that can support the resource assignment, communication, computation, and control functions necessary to provide robustness and to prevent incidents such as cascading blackouts. The key contribution of this dissertation is to design, develop, and test a resource-allocation process through a decomposition principle in a Smart grid. I have implemented and tested the Dantzig-Wolfe decomposition process in standard IEEE 14-bus and 30-bus systems. The dissertation provides details about how to formulate, implement, and test such an LP-based design to study the dynamic behavior and impact of an electrical network while considering its failure and repair rates. The computational benefits of the Dantzig-Wolfe approach to find an optimal solution and its applicability to IEEE bus systems are presented