  The growing penetration of distributed energy resources (DERs) is leading to
continually changing operating conditions, which need to be managed efficiently
by distribution grid operators. The intermittent nature of DERs such as solar
photovoltaic (PV) systems as well as load forecasting errors not only increase
uncertainty in the grid, but also pose significant power quality challenges
such as voltage unbalance and voltage magnitude violations. This paper
leverages a chance-constrained optimization approach to reduce the impact of
uncertainty on distribution grid operation. We first present the
chance-constrained optimal power flow (CC-OPF) problem for distribution grids
and discuss a reformulation based on constraint tightening that does not
require any approximations or relaxations of the three-phase AC power flow
equations. We then propose two iterative solution algorithms capable of
efficiently solving the reformulation. In the case studies, the performance of
both algorithms is analyzed by running simulations on the IEEE 13-bus test
feeder using real PV and load measurement data. The simulation results indicate
that both methods are able to enforce the chance constraints in in- and
out-of-sample evaluations.

Systems and Control;Systems and Control