Algorithm for optimal control of a gas network with any configuration based upon hierarchical control and decomposition of the network is described. An algorithm is capable of finding time - profiles of pressure and flow throughout network, over 24 hours period, which minimizes the running costs of compressors whilst satisfying all imposed equality and inequality constraints. Local problems are solved using gradient technique. The subsystems are coordinated using "goal coordination" method to find the overall optimum. Correctness of the elaborated algorithm has been checked using non-trivial network.
There are many aspects to optimization of gas networks. Optimization can mean searching, according to a certain objective function, for optimal design parameters, optimal structures for development or optimal parameters for operation of networks. The cost of operating network when gas is at high pressure is determined mainly by mode of operation of compressors. This operating cost of running the compressor stations represents anywhere between 25% and 50% of the total company's operating budget. For low and medium pressure gas networks, minimization of operating costs means leakage reduction by optimizing nodal pressures. This work is concerned with the minimization of operating costs for high pressure gas networks under transient conditions. Depending on the character of gas flow in the system we distinguish steady and unsteady states. 2. Steady state optimization of large gas networks The steady state in a gas network is described by systems of algebraic non-linear equations. In steady-state problems, since loads and supplies are not functions of time, an algorithm for optimization determines, once and for all, the structure of the network (i.e. the number of sources, compressors, values and regulators called mits which must be on). In addition, the algorithm must determine the optimal parameters of the operation, namely nodal pressures and flows through branches (pipes). For these reasons, the problem of optimization is formulated in (Wilson et al. 1988) as a mixed integer problem. Each unit operates subject to a set of linear and nonlinear Alternatively, assuming that the structure is known, an algorithm for steadystate optimization of large gas networks is described in (Osiadacz and Bell, 1988). In this case the problem of optimization has been treated without simplification, i.e. as a nonlinear problem with nonlinear constraints. In the first case the problem has been solved using the Branch and Bound method. In the second case, the chosen method at each iteration minimizes a quadratic approximation to the Langrangian function subject to linear approximations to the constraints. A line search procedure utilizing the "watchdog technique" is used to force convergence when the initial values of the variables are far from the solution. In both cases the problem of optimization has been solved without the necessity of using hierarchical systems theory. Described in (Luongo et al.1989) the optimization strategy consists of two levels. The first level involves optimizing the system with suction/discharge pressures as variables.