Stochastic gradient approach for energy and supply optimisation in water systems management

Under conditions of water scarcity, energy saving in operation of water pumping plants and the minimisation of water deficit for users and activities are frequently contrasting requirements, which should be considered when optimising large-scale multi-reservoirs and multi-users water supply systems. Undoubtedly, a high uncertainty level in predicted water resources due to hydrologic input variability and water demand behaviour characterizes this problem. The aim of this paper is to provide an efficient decision support system considering emergency water pumping plants activation schedules. The obtained results should allow the water system’s authority to adopt a robust decision policy, minimising the risk of harmful future decisions concerning the water resource management. The model has been here developed to manage this problem, in order to reduce the damages due to shortage of water and the energy-cost requirements of pumping plants. Particularly, in optimisation, we look for optimal rules considering both historical and generated synthetic scenarios of hydrologic inputs to reservoirs. Hence, using synthetic series, we can analyse climate change impacts and optimise the activation rules considering future hydrologic occurrences. A simulation model has been coupled with an optimization module using the stochastic gradient method to get robust pumping activation thresholds. This method allows to solve complex problems, solving efficiently large size real cases due to high number of data and variables. Thresholds values are identified in terms of critical storage levels in supply-reservoirs. Application of the modelling approach has been developed on a real case study in a water-shortage prone area in south-Sardinia (Italy), characterized by Mediterranean climate and high annual variability in hydrological input to reservoirs. By applying the combined simulation procedure, a robust decision strategy in pumping activation was obtained. Developing the stochastic gradient model, a main programming supports has been built by MATLAB efficiently interfaced with CPLEX for optimisation and Excel for inputs and results representation.