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Recent studies identified compressed air systems as one of the major consumers of electrical energy in the transnational system. As the importance of compressed air energy efficiency grows for companies and government regulators, so does the need for theoretical analysis. Currently, the modelling process of pneumatic infrastructure focuses on the detailed mathematical description of pneumatic drive components such as valves, cylinders and storages. To speed up calculations, the effects introduced by long pipes (dead volume, delay time and pressure drop) are often neglected. However, they are the main components in any compressed air distribution network. In the present paper, a low-order dynamic transmission line model is derived which is numerically well-conditioned for the implementation in signal flow oriented simulation programs such as MATLAB/SIMULINK. The model works with industry standard parameters, and is able to accurately replicate dynamic and steady-state behavior.