2018/09/11 by Kyri Baker, Baker, Kyri, Andrey Bernstein +1 · 2 citations
Decision Sciences · Engineering · #FOS: Mathematics #Fault Detection and Control Systems #Optimal Power Flow Distribution #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.1809.04153
openalex publication_date 2018/09/11 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
This paper considers distribution systems with a high penetration of\ndistributed, renewable generation and addresses the problem of incorporating\nthe associated uncertainty into the optimal operation of these networks. Joint\nchance constraints, which satisfy multiple constraints simultaneously with a\nprescribed probability, are one way to incorporate uncertainty across sets of\nconstraints, leading to a chance-constrained optimal power flow problem.\nDeparting from the computationally-heavy scenario-based approaches or\napproximations that transform the joint constraint into conservative\ndeterministic constraints, this paper develops a scalable, data-driven approach\nwhich learns operational trends in a power network, eliminates zero-probability\nevents (e.g., inactive constraints), and accurately and efficiently\napproximates bounds on the joint chance constraint iteratively. In particular,\nthe proposed framework improves upon the classic methods based on the union\nbound (or Boole's inequality) by generating a much less conservative set of\nsingle chance constraints that also guarantees the satisfaction of the original\njoint constraint. The proposed framework is evaluated numerically using the\nIEEE 37-node test feeder, focusing on the problem of voltage regulation in\ndistribution grids.\n