Global optimization methods for optimal power flow and transmission switching problems in electric power systems
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Power engineering is concerned with the generation, transmission, and distribution of electricity over electric power network, which is arguably one of the largest engineering systems in the world. The size of electric utility industry exceeds billions of dollars and its utilization in a cost-effective manner while providing reliable accessibility is extremely important. Power system planning is a hierarchical decision making environment. In this thesis, we focus on two operational level optimization problems, namely the Optimal Power Flow Problem and the Optimal Transmission Switching Problem. The former is a nonlinear network problem and the latter is the network design version of the first one. Due to nonlinearity induced by alternating current power flow equations, these two optimization problems are nonconvex and require efficient global optimization methods. We make effective use of several different strategies to handle nonconvexity, including conic relaxations, envelopes, disjunctive extended formulations, cutting planes, variable bound tightening techniques and feasibility heuristics. Our approaches scale well to large power systems problems and provide provably good solutions in time compatible with the needs of the system operators.