Abstract:
We consider the problem of modeling and simulation of large-scale gas distribution
network. In general, a gas distribution network is described by the pressure at
the nodes and
ow through branches of the network. There are di erent elements
in the gas network that include pipes, valves, resistors, compressors, preheaters and
coolers. The
ow through these elements can be mathematically modeled by di erential
as well as algebraic equations. The complete model of the network becomes a
system of nonlinear Di erential Algebraic Equations (DAEs) also called descriptor
systems. Often these systems are represented by large scale models in order to get
more and accurate details of the system. Simulation of such large scale models is
computationally expensive and prohibitive. An alternate option is to reduce the
model mathematically such that the response of reduced and actual model is almost
comparable. The reduced model is then used for simulation or control instead of
the original large-scale model. In this thesis our focus is on model reduction of
nonlinear DAEs. Existing model reduction techniques are not directly applicable to
nonlinear DAEs as they are unable to retain the structure of DAEs. This may result
in unbounded approximation error. We proposed a new model reduction framework
for some special linear and nonlinear DAEs that ensure the structure of original system.
For our numerical results we used Proper Orthogonal Decomposition (POD)
in the existing framework and in the proposed settings to compare the results. It is
observed that the proposed method gives 10% to 15% better relative approximation
error as compared to the direct use of standard reduction method and also retain
the original structure of the model representing the gas distribution network.
