# 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.

- Authors:

- National Renewable Energy Laboratory (NREL), Golden, CO (United States)
- University of Minnesota
- University of Toronto

- Publication Date:

- Research Org.:
- National Renewable Energy Lab. (NREL), Golden, CO (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE), NREL Laboratory Directed Research and Development (LDRD)

- OSTI Identifier:
- 1421914

- Report Number(s):
- NREL/JA-5D00-69064

Journal ID: ISSN 2325-5870

- DOE Contract Number:
- AC36-08GO28308

- Resource Type:
- Journal Article

- Journal Name:
- IEEE Transactions on Control of Network Systems

- Additional Journal Information:
- Journal Volume: PP; Journal Issue: 99; Journal ID: ISSN 2325-5870

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; power systems; water systems; optimal power flow; optimal water flow; successive convex approximation; distributed algorithms

### Citation Formats

```
Dall-Anese, Emiliano, Zhao, Changhong, Zamzam, Admed S., Sidiropoulos, Nicholas D., and Taylor, Josh A.
```*Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution*. United States: N. p., 2018.
Web. doi:10.1109/TCNS.2018.2792699.

```
Dall-Anese, Emiliano, Zhao, Changhong, Zamzam, Admed S., Sidiropoulos, Nicholas D., & Taylor, Josh A.
```*Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution*. United States. doi:10.1109/TCNS.2018.2792699.

```
Dall-Anese, Emiliano, Zhao, Changhong, Zamzam, Admed S., Sidiropoulos, Nicholas D., and Taylor, Josh A. Fri .
"Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution". United States. doi:10.1109/TCNS.2018.2792699.
```

```
@article{osti_1421914,
```

title = {Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution},

author = {Dall-Anese, Emiliano and Zhao, Changhong and Zamzam, Admed S. and Sidiropoulos, Nicholas D. and Taylor, Josh A.},

abstractNote = {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.},

doi = {10.1109/TCNS.2018.2792699},

journal = {IEEE Transactions on Control of Network Systems},

issn = {2325-5870},

number = 99,

volume = PP,

place = {United States},

year = {2018},

month = {1}

}