Intertemporal uncertainty management in gas-electric energy systems using stochastic finite volumes

The reliance of power systems on gas-fired generators that run on timely delivery of natural gas compels new methods for coordinating electricity markets and gas pipeline operations. Concurrently, the growth in power generation by intermittent and uncontrollable renewable energy sources increases uncertainty in spatiotemporal electricity loads that propagates to interconnected pipeline systems. This has been addressed by day-ahead uncertainty management frameworks, including a joint optimization problem with chance constraints for optimal power flow and robust optimization to handle interval uncertainty in pipeline scheduling. While that formulation is tractable and ensures feasibility of the integrated system with high probability, it results in highly conservative pipeline flow scheduling. We propose a two-stage formulation where a stochastic finite volume representation for nonlinear gas flow with uncertain boundary conditions is used to manage intertemporal uncertainties for a pipeline that supplies fuel to peaking plants that provide operating reserves to an electricity market. This allows calibration of power production and reserves together with pipeline flow schedules with probabilistic guarantees using chance constraints for both networks. We describe chance-constrained formulations for power and gas networks and demonstrate the workflow using 3-bus, 1-pipe and 24-bus, 24-pipe gas-electric network cases.