High-performance interior point methods: application to power grid problems

A software library for the solution of large-scale structured nonconvex optimization problems is presented in this work, with the purpose of accelerating the solution on single- core, multicore, or massively parallel high-performance distributed memory computing infrastructures. A large class of industrial and engineering problems possesses a particular structure, motivating the development of structure exploiting interior point methods. Interior point methods are among the most popular techniques for large-scale nonlinear optimization and their efficiency has attracted a lot of attention in recent years. Since the overall performance of interior point methods relies heavily on scalable sparse linear algebra solvers, this work thoroughly analyzes cutting-edge research based on the sparse linear algebra and structure exploiting methods presented over recent years, and further advances the performance by inspecting the structure of the underlying linear systems, resulting in an additional computational time and memory savings. The primal-dual interior point framework is applied for the solution of optimal power flow problems, a class of optimization problems attracting increasing attention in power system research, operations, and planning. Optimal power flow involves large-scale nonconvex optimization problems with a number of variables and constraints ranging up to hundreds of millions depending on the grid resolution and specific problem formulation. 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 to 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 of the structure exploiting approach is demonstrated