As natural gas is becoming increasingly important in modern life, its distribution through ever expanding pipeline networks is dependent on optimized control and management. The problem of dynamic optimization is difficult to resolve due to its inherent characteristics. We propose a two-stage approach, where both space and time decomposition are applied, and as a result the problem can be formulated as one of dynamic optimization. The objective is a deadlock-free distributed model, where the computation order is assured correct, and the communication time is minimized. The proposed decentralized mathematical model, which will conduct to the distributed design, has been proven correct on an abstract algebraic model, with the same structure as the real problem. This modular approach is well suited to the high and ever increasing dimension of gas networks, and to the nature of the problem, as well as to the tendency to decentralize services - e.g. BG plc. A decentralized approach also makes the network less dependent on communication hazards and diminishes communication delays and lags, contributing in this manner to a more accurate approach. Solution efficiency is also expected since smaller problems are solved simultaneously with the communication overhead being minimized.
Gas networks are composed of geographically dispersed controllable elements communicating between themselves. Their large extent, high complexity, inherent nonlinearities, and transient nature make the optimisation of their operation and management a difficult computational task. Long computational times, as well as communication unreliability caused by their decentralised nature, result into a loss of solution accuracy. One of the ways to improve computational efficiency is system decomposition and subsequent use of parallelism. A temporal decomposition is suitable to the problem's mathematical structure, whereas a spatial decomposition suits its decentralised nature. Our works fits in a broader line of research, which consists on an examination of the possibility that present global optimisation methods used in gas networks could be replaced by a decentralised approach. This could significantly reduce the computation time, as well as being more closely related to the organisational realities of modern life. Since we work from a theoretical and abstract point of view, we are not concerned with network subtleties which we view as physical details. Our aim is to capture main features of the network organisation that determine the basic network structure and operation. It is our main objective to examine the overall structure of an iterative formulation of the problem of transient optimisation of networks, and then decide on its partition whether it be according to time or space. However, owing to the complexity of the problem studied, its decomposition and the basic structure of the proposed approach to optimisation will be described on an abstract algebraic setting of the kind of the transient optimisation problem.