Stochastic Control and Pricing for Natural Gas Networks

Multi-stage linear decision rules for stochastic control of natural gas networks with linepack

“…(1) for the deterministic (mean) gas extraction values. Then, according to [6], the following linear equation…”

“…Such a control task requires a multi-stage stochastic modeling of network state, i.e., optimizing the network state as a function of all prior uncertainty realizations at any given stage, which is computationally challenging [5]. This problem is thus typically limited to two subsequent stages [6] or enjoys overly-conservative robust optimization techniques that disregard the temporal evolution of the stochastic renewable generation process [7].…”

“…(1) We develop multi-stage policies for controllable network assets that invoke linepack flexibility to guide operations within a finite discrete control horizon. These policies are based on multi-stage linear decision rules [8] that model uncertain network state through random trajectories and produce control inputs to maintain those trajectories within technical limits, hence expanding a two-stage stochastic control horizon modeled in [6].…”

“…https://doi.org/ (2) We provide a multi-stage distributionally robust optimization problem and its second-order cone program (SOCP) reformulation to optimize control policies. We use the exact reformulation of double-sided distributionally robust chance constraints from [9] to reduce the conservatism of models in [4,6]. (3) We provide several applications for the proposed multi-stage control policies in the sequential system coordination setting, where power system dispatch is followed by the gas network optimization problem.…”

“…The costsaving potential of linepack storage in our setting amounts to 10.3% in expectation. (b) The proposed multi-stage control policies can be optimized to simultaneously minimize the variability (due to intermittency of renewable generation) and the variance (due to uncertainty) of the network state, thus improving on the variance-only control in [6]. (c) Recognizing the role of network effects, the proposed control policies are additionally co-optimized with the binary valve deployment to identify the optimal network topology, which limits spatio-temporal disturbance propagations within a control horizon.…”