Computing Surrogates for Gas Network Simulation Using Model Order Reduction

State and Parameter Estimation for Natural Gas Pipeline Networks Using Transient State Data

“…We shall now establish the nodal balance equations that characterize the boundary conditions for the dynamics in Eq. (7). To that end, we define the densities and flows at edge domain boundaries bȳ…”

“…In this section, we develop a reduced order model that represents the dynamics of gas flow through a network using a synthesis of Eqs. (7), (10), (11), and (12). Specifically, we create a control system model using a lumped element approximation to characterize the dynamics for each edge in Eq.…”

“…This is done to provide additional structure to the dynamics in order to render the underlying approximation of the PDE constraints well-posed, as discussed in more detail in section II-B. In contrast to previous estimation approaches proposed in the literature on pipeline systems, which relied on linearization techniques [9], [19], [1], we approximate the system of PDEs using a new nonlinear control system model, the reduced network flow (RNF), derived from a model reduction of the gas network dynamics [7], [29], [30]. The resulting RNF is a system of implicit nonlinear differential algebraic equations (DAEs) with time-varying injections and compression as control inputs; time-varying withdrawals and Darcy-Wiesbach friction factor as the parameters; and density and mass flow rates as states.…”

Optimal Control for Scheduling and Pricing Intra-day Natural Gas Transport on Pipeline Networks

“…We apply the above optimization technique to formulate a rolling-horizon model predictive OCP for a gas pipeline auction market of the form (27). We consider the internal system density ρ and flow q to describe the system state x, and the compressor ratiosᾱ ij andᾱ ij for (i, j) ∈ C and the transfer node demands d m and supplies s m for m ∈ G are the controls u.…”

Dynamic Compressor Optimization in Natural Gas Pipeline Systems

“…Recently developed approaches to reduced order representation of PDE dynamics on graphs [36], and their extension to control system modeling [34,35], have enabled tractable representations of gas pipeline system dynamics. Such models are used to express constraints in dynamic optimization problems as well as to perform simulations of IVPs.…”