Stochastic gradient methods for energy saving and a correct management in complex water supply systems

The management optimization of complex multi-source and multi-demand water resource systems under a high uncertainty level has been a subject of interest in the research literature (Labadie, 2004; Cunha & Sousa, 2010; Yuan et al., 2016). In this context, energy saving in operation of water pumping plants and reduction of water deficit for users and activities are frequently conflicting issues. Dealing with these problems, the definition of optimal activation rules for emergency activation of pumping stations are a relevant topic recently treated in Lerma et al. (2015) and Napolitano et al. (2016). In this study we want to define a trade-off between costs and risks considering the minimization of water shortage damages and the pumping operative costs, under different hydrological scenarios occurrences possibilities. Consequently, optimization results should provide the water system Authorities with a robust information about the optimal activation rules considering a large set of generated scenarios of hydrologic inputs to reservoirs. Using synthetic series it is possible to take into account the climate change impacts and balance the rules while also considering future behavior under the risk of the occurrence of shortages and the cost of early warning procedures to avoid water scarcity, mainly related to activation of emergency water transfers. Thereafter, this problem has been faced considering an efficient optimization tool based on the Stochastic Gradient method (SQG), see Ermoliev & Wets (1988) and Gaivoronski (2005). Testing the effectiveness of this proposal, an application of the modelling approach has been developed in a water shortage prone area in South-Sardinia (Italy)