Analytical Sensitivity Analysis and Optimization for Cost-Efficient Operation of Water Supply Systems

Water supply systems (WSS) transport water from the source to the population, requiring a significant amount of energy, particularly for hydraulic pumps. To improve the efficiency of WSS, the use of hydraulic models and optimization algorithms can provide valuable insights for their operation and management. However, the efficient combination of these tools requires an effective and reliable sensitivity analysis. This work presents a novel and precise calculation of the sensitivities for the pump scheduling problem using a real continuous formulation and the extended period simulation (EPS) hydraulic analysis, as used in the generality of hydraulic simulators, such as EPANET. The work was validated through comparison with the finite-difference method (FDM) in two numerical case studies: a simple pump-tank network and the AnyTown Modified benchmark. For the last case study, an optimization process was carried out comparing the results obtained by the FDM and the analytical approach previously validated. The analytical sensitivities were found to be more accurate and require lower computational resources than the alternative approaches.