Optimal Water–Power Flow-Problem: Formulation and Distributed Optimal Solution

Abstract

This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps. Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successive convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.A. S. Zamzam is with the Power systems, water systems, optimal power flow, optimal water flow, successive convex approximation, distributed algorithms.

Receding Horizon Control for Drinking Water Networks: The Case for Geometric Programming

“…However, this approach operates under the assumption that the network has a tree topology or that flow directions are known. Studies making similar assumptions include [8], [37]. The authors in [9] model the optimal scheduling of WDNs as a mixed-integer second-order cone program, which is analytically shown to yield WDN-feasible minimizers under certain sufficient conditions.…”

State Estimation in Water Distribution Networks through a New Successive Linear Approximation

“…(7) where h TK i , A TK i respectively stand for the head, cross-sectional area of the i th tank, and ∆t is sampling time; q ji pkq, j P N in i is inflow, while q ij pkq, j P N out i is outflow of the j th neighbor. We assume that reservoirs have infinite water supply and the head of the i th reservoir is fixed as h Rset i [17], [18] which is perfectly accurate. This also can be viewed as an operational constraint (9a).…”

Geometric Programming-Based Control for Nonlinear, DAE-Constrained Water Distribution Networks

“…In this section, we covert the control objectives in the nonconvex problem (16) to their convex, GP-based form. In (14), notice that x is a vector collecting the head h i at tanks.…”

“…The two works closest to our paper are [16] and [14]. The authors in [16] model WDNs as a directed graph, assume the directions of water flow in pipes do not change, and choose the Darcy-Weisbach equation to model head loss in pipes.…”

“…The two works closest to our paper are [16] and [14]. The authors in [16] model WDNs as a directed graph, assume the directions of water flow in pipes do not change, and choose the Darcy-Weisbach equation to model head loss in pipes. In [14], the authors convert the nonconvex head loss equations into convex models using geometric programming (GP) approximations, and hence a globally optimal solution is guaranteed.…”