Data Driven Model Order Reduction of Gas Distribution Network

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.