Optimal Control of Fluid Transport Networks

Wednesday, November 11, 2020 - 10:40am - 11:25am
Anatoly Zlotnik (Los Alamos National Laboratory)
A fundamental application for optimal control of physical flows on networks is the operation of large-scale natural gas transmission pipelines. A control system model has been developed for the distributed dynamics of compressible gas flow through large-scale pipeline networks with time-varying injections, withdrawals, and control actions of compressors and regulators. The gas dynamics PDE equations over the pipelines, together with boundary conditions at junctions, are reducible using lumped elements to a sparse nonlinear ODE system with compact expression in graph theoretic notation.

This system is a consistent discretization of the PDE equations for gas flow that can be used to represent the dynamic constraints for optimal control problems for pipeline systems with known time-varying withdrawals and injections and gas pressure limits throughout the network. The model has also been extended for use in state and parameter estimation, and updated to include a reduced order model of the dynamics of subsurface storage facilities. Certain properties that facilitate tractable optimal control under uncertainty, including monotonicity and friction-dominated approximation, have been shown to be applicable under certain conditions. A number of validation and verification exercises have shown the approach to effectively represent the dynamics in the regime of interest. This talk will present an optimal control formulation for intra-day scheduling of large-scale pipeline operations, and discuss open theoretical and practical problems.