Abstract:
Natural gas is distributed through a complex network of pipes, nodes (supply and demand),
compressors and control valves covering a large geographical area. To observe
the behaviour of such complex network, typical procedure is to use multiple measurement
devices at different nodes/regions and record the flow and pressure of gas at those
points. This procedure is complex, time consuming, requires large number of human
resources and involves human/ measurement device errors. An alternate is to use mathematical
modelling and simulation of gas distribution network where the mathematical
model involves differential as well as algebraic equations that lead to the so-called descriptor
system. It is known in the literature that simulation of such complex systems is
computationally expensive. To resolve this issue, the concept of model order reduction
can be used in which a reduced order model is constructed from the original large scale
model such that the behaviour is approximately same. In this thesis we used a specific
model order reduction technique that is the Loewner framework which is data driven
and interpolating the original system. The Loewner framework constructs reduced order
model without relying on the use of original model; instead, it uses pair of datasets at
given interpolation points. The approach provides trade-off between the accuracy of
fit and size of reduced order model. In this thesis, the applicability of Loewner framework
for reduction of gas distribution network has been tested and implemented on
some numerical examples. The expansion to nonlinear (quadratic-bilinear) model of gas
distribution network is also considered using nonlinear projection based interpolatory
model order reduction techniques. Numerical results show that reduced order model is
highly accurate, stable and takes lesser time to simulate as compared to the original
model.
