(623a) Multistage NMPC for Demand Uncertainty of Gas Pipeline Networks

The operation of gas pipelines is dynamic due to time-varying demands, com-
position, and ambient conditions. It is therefore necessary to consider these un-
certainties while modeling, as not considering them might lead to performance
deterioration and inability to meet the demand. This leads to a non-linear dy-
namic optimization problem with model constraints, operation bounds and un-
certainties. Previously, Zavala[6] did stochastic optimal control of gas pipelines
under demand uncertainties. There has also been a focus on robust optimiza-
tion under demand and gas composition uncertainty [2]. However, none of these
studies consider NMPC with an explicit consideration of various uncertain sce-
narios. This work focuses in embedding dynamic pipeline network models with
explicit consideration of demand uncertainty in a NMPC controller.
A standard NMPC, designed with a nominal value of demands, fails to meet
the terminal demand pressure requirements or depletes the line pack inventory to
meet the demand. Therefore we propose to use multistage NMPC[1] to consider
the various uncertain scenarios in demand profiles to optimize the cost. This
approach relies on constructing a scenario tree by generating extreme cases of
the uncertain parameters with separate control sequences to address constraint
violations. The advantage of this formulation is that it reduces the conserva-
tiveness of the standard robust NMPC and prevents constraint violation in all
realizations of uncertainty. To demonstrate the potential of this approach to
yield more reliable controls, we show how a nominal NMPC fails to meet the
demand under demand uncertainty and use multistage NMPC to meet the de-
mands for instances of real-world gas pipeline networks taken from gaslib [4]
modeled in IDAES and Pyomo.DAE[3] with IPOPT[5].
In this talk we describe our model formulation, including methods used for
generation of extreme cases, give the details of our implementation in the IDAES
software framework, and describe our results obtained on network instances by
solving the models with different uncertainty considerations.