  Natural gas-fired generation units can hedge against the volatility in the
uncertain renewable generation, which may occur during very short periods. It
is crucial to utilize models capable of correctly capturing the natural gas
network dynamics induced by the volatile demand of gas-fired units. The
Weymouth equation is commonly implemented in literature to avoid dealing with
the mathematical complications of solving the original governing differential
equations of the natural gas dynamics. However, it is shown in this paper that
this approach is not reliable in the short-term operation problem. Here, the
merit of the non-convex transient model is compared with the simplified
Weymouth equation, and the drawbacks of employing the Weymouth equation are
illustrated. The results demonstrate how changes in the natural gas demand are
met by adjustment in the pressure within pipelines rather than the output of
natural gas suppliers. This work presents a convex relaxation scheme for the
original non-linear and non-convex natural gas flow equations with dynamics,
utilizing a rank minimization approach to ensure the tightness. The proposed
method renders a computationally efficient framework that can accurately solve
the non-convex non-linear gas operation problem and accurately capture its
dynamics. Also, the results suggest that the proposed model improves the
solution optimality and solution time compared to the original non-linear
non-convex model. Finally, the scalability of the proposed approach is verified
in the case study.
