Optimization for operation of power systems with performance guarantee
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Day by day, electrical energy is getting more important than ever for the developed World. Its absence creates catastrophic financial consequences and also brings safety concerns for digital world. Although the reliable and stable energy supply is the main concern for power industry, the technological improvements must be aggregated into the system to meet increasing need of electricity. One of the most important properties of electrical energy as a commodity is its necessity to be consumed at the time of its generation. Therefore, operations of power systems deal with complex physical requirements that may need instantaneous actions for the system's safety. All those actions create a financial burden for the system that affects the society's life quality. The optimal economic dispatch of generation units therefore seeks the maximal social welfare while the power system parameters satisfy all required physical requirements. The study covered in this thesis explores particularly the valuation of transmission switching for power system operations. Transmission switching is one of the methods for power systems that promises a positive impact on maximizing social welfare. It is introduced as an idea to alter the power transmission assets that are always in use in today's power systems. The recent studies have shown that the changing the status of transmission assets (ON/OFF) rather than keeping them all in use can provide up to 9% financial savings. The size of the mathematical problem and the computational tardiness, however, are the challenges to overcome before implementing the method as a real-time application for power systems. In order to address these challenges separately, this thesis is divided into two parts. The first part includes a novel solution methodology and an algorithm to overcome the computational tardiness observed by early studies on the subject. The proposed algorithm includes a semi-definite relaxation of the original non-linear mathematical problem. Then, a method is introduced to identify the best candidate list of transmission lines. Finally, the advantage of parallel computation is discussed for the proposed solution method in order to reduce computational time to solve the problem. The second part of this thesis proposes a novel application of transmission switching in centralized transmission line maintenance scheduling. The reason lying behind this idea is to introduce the first attempt in related literature that applies the method of transmission switching into the real world power systems. In practice, transmission owners request approval from the Independent System Operator (ISO) to take down the transmission line for maintenance and they have to denote the day and time of the maintenance. However, in this study the theory of transmission switching method is applied to the maintenance scheduling problem in order to explore the benefits of the centralized scheduling at ISO level. The proposed problem formulation is the first attempt in related literature that incorporates both transmission line maintenance scheduling and unit commitment problems in to a single objective mathematical problem.