  High Voltage Direct Current (HVDC) systems interconnect AC grids to increase
reliability, connect offshore wind generation, and enable coupling of
electricity markets. Considering the growing uncertainty in power infeed and
the complexity introduced by additional controls, robust decision support tools
are necessary. This paper proposes a chance constrained AC-OPF for AC and HVDC
grids, which considers wind uncertainty, fully utilizes HVDC control
capabilities, and uses the semidefinite relaxation of the AC-OPF. We consider a
joint chance constraint for both AC and HVDC systems, we introduce a piecewise
affine approximation to achieve tractability of the chance constraint, and we
allow corrective control policies for HVDC converters and generators to be
determined. An active loss penalty term in the objective function and a
systematic procedure to choose the penalty weights allow us to obtain
AC-feasible solutions. We introduce Benders decomposition to maintain
scalability. Using realistic forecast data, we demonstrate our approach on a
53-bus and a 214-bus AC-DC system, obtaining tight near-global optimality
guarantees. With a Monte Carlo analysis, we show that a chance constrained
DC-OPF leads to violations, whereas our proposed approach complies with the
joint chance constraint.
