  As the share of renewables in the grid increases, the operation of power
systems becomes more challenging. The present paper proposes a method to
formulate and solve chance-constrained optimal power flow while explicitly
considering the full nonlinear AC power flow equations and stochastic
uncertainties. We use polynomial chaos expansion to model the effects of
arbitrary uncertainties of finite variance, which enables to predict and
optimize the system state for a range of operating conditions. We apply chance
constraints to limit the probability of violations of inequality constraints.
Our method incorporates a more detailed and a more flexible description of both
the controllable variables and the resulting system state than previous
methods. Two case studies highlight the efficacy of the method, with a focus on
satisfaction of the AC power flow equations and on the accurate computation of
moments of all random variables.
