Hierarchical optimisation of a water-supply network

The paper presents the results of an investigation of the feasibility and implementation of an optimal online control to a water-supply network in the United Kingdom. The network, which has over 70 principal nodes, is reduced to an equivalent control problem with 6 state variables, which are the dominant reservoir heights, 10 control inputs, which are the major pump-station outputs, and 6 disturbances, which are the lumped zone consumptions. The control objective is the supply of water to the consumer over a 24 h period at minimum cost, subject to the 16 constraints on controls and states at each interval. To overcome the dimensionality problem associated with discrete-time optimal control the optimisation is carried out using a decomposition technique due to Lasdon and Tamura, which employs Lagrange duality theory. The paper describes the formulation of the network equations, the theory of the optimisation method, and gives typical results for the optimal operation of the system for typical weekday consumption. The results show a worthwhile cost saving over the control strategy in use during the study period, and computational experience indicates that the method is appropriate for optimal online control in a predictive environment.