A Hierarchical Optimization of a Wide Region Water Supply System with Transport Lags

Abstract In a wide region water supply system, a water transport by open channel or conduit has an advantage of the low cost for the effective use of the potential energy to realize greater capacity of water transportation to a point in the great distance. But we must take into consideration of transport lag varying with flow for the optimal operation or management. Hitherto, however, the optimization technique has neglected this kind of lag. We have developed the hierarchical optimization technique for the system with constant lag. In this paper we consider the system coupled by the long transport channels or conduits and present the hierarchical optimization technique, taking account of transport lags varying with flow. The optimization of this kind of system encounters the difficulty because the solution of the problem depends implicitly on the transport lags varying with flow. To overcome this difficulty we use a two-level decomposition-coordination technique by Lagrange duality theorem. The tasks of the supremal level are to coordinate the interconnection-unbalance between sub-systems and to improve successively the transport equations according to flow decided by the infimal level units. The task of the infimal level units is to optimize the non-interacted subsystem problems on fixed transport equations. The overall system optimality is obtained within reasonable computing time. An actual example shows this method useful.