  As a natural approach to modeling system safety conditions, chance constraint
(CC) seeks to satisfy a set of uncertain inequalities individually or jointly
with high probability. Although a joint CC offers stronger reliability
certificate, it is oftentimes much more challenging to compute than individual
CCs. Motivated by the application of optimal power flow, we study a special
joint CC, named two-sided CC. We model the uncertain parameters through a
Wasserstein ball centered at a Gaussian distribution and derive a hierarchy of
conservative approximations based on second-order conic constraints, which can
be efficiently computed by off-the-shelf commercial solvers. In addition, we
show the asymptotic consistency of these approximations and derive their
approximation guarantee when only a finite hierarchy is adopted. We demonstrate
the out-of-sample performance and scalability of the proposed model and
approximations in a case study based on the IEEE 118-bus and 3120-bus systems.
