  Higher shares of electricity generation from renewable energy sources and
market liberalization is increasing uncertainty in power systems operation. At
the same time, operation is becoming more flexible with improved control
systems and new technology such as phase shifting transformers (PSTs) and high
voltage direct current connections (HVDC). Previous studies have shown that the
use of corrective control in response to outages contributes to a reduction in
operating cost, while maintaining N-1 security. In this work, we propose a
method to extend the use of corrective control of PSTs and HVDCs to react to
uncertainty. We characterize the uncertainty as continuous random variables,
and define the corrective control actions through affine control policies. This
allows us to efficiently model control reactions to a large number of
uncertainty sources. The control policies are then included in a chance
constrained optimal power flow formulation, which guarantees that the system
constraints are enforced with a desired probability. By applying an analytical
reformulation of the chance constraints, we obtain a second-order cone problem
for which we develop an efficient solution algorithm. In a case study for the
IEEE 118 bus system, we show that corrective control for uncertainty leads to a
decrease in operational cost, while maintaining system security. Further, we
demonstrate the scalability of the method by solving the problem for the IEEE
300 bus and the Polish system test cases.
