Optimization of stationary expansion planning and transient network control by mixed-integer nonlinear programming

Nowadays, transmission system operators of energy networks (TSO) have to enable secure energy supply even under challenging transport situations and increasing demand. Hence, they seek a stable network control and regularly expand the capacity of their networks. The challenging questions arise of how to obtain safe network operations for fixed network infrastructure and how to extend the network capacity at minimum cost. In this thesis, we formulate these two questions as mathematical optimization problems and present solution approaches that scale to real-world instances of size and complexity encountered in practice. Model formulations of both problems are located in the field of Mixed-Integer Nonlinear Programming (MINLP). However, global state-of-the-art MINLP solvers are not mature enough to solve or even find primal solutions on large-scale real-world instances since the resulting degree of nonconvexity and nonlinearity pose principal difficulties. For this reason, we develop novel model formulations and optimization algorithms that significantly improve the performance of the solver SCIP. The first part of the thesis focuses on the optimization of stationary network expansions by building new pipelines in parallel to existing ones, so-called looping. Based upon a model reduction approach for multiple loops, we introduce new models for the discrete and split-pipe looping paradigm and compare them with existing models in the literature, both theoretically and empirically. It turns out that our novel split-pipe model performs best in several respects: running time, number of instances solved, and cost savings by up to 7000% over the discrete models. To further improve the performance, we analytically calculate the convex envelope of the nonconvex, nonlinear constraint function f(x,y) = y sgn(x) |x|^a, which models the physical effect of the expansion. In this way, we considerably tighten the convex relaxation of the network expansion problem. The resulting implementation significantly reduces the average solving time by up to 58% on difficult instances. The second part of the thesis deals with the optimization of operations in transient large-scale networks. The problem consists of making day-ahead control decisions that enable feasible energy transport. To this end, we propose a specially-tailored solution approach. First, we aggregate network structures, which TSOs typically consider as of minor importance for the decision-making process. Then, we apply model reformulations that exploit the disjunctive nature of certain network structures and strengthen the linear relaxation. Finally, we present a primal heuristic based on time decomposition. The heuristic solves MINLP sub-models to acquire transport decisions for single time steps. We equip the heuristic with a mechanism that enables moving forward and backward on the time scale to compensate for possibly disadvantageous decisions taken at earlier stages. An extensive computational study shows that our approach reliably generates solutions for 96% to 100% of the instances for three different large-scale real-world networks. Parts of the developed methods are already in use by our industrial cooperation partner Open Grid Europe GmbH to facilitate the respective decision-making processes.

Author dc:creator

• Lenz, Ralf

Advisor dc:contributor.advisor

• Koch, Thorsten

Licence dc:rights.uri

• https://creativecommons.org/licenses/by/4.0/

Language dc:language.iso

en

Identifier URI

http://dx.doi.org/10.14279/depositonce-12765

OAI identifier oai:identifier

oai:depositonce.tu-berlin.de:11303/13992