  Power systems are shifted from conventional bulk generation toward renewable
generation. This trend leads to the frequency security problem due to the
decline of system inertia. On the other hand, natural gas-fired units are
frequently scheduled to provide operational flexibility due to their fast
adjustment ability. The interdependence between power and natural gas systems
is thus intensified. In this paper, we study the frequency constrained
scheduling problem from the perspective of an integrated electricity-gas system
under variable wind power. We propose a distributionally robust (DR) chance
constrained optimization model to co-optimize the unit commitment and virtual
inertia provision from wind farm systems. This model incorporates both
frequency constraints and natural gas system (NGS) operational constraints and
addresses the wind power uncertainty by designing DR joint chance constraints.
We show that this model admits a mixed-integer second-order cone programming.
Case studies demonstrate that the proposed approach can provide a highly
reliable and computationally efficient solution and show the importance of
incorporating NGS operational constraints in the frequency constrained
scheduling problem.
