  Recent work has demonstrated that water supply pumps in the drinking water
distribution network can be leveraged to provide flexibility to the power
network, but existing approaches are computationally demanding and/or overly
conservative. In this paper, we develop a computationally tractable
probabilistic approach to schedule and control water pumping to provide voltage
support to the power distribution network subject to power and water
distribution network constraints under power demand uncertainty. Building upon
robust and chance-constrained reformulation approaches, we analytically
reformulate the probabilistic problem into a deterministic one and solve for
the scheduled pump operation and the control policy parameters that adjust the
pumps based on the power demand forecast error realizations. In a case study,
we compare our proposed approach to an adjustable robust method and investigate
the performance in terms of computation time, cost, and empirical violation
probabilities. We find that our proposed approach is computationally tractable
and is less conservative than the robust approach, indicating that our
formulation would be scalable to larger networks.
