Optimization of pump schedules in water distribution networks with uncertain nodal demands

Water distribution networks are inherently subject to uncertain conditions, such as unpredictable user demands, and their operation must achieve a highly reliable performance. In this setting, the definition of pump schedules is an important task, whereby pump states over a reference operational period are determined [1]. This work focuses on the identification of optimal pump schedules in water distribution networks with explicit quantification of demand uncertainty. The latter is modeled using random variables, and thus, system responses such as nodal pressures and pump energy consumption also become random. Then, the network level of service is measured using the concept of hydraulic reliability, i.e., the probability of all nodal pressures exceeding a minimum allowable level over a reference operational period. Moreover, expected pumping energy costs are adopted as a metric of economic performance. Consequently, an optimization problem is formulated as the minimization of expected pumping costs under constraints on the hydraulic reliability. For any given pump schedule, these measures are estimated by integrating subset simulation with the hydraulic simulation software EPANET [2]. A stochastic search technique is employed to obtain a set of nearly optimal pump schedules rather than a single final solution. The capabilities of the resulting approach are showcased in a benchmark water distribution network subject to stochastic nodal demands. [1] L. E. Ormsbee and K. E. Lansey, “Optimal control of water supply pumping systems,” Journal of Water Resources Planning and Management, vol. 120, no. 2, pp. 237–252, 1994. [2] H. A. Jensen and D. J. Jerez, “A stochastic framework for reliability and sensitivity analysis of large scale water distribution networks,” Reliability Engineering & System Safety, vol. 176, pp. 80–92, 2018.