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Modelling and Optimization of the Operation of a Multiple Tank Water Pumping System

This paper studies the optimization of the operation of a water supply pumping system by means of standard solvers. The system consists of several tanks that supply the water to several districts in a town. Each tank can be filled from several wells through a hydraulic system that can be reconfigured by means of several valves. The automatic operation of the system tries to determine which valves and pumps must be active at each instant in order to minimise the operation cost, taking into account the tariff periods. The main constraints are the maximum and minimum volumes of the tanks. A mathematical model of the problem is proposed in order to formulate, in matrix form, the cost index and the constraints, to be able to use standard solvers as Mosek. A basic optimization problem is proposed, that only imposes the constraints of the finite volume of the tanks. The result of this basic problem tends to produce a large number of pump and valve commutations, that is not adequate in practice. To solve this problem, two alternatives are proposed: to include the number of commutations in the cost index, and to add as a constraint the maximum number of commutations. Both approaches lead to an adequate result, but the second one is easier to use, as the number of commutations can be fixed in an explicit way. An example of a real water supply system is analysed to demonstrate the validity of the approach, using Yalmip as parser and Mosek as solver.