  We examine the convexity and tractability of the two-sided linear chance
constraint model under Gaussian uncertainty. We show that these constraints can
be applied directly to model a larger class of nonlinear chance constraints as
well as provide a reasonable approximation for a challenging class of quadratic
chance constraints of direct interest for applications in power systems. With a
view towards practical computations, we develop a second-order cone outer
approximation of the two-sided chance constraint with provably small
approximation error.
