Tight and Compact Models for Power Systems Operation.

Abstract

Power systems are among the most complex and colossal engineering structures in modern society, whose operation implies a challenge due to the coordination of multiple generating units to ensure a safe and dependable energy supply. In the last decades, significant changes have occurred in power systems globally with the purpose of transitioning to sustainable systems, which has brought about new challenges in their operation. In this context, this thesis tackles two of the most significant problems in power system operations, namely, the unit commitment (UC) and the optimal power flow (OPF). Both UC and OPF constitute optimization problems that pose considerable computational challenges. Firstly, UC requires the use of binary variables to model the on/off state of generating units, resulting in a combinatorial decision-making process that incurs a significant computational burden. Furthermore, addressing network constraints escalates the complexity of attaining an optimal solution. Leveraging the fact that most transmission lines are oversized in today's power systems, this thesis introduces a cost-driven optimization approach aimed at eliminating superfluous network-constraints, leading to a notable reduction in the computational burden associated with UC. Secondly, OPF problems often involve the incorporation of stochastic factors, demanding a sophisticated modeling approach to capture their impact. In line with a current trend, we resort to the joint chance-constrained OPF model that improves the power systems operation disregarding system's security in low probable, high impact uncertainty realizations. Without a finite, tractable reformulation, we use the sample average approximation which produces a mixed-integer problem cursed by big-Ms. To solve it efficiently, in this thesis, we propose a novel methodology based on a tightening-and-screening procedure and valid inequalities.