Chance-constrained water pumping managing power distribution network constraints

We formulate a chance-constrained optimization problem to schedule water distribution network (WDN) pumping subject to water and power distribution network (PDN) constraints while managing water demand uncertainty. In addition to an optimal pumping schedule, we also determine optimal control policy parameters used to compute real-time control actions to compensate for demand forecast error. The resulting problem includes nonconvex constraints, and so conventional solution approaches for chance-constrained problems do not work. We heuristically apply a scenario-based method and investigate the control policy's performance to ensure all WDN and PDN constraints are satisfied despite uncertainty. Through case studies with a detailed model of a coupled WDN/PDN, we find that WDN pumping can be scheduled and controlled to manage PDN voltage constraints and that the scenario-based method provides feasible real-time control actions for many realistic water demand scenarios but more work is needed to identify computationally tractable approaches with probabilistic guarantees.