Tight and Compact Models for Power Systems Operation

• Autores: Álvaro Porras Cabrera
• Directores de la Tesis: Salvador Pineda Morente (dir. tes.), Juan Miguel Morales Gonzalez (dir. tes.)
• Lectura: En la Universidad de Málaga ( España ) en 2023
• Idioma: español
• Tribunal Calificador de la Tesis: Hrvoje Pandzic (presid.), Juan Pérez Ruiz (secret.), Miguel Carrion Ruiz-Peinado (voc.)
• Programa de doctorado: Programa de Doctorado en Sistemas de Energía Eléctrica por la Universidad de Málaga; la Universidad de Sevilla; la Universidad del País Vasco/Euskal Herriko Unibertsitatea y la Universidad Politécnica de Catalunya
• Materias:
  • Matemáticas
    • Investigación operativa
      • Programación entera
    • Probabilidad
      • Procesos estocásticos
  • Ciencias tecnológicas
    • Ingeniería y tecnología eléctricas
      • Aplicaciones eléctricas
      • Transmisión y distribución
• Enlaces
  • Tesis en acceso abierto en:  TESEO  RIUMA 
• Resumen

  • 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.

    Most of the existing joint chance-constrained OPF models provide a limited vision of power systems operation, since, under extreme circumstances, these approaches may leave the system vulnerable. Otherwise, ensuring the system's security for the whole spectrum of uncertainty realizations would result in excessive operating costs. To circumvent such a caveat, we introduce a novel stochastic OPF model that integrates both automatic and manual reserves.