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Higher levels of renewable electricity generation increase uncertainty inpower system operation. To ensure secure system operation, new tools thataccount for this uncertainty are required. In this paper, we formulate achance-constrained AC optimal power flow problem, which guarantees thatgeneration, power flows and voltages remain within their bounds with apre-defined probability. We then propose an accurate, yet tractable analyticalreformulation of the chance constraints. The reformulation maintains the full,non-linear AC power flow equations for the forecasted operating point, andmodels the impact of uncertainty through a linearization around this point. Wediscuss different solution algorithms, including one-shot optimization with andwithout recourse, and an iterative algorithm which enables scalableimplementations. We further discuss how more general chance constraintreformulations can be incorporated within the iterative solution algorithm. Ina case study based on four different IEEE systems, we compare the performanceof the solution algorithms, and demonstrate scalability of the iterativescheme. We further show that the analytical reformulation accurately andefficiently enforces chance constraints in both in- and out-of-sample tests,and that the analytical approach outperforms two alternative, sample basedchance constraint reformulations.

Chance-Constrained AC Optimal Power Flow: Reformulations and Efficient Algorithms