High-performance interior point methods - Application to power grid problems

You are cordially invited to attend the PhD Dissertation Defense of Juraj Kardoš on Thursday March 26th, 2020 at 15:30.

Abstract:
Interior point methods are among the most popular techniques for large-scale nonlinear optimization. In recent years, their efficiency has attracted a lot of attention due to increasing demand for large-scale optimization in industry and engineering. Interior point methods rely on the Newton’s method for solving systems of nonlinear equations, where the linear system solution is the most computationally expensive task of an interior point iteration. A large class of industrial and engineering problems possesses a particular structure, motivating the development of structure-exploiting interior point methods. In this work a software library for the solution of large-scale structured nonconvex optimization problems is introduced, with the purpose of accelerating the solution for both, single-core or multicore execution and massively parallel high-performance distributed memory computing infrastructures. Particular emphasis is put on the underlying algorithms for the solution of the associated sparse linear systems obtained at each iteration from the linearization of the optimality conditions. The interior point framework is applied to a class of nonlinear optimization problems known as optimal power flow, which is one of the most important and widely studied constrained nonlinear optimal control problems, since it is a fundamental building block in power system research, planning and operation. Optimal power flow is a large-scale nonconvex optimization problem with up to hundreds of millions of variables and constraints. The robustness and reliability of interior point methods is investigated for different optimal power flow formulations for a wide range of realistic power grid networks. Furthermore, the object-oriented parallel and distributed scalable solver is implemented and applied for the solution of large-scale problems solved on a daily basis for the secure transmission and distribution of electricity in modern power grids. Similarly, an efficient algorithm is investigated for optimal power flow spanning long time horizons. Using computational studies from security-constrained and multiperiod optimal power flow problems, the robustness and scalability is demonstrated.

Dissertation Committee:
- Prof. Olaf Schenk, Università della Svizzera italiana, Switzerland (Research Advisor)
- Prof. Illia Horenko, Università della Svizzera italiana, Switzerland (Internal Member)
- Prof. Igor Pivkin, Università della Svizzera italiana, Switzerland (Internal Member)
- Prof. Petr Korba, Zurich University of Applied Sciences, Switzerland (External Member)
- Prof. Tomas Kozubek, Technical University of Ostrava, Czech Republic (External Member)
- Prof. Andreas Waechter, Northwestern University, USA (External Member)