Tractable Robust Drinking Water Pumping to Provide Power Network Voltage Support

Abstract

Drinking water distribution networks can be treated as flexible, controllable assets for power distribution networks (e.g., to provide voltage support) by leveraging the power consumption of water pumps and storage capabilities of water tanks. We formulate an adjustable robust optimization problem to determine the scheduled water distribution network pumping and real-time pump adjustments that ensure that the power and water distribution network constraints are satisfied with respect to uncertain power demand. We extend the monotonicity properties of dissipative flow networks to water distribution networks which requires assumptions on water tank operation. Then, to make the problem tractable, we leverage these properties, along with constraint approximations and an affine pump control policy, to reformulate the problem as an affinely adjustable robust counterpart that solves for the pumping schedule and the parameters of an affine control policy that determines the real-time pump adjustments. Through a case study, we demonstrate that the approach produces robust solutions and is computationally tractable. We also evaluate the impact of restricting water tank operation to enforce monotonicity and find it leads to a significantly restricted feasible region and more conservative solutions.