  This paper considers distribution systems with a high penetration of
distributed, renewable generation and addresses the problem of incorporating
the associated uncertainty into the optimal operation of these networks. Joint
chance constraints, which satisfy multiple constraints simultaneously with a
prescribed probability, are one way to incorporate uncertainty across sets of
constraints, leading to a chance-constrained optimal power flow problem.
Departing from the computationally-heavy scenario-based approaches or
approximations that transform the joint constraint into conservative
deterministic constraints, this paper develops a scalable, data-driven approach
which learns operational trends in a power network, eliminates zero-probability
events (e.g., inactive constraints), and accurately and efficiently
approximates bounds on the joint chance constraint iteratively. In particular,
the proposed framework improves upon the classic methods based on the union
bound (or Boole's inequality) by generating a much less conservative set of
single chance constraints that also guarantees the satisfaction of the original
joint constraint. The proposed framework is evaluated numerically using the
IEEE 37-node test feeder, focusing on the problem of voltage regulation in
distribution grids.
