Optimal Sensor Placement and PRV Localization under Demand Uncertainty

The implementation of real-time pressure management requires the acquisition of online measurement data, which is essential for the design of a closed-loop control system. In order to achieve this, it is necessary to determine in advance the locations for the installation of pressure sensors and pressure reducing valves (PRVs) for pressure reduction and control in a water distribution system (WDS). The sensors should be positioned at the most sensitive points to pressure variation, while the PRVs should be located at the points with the largest pressure drops. In this study, we solve this problem by extending an existing deterministic approach to a stochastic one with uncertain demand. For this purpose, we use the gap statistic to determine the number of sub-regions, the k-means++ to select the sensor positions, an edge-selection scheme for PRV localization, and differential evolution to minimize the total operating pressure. More importantly, we propose a scheme to calculate the sensitivity of the pressure and the pressure reduction due to the variation of the demand, based on which the formulated optimization is solved. Furthermore, the satisfaction of operational constraints, such as ensuring the pressure lower and upper bounds in the network, is formulated as chance constraints. Finally, a two-stage optimization framework is developed to solve this problem. In the lower level, Monte Carlo simulation is used to evaluate the impact of the uncertainties on the WDS performance. In the upper level, an optimizer determines the optimal locations for the pressure sensors and PRVs.