Branch Flow Model: Relaxations and Convexification—Part I

We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks…

• NS
  National Science Foundation

  Awards: 0911041, CNS 0911041
• CS
  Cisco Systems
• CI
  California Institute of Technology
• RS
  Resnick Sustainability Institute for Science, Energy and Sustainability, California Institute of Technology
• NS
  National Science Council

  Awards: NSC 101-3113-P-008-001, 101-3113-P-008-001
• OF
  Okawa Foundation for Information and Telecommunications
• AR
  Advanced Research Projects Agency - Energy

  Award: DE-AR0000226
• AR
  Advanced Research Projects Agency