Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Dr. A. P. Meliopoulos; Committee Member: Dr. David Taylor; Committee Member: Dr. Ronald Harley; Committee Member: Dr. Shijie Deng. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Call number: LD2668 .T4 1985 E34 / Master of Science

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

A load flow and contingency analysis program for secure design, planning and operation of power systems. Depending on the application either Newton-Raphson or Fast- Decoupled method is employed to solve the load flow. Fault analysis is done by Z bus method. Contingency analysis may be done following the load flow solution by Fast-Decoupled method. The program is also interfaced with a graphic system which displays a single line diagram of the system on the graphic screen along with relevant data and informs the operator of any change by flashing the faulted bus or the line outage.

This thesis contains contributions in three areas: the theory of generalized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geometric approach is used to advance the theory and tools used for studying generalized notions of derivatives for nonsmooth functions. These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions. A strong understanding of the subdifferential is essential for numerical optimization algorithms, which are developed and applied to nonsmooth problems in operations research, including non-convex problems. Finally, an optimization framework is applied to solve a problem in electric power systems involving a smart solar inverter and battery storage system providing energy and ancillary services to the grid.

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The present thesis, for the most part, is concerned with the application of continuous optimization to the secure-economic dispatching of thermal power plants. / The general concept of the continuous simulation of the optimum operation of power systems is introduced. This is the characterization of the solution trajectory of the underlying dispatching model as the loads vary along a forecasted trajectory, or as the system parameters continuously change. An efficient continuation algorithm is developed which characterizes the solution trajectory of a secure-economic dispatch model, given a piecewise linear trajectory of the bus loads, parameterized in terms of the system load. The algorithm considers piecewise quadratic generation cost functions, a DC load flow model, and the limits on generations and power flows in the normal and post transmission line outage states. The solution trajectory is provided in an analytic form over the entire loadability range of the system. Applications of the algorithms to systems with up to 118 buses show that it is fast, reliable, and well-suited for many applications in power system planning and operation. / The continuation algorithm, as the thesis describes, in essence applies the Incremental Loading procedure to the secure-economic dispatching. In this light, it can be viewed as a natural extension of the highly successful classical dispatching techniques such as Lambda Dispatching. A reexamination of the classical economic dispatching is presented early in the thesis. Highlights of this phase of the study include: generation scheduling with general (i.e., possibly non-convex) generation cost functions, an analytic study of the Valve Point Loading based on the general characterization of the valve loop based system incremental cost curve, an in-depth study of the system incremental cost in the context of the modified coordination equations, and a stochastic formulation and analysis of economic dispatching of regulating plants.