Convex Relaxations of Probabilistic AC Optimal Power Flow for Interconnected AC and HVDC Grids

High Voltage Direct Current (HVDC) lines and grids interconnect AC grids to increase reliability, facilitate integration of electricity markets and connect offshore wind generation. To address the growing uncertainty in the operation of such systems and fully utilize HVDC control capabilities, this work proposes a semidefinite relaxation of a chance constrained AC optimal power flow (OPF) for interconnected AC and HVDC grids, which can achieve zero relaxation gap and provide guarantees for (near-)global optimality. To achieve tractability of the joint chance constraint, a piecewise affine approximation and a combination of randomized and robust optimization is used. We include corrective control policies for HVDC converter active and reactive power, and generator active power and voltage. Using realistic day-ahead forecast data, we demonstrate the performance of our approach on two IEEE 24 bus systems interconnected with an HVDC grid and offshore wind generation, obtaining tight nearglobal optimality guarantees.