Abstract: The goal of global optimisation is to find globally optimal solutions, avoiding local optima and other stationary points. It has a number of practical applications, and the aim of this thesis is to provide more efficient optimisation tools for energy systems planning and operation. Due to the ongoing increasing of complexity and decentralisation of power systems, the use of advanced mathematical techniques that produce reliable solutions becomes necessary. The task of developing such methods is complicated by the fact that most energy-related problems are non-convex due to the nonlinear Alternating Current Power Flow equations and the existence of discrete elements. We tackle this problem by improving convexification techniques and identifying generalised convexity properties that are sufficient for global optimality of stationary points.
Bio: Ksenia Bestuzheva is a PhD student in Computer Science at ANU and is affiliated with CSIRO/Data61. Her research focus is on global optimisation of problems with continuous and/or discrete non-convexities with applications in energy systems. Prior to studying at ANU, she received a Specialist degree (equivalent to combined Bachelor's and Master's degrees) in Applied Mathematics and Informatics from the State Management University, Moscow, Russia in 2014.