The objective of the research presented in this dissertation is to push forward the boundaries of the types of power systems optimization problems that can be solved, especially when fast solutions are required for online decision making.

There is no shortage of complex optimization problems in the area of Power Systems. The inherent physics of power flow through an electric power system, as well as the need to model networks that encompass anything from a local three-phase distribution feeder to a country's entire transmission system make some of these optimization problems very computationally challenging. Furthermore, the answers to some of these problems may also need to be computed quickly during real-time operation or under other time constraints, thereby adding additional difficulties to already complicated problems. These are the challenges that motivate the work presented in this document. This dissertation  proposes, investigates, and validates offline computing strategies to reduce the size and complexity of power system optimization problems used online. The objective of the proposed strategies is to leverage the increased computational power usually available when solution time is not critical, to come up with tailor-made reduced, simplified, or surrogate models that can produce fast, yet accurate results. These techniques are proposed and then applied to different challenging problems that serve as case studies and validation.

To that end, this dissertation presents a non-convex constraint screening methodology, a single-level reformulation strategy for bilevel optimization problems using surrogate neural networks, and an application of a linearizing approach to represent large three-phase unbalanced distribution networks. Furthermore, the techniques presented here are used to solve modern day complex problems, showcasing possible applications including the ACOPF problem, the N-k Interdiction problem, and an Emergency Electric Vehicle Charging problem.