Optimal Control of Water Supply in Pipe Networks by Retention Tanks: A Linear Case

The methodology for optimal control of supply in water networks is presented. It is based on the assumption that the water network exhibits a steady state of flow and the water heads in the network's nodes can be measured for an inspected part of the network. Making use of the graph based model of a water network and employing the so-called Virtual Distortion Method, the problem of optimal control can be formulated as a constrained optimisation problem. The water supply is minimised subject to constraints on the water head in the network's nodes. The optimal solution is expected for active constraints. Analogies between the presented water network modelling and the truss modelling in structural mechanics are described. The paper deals with the optimal control of water supply in pipe networks based on the graph-based model of a water network, the problem of optimal control has been formulated as a constrained optimisation problem in the paper. Linear constitutive relation (water flow vs. pressure head) has been assumed in order to develop the first step of the methodology. However, generalisation of the proposed approach for a piece-wise-linear case is planned in the near future.