Model Reduction of Large Scale Gas Distribution Networks

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.