This dissertation contains an examination of the problem of reconfiguration for restoration in critical infrastructure systems, with regard for the prioritization of those systems and the relationships between them. The complexity of the reconfiguration problem is demonstrated, and previous efforts to present solutions to the problem are discussed. This work provides a number of methods by which reconfiguration for restoration of an arbitrary number of prioritized interdependent critical infrastructure systems can be achieved. A method of modeling systems called Graph Trace Analysis is used to enable generic operation on various system types, and a notation for writing algorithms with Graph Trace analysis models is presented. The algorithms described are compared with each other and with prior work when run on a model of actual electrical distribution systems. They operate in a greedy fashion, attempting to restore loads in decreasing priority order. The described algorithms are also run on example models to demonstrate the ability to reconfigure interdependent infrastructure systems and systems which do not operate radially. / Ph. D.

Since the advent of the computer in the late 1950s, scientists and engineers have pushed the limits of the computing power available to them to solve physical problems via computational simulations. Early computer languages evaluated program logic in a sequential manner, thereby forcing the designer to think of the problem solution in terms of a sequential process. Object-oriented analysis and design have introduced new concepts for solving systems of engineering problems. The term object-oriented was first introduced by Alan Kay [1] in the late 1960s; however, mainstream incorporation of object-oriented programming did not occur until the mid- to late 1990s. The principles and methods underlying object-oriented programming center around objects that communicate with one another and work together to model the physical system. Program functions and data are grouped together to represent the objects. This dissertation extends object-oriented modeling concepts to model algorithms in a generic manner for solving interconnected, multi-domain problems. This work is based on an extension of Graph Trace Analysis (GTA) which was originally developed in the 1990's for power distribution system design. Because of GTA's ability to combine and restructure analysis methodologies from a variety of problem domains, it is now being used for integrated power distribution and transmission system design, operations and control. Over the last few years research has begun to formalize GTA into a multidiscipline approach that uses generic algorithms and a common model-based analysis framework. This dissertation provides an overview of the concepts used in GTA, and then discusses the main problems and potential generic algorithm based solutions associated with design and control of interdependent reconfigurable systems. These include: • Decoupling analysis into distinct component and system level equations. • Using iterator based topology management and algorithms instead of matrices. • Using composition to implement polymorphism and simplify data management. • Using dependency components to structure analysis across different systems types. • Defining component level equations for power, gas and fluid systems in terms of across and though variables. This dissertation presents a methodology for solving interdependent, multi-domain networks with generic algorithms. The methodology enables modeling of very large systems and the solution of the systems can be accomplished without the need for matrix solvers. The solution technique incorporates a binary search algorithm for accelerating the solution of looped systems. Introduction of generic algorithms enables the system solver to be written such that it is independent of the system type. Example fluid and electrical systems are solved to illustrate the generic nature of the approach. / Ph. D.

This work presents an alternative approach to power system computations, Graph Trace Analysis (GTA), and applies GTA to the power flow problem. A novel power flow algorithm is presented, where GTA traces are used to implement a modified Gauss-Seidel algorithm coupled with a continuation method. GTA is derived from the Generic Programming Paradigm of computer science. It uses topology iterators to move through components in a model and perform calculations. Two advantages that GTA brings are the separation of system equations from component equations and the ability to distribute calculations across processors. The implementation of KVL and KCL in GTA is described. The GTA based power flow algorithm is shown to solve IEEE standard transmission models, IEEE standard distribution models, and integrated transmission and distribution models (hybrid models) constructed from modifying IEEE standard models. The GTA power flow is shown to solve a set of robustness testing circuits, and solutions are compared with other power flow algorithms. This comparison illustrates convergence characteristics of different power flow algorithms in the presence of voltage stability concerns. It is also demonstrated that the GTA power flow solves integrated transmission and distribution system models. Advantages that GTA power flow bring are the ability to solve realistic, complex circuit models that pose problems to many traditional algorithms; the ability to solve circuits that are operating far from nominal conditions; and the ability to solve transmission and distribution networks together in the same model. / PHD / Power system engineers rely on modeling and analysis of the electric grid to ensure reliable delivery of that electricity to consumers. The algorithms currently being used for this purpose are designed to simulate either the high voltage transmission networks, or the low voltage distribution networks. The rapid growth solar photovoltaics (PV) based distributed generation over the last few years, which is expected to continue in the near future, has demanded a change in this modeling and analysis approach. As the penetration levels of distributed generation increase, accurate analysis of such an electric grid cannot be performed if either the distribution or the transmission network topology is neglected in the models. Integrated transmission and distribution system modeling and simulation, where transmission and distribution networks are modeled as one single unit, has become an important research area in recent years. This work contributes to this research area by presenting an algorithm that can be used to solve (find operating point) of integrated transmission and distribution system models. An algorithm that can find a solution of challenging network topologies and operating under severe conditions is also presented. Finally, an application of the algorithm is discussed where the impact of solar PV-based distributed generation on voltage stability limits of the electric grid is studied by using an integrated transmission and distribution system model. The dissertation shows that by solving integrated transmission and distribution system models using this algorithm, insights about the impact of solar PV-based distributed generation on the stability limits of the electric grid can be obtained, which the transmission only or distribution only models cannot provide.

Solar PV-based distributed generation has increased significantly over the last few years, and the rapid growth is expected to continue in the foreseeable future. As the penetration levels of distributed generation increase, power systems will become increasingly decentralized with bi-directional flow of electricity between the transmission and distribution networks. To manage such decentralized power systems, planners and operators need models that accurately reflect the structure of, and interactions between the transmission and distribution networks. Moreover, algorithms that can simulate the steady state and dynamics of power systems using these models are also needed. In this context, integrated transmission and distribution system modeling and simulation has become an important research area in recent years, and the primary focus so far has been on studying the steady state response of power systems using integrated transmission and distribution system models. The primary objective of this dissertation is to develop an analysis approach and a program that can simulate the dynamics of three phase, integrated transmission and distribution system models, and use the program to demonstrate the advantages of evaluating the impact of solar PV-based distributed generation on power systems dynamics using such models. To realize this objective, a new dynamic simulation analysis approach is presented, the implementation of the approach in a program is discussed, and verification studies are presented to demonstrate the accuracy of the program. A new dynamic model for small solar PV-based distributed generation is also investigated. This model can interface with unbalanced networks and change its real power output according to the incident solar irradiation. Finally, application of the dynamic simulation program for evaluating the impact of solar PV units using an integrated transmission and distribution system model is discussed. The dissertation presents a new approach for studying the impact of solar PV-based distributed generation on power systems dynamics, and demonstrates that the solar PV impact studies performed using the program and integrated transmission and distribution system models provide insights about the dynamic response of power systems that cannot be obtained using traditional dynamic simulation approaches that rely on transmission only models. / Ph. D. / To ensure that electricity is delivered to consumers in a reliable manner, power system planners and operators rely on computer-based modeling and analysis of the electric grid. The software currently being used for this purpose are designed to simulate either the high voltage transmission networks, or the low voltage distribution networks. Till now these software have worked well as the electricity flow in the electric grid is largely unidirectional, from the transmission network to the distribution network. Neglecting the distribution network topology in transmission network models or vice-versa in such a structure of the electric grid does not introduce significant calculation errors. However, the rapid growth of consumer-owned and operated solar photovoltaics (PV) based distributed generation over the last few years, which is expected to continue in the foreseeable future, has necessitated a rethink of this modeling and analysis paradigm. As the penetration levels of distributed generation increase, the electric grid will become increasingly decentralized and there will be bi-directional flow of electricity between the transmission and distribution networks. Accurate analysis of such a decentralized electric grid cannot be performed if either the distribution or the transmission network topology is neglected in the models. Integrated transmission and distribution system modeling and simulation, where transmission and distribution networks are modeled as one single unit, has, therefore, become an important research area in recent years. This dissertation makes a contribution to this research area by presenting an analysis approach and a program that can be used to simulate the dynamics (time varying behavior of the electric grid when subjected to disturbances such as short-circuits) of integrated transmission and distribution system models. A dynamic model of solar PV-based distributed generation that can be used to simulate their behavior during dynamic simulations is also investigated. Finally, an application of the program is discussed where the impact of solar PV-based distributed generation on the dynamics of the electric grid is studied by using the solar PV model and an integrated transmission and distribution system model. The dissertation shows that by simulating integrated transmission and distribution system models using the dynamic simulation program, insights about the impact of solar PV-based distributed generation on the dynamics of the electric grid can be obtained, which the transmission only models cannot provide.