Multi-Objective Operation-Leakage Optimization and Calibration of Water Distribution Systems

This study aims to develop and solve a multi-objective water distribution systems optimization problem incorporating pumps’ optimal scheduling and leakage minimization. An iterative optimization model was presented for calibrating and computing leakages in water distribution systems to recognize the critical impact of leakage control on system operation. The multi-dimensional and nonlinear optimization model, incorporating pump control, consumer demands, storage, and other water distribution systems’ components, was constructed and was minimized using a multi-objective genetic algorithm coupled with hydraulic simulations. The model was demonstrated on two example applications with increasing complexity through base runs and sensitivity analyses. Results showed that leakage minimization competes against pumping, mainly when significant differences occur between demands during low and high energy tariffs. Pumping during the periods with high electricity tariffs (when the demands are high) generated pressure distribution that decreased the overall leakage related to pump scheduling that replicated the natural inclination to pump as much as possible at low tariffs (when the demands are low). The optimal fronts were found to be very sensitive to the leakage exponent value, and changing its value indeed contradicted the balance between minimizing the leakage and the energy cost significantly. Altogether, the idea presented in this paper was found capable of facilitating the decision-makers to conveniently select between the energy-efficient pump scheduling and pump scheduling reflecting minimum leakage based on the system operator’s preferences. The research also paves the way to rebuild the optimization model by incorporating water distribution reliability and water quality that, in some cases, may also contradict the choice between energy cost and leakage minimization.

Active learning of optimal controls for pump scheduling optimization

<p>Two approaches are possible in Pump Scheduling Optimization (PSO): <em>explicit</em> and <em>implicit control</em>. The first assumes that decision variables are pump statuses/speeds to be set up at prefixed time. Thus, the problem is to efficiently search among all the possible schedules (i.e., configurations of the decision variables) to optimize the objective function – typically minimization of the energy-related costs – while satisfying hydraulic feasibility. Since both the energy cost and the hydraulic feasibility are black-box, the problem is usually addressed through simulation-optimization, where every schedule is simulated on a “virtual twin” of the real-world water distribution network. A plethora of methods have been proposed such as meta-heuristics, evolutionary and nature-inspired algorithms. However, addressing PSO via explicit control can imply many decision variables for real-world water distribution networks, increasing with the number of pumps and time intervals for actuating the control, requiring a huge number of simulations to obtain a good schedule.</p><p>On the contrary, implicit control aims at controlling pump status/speeds depending on some control rules related, for instance, to pressure into the network: pump is activated if pressure (at specific locations) is lower than a minimum threshold, or it is deactivated if pressure exceeds a maximum threshold, otherwise, status/speed of the pump is not modified. These thresholds are the decision variables and their values – usually set heuristically – significantly affect the performance of the operations. Compared to explicit control, implicit control approaches allow to significantly reduce the number of decision variables, at the cost of making more complex the search space, due to the introduction of further constraints and conditions among decision variables. Another important advantage offered by implicit control is that the decision is not restricted to prefixed schedules, but it can be taken any time new data from SCADA arrive making them more suitable for on-line control.</p><p>The main contributions of this paper are to show that:</p><ul><li>thresholds-based rules for implicit control can be learned through an active learning approaches, analogously to the one used to implement Automated Machine Learning;</li> <li>the active learning framework is well-suited for the implicit control setting: the lower dimensionality of the search space, compared to explicit control, substantially improves computational efficiency;</li> <li>hydraulic simulation model can be replaced by a Deep Neural Network (DNN): the working assumption, experimentally investigated, is that SCADA data can be used to train and accurate DNN predicting the relevant outputs (i.e., energy and hydraulic feasibility) avoiding costs for the design, development, validation and execution of a “virtual twin” of the real-world water distribution network.</li> </ul><p>The overall system has been tested on a real-world water distribution network.</p>