Optimization Methodologies in Complex Water Supply Systems for Energy Saving and a Correct Management under Uncertainty

Nowadays, the management of complex water supply systems needs to pay a close attention to economic aspects concerning high costs due to energetic management. Among them, the optimization of water pumping plants activation schedules is a significant issue when managing emergency and costly water transfers under drought risk. These problems are affected by a high uncertainty level, which is difficult to be faced. In this class of problems, uncertainty lies in water availability, demand behavior, electric prices and so on. Therefore, in order to provide a reliable solution, this research wants to develop some approaches of optimization under uncertainty, dealing with water resources management problems concerning multi-users and multi-reservoirs systems, especially referring to the definition of optimal activation rules for emergency pumping stations in drought conditions. In scarcity situations, the evaluation of different solutions is intimately related to the future water resource availability and the opportunity to provide water through the activation of emergency and costly water transfers. Hence, the water system optimization problem needs to deal with uncertainties particularly in treating the effectiveness of emergency measures activation to face droughts. The research analysis wants to assure simultaneously an energy saving and a correct management in complex water supply system under uncertainty conditions. The formulation of this problem highlights a complicated decision procedure, considering the requirements duality: to guarantee a complete water demands fulfilment respecting an energy saving policy. The obtained results should allow the water system’s authority to get a robust decision policy, minimizing the risk of wrong future decisions. A cost-risk balancing approach has been here developed to manage this problem, in order to balance the damages due to shortages of water and the energy-cost requirements of pumping plants. In a first step, the problem has been solved using a traditional Scenario Analysis Approach with a two stages stochastic programming. The obtained results using Scenario Analysis Approach were appreciable considering a limited number of historical scenarios characterized by a short time horizon. Nevertheless, in a second phase, when increasing the number of considered scenarios by generation of a new synthetic database in order to take into account the effect of climate and hydrological changes, some computational problems related to the dimensions of the model arose. Therefore, to solve these computational difficulties, it is been necessary to apply a specialized approach for optimization under uncertainty. Hence, a simulation model has been coupled with an optimization module using the Stochastic Gradient Methods. 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), characterized by Mediterranean climate and high annual variability in hydrological inputs to reservoirs. By applying the combined simulation and optimization procedure a robust decision strategy in pumping activation was obtained considering also the synthetic database.