Modelling and Minimum Cost Control of Multiple Tank Pumping Systems

Abstract

This paper studies the minimization of the operation cost of a water supply pumping system by means of standard solvers. The system consists of a set of tanks that supply the water to different districts in a city. The tanks can be filled from different wells through a hydraulic system that can be reconfigured by means of several valves. The aim of the automatic operation is to determine which valves and pumps must be active at each instant of time in order to minimise the overall cost, taking into account the tariff periods. We propose a mathematical model of the problem to be able to formulate, in matrix form, the cost index and the constraints, such that standard solvers as Mosek or CBC can be used. The optimization problem is a mixed integer one, with a high computational cost. To reduce this cost, we propose to reduce the number of integer variables, replacing them with real variables from a given moment in the optimization horizon. An important part of the problem is the future output flow, that must be predicted in order to use that data in the optimization. We propose a prediction strategy that takes into account the different behaviour of working and weekend days. A simulation example based on a a real water supply system model is analysed to demonstrate the validity of the approach, using Yalmip as parser and CBC as solver.