  Gas-fired generators, with their ability to quickly ramp up and down their
electricity production, play an important role in managing renewable energy
variability. However, these changes in electricity production translate into
variability in the consumption of natural gas, and propagate uncertainty from
the electric grid to the natural gas system. To ensure that both systems are
operating safely, there is an increasing need for coordination and uncertainty
management among the electricity and gas networks. A challenging aspect of this
coordination is the consideration of natural gas dynamics, which play an
important role at the time scale of interest, but give rise to a set of
non-linear and non-convex equations that are hard to optimize over even in the
deterministic case. Many conventional methods for stochastic optimization
cannot be used because they either incorporate a large number of scenarios
directly or require the underlying problem to be convex. To address these
challenges, we propose using a Stochastic Hybrid Approximation algorithm to
more efficiently solve these problems and investigate several different
variants of this algorithm. In a case study, we demonstrate that the proposed
technique is able to quickly obtain high quality solutions and outperforms
existing benchmarks such as Generalized Benders Decomposition. We demonstrate
that coordinated uncertainty management that accounts for the gas system can
significantly reduce both electric and gas system load shed in stressed
conditions.
