Stochastic Hybrid Approximation for Uncertainty Management in Gas-Electric Systems

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.