Optimal pump scheduling in multi-phase distribution networks using Benders decomposition

Abstract

With the growing adoption of renewable energy resources in the power grid, co-optimizing the operation of water and power distribution networks (WDNs and PDNs) increases the flexibility of both systems. The optimal water power flow problem (OWPF) is formulated to manage resource utilization across the WDNs and multi-phase PDNs. The nonlinear WDN hydraulic constraints and PDN ac power flow equations render the OWPF problem nonconvex. This paper formulates a convex optimal water power flow (C-OWPF) problem adopting successive approximations in WDNs and branch-flow relaxations in PDNs. The C-OWPF problem is a mixed-integer semidefinite program, which is computationally challenging even for small instances. Additionally, privacy considerations of WDN and PDN operators motivate the need for solving the C-OWPF in a distributed fashion. This paper develops a C-OWPF solver based on Benders decomposition that overcomes computational complexity challenges and preserve the privacy of the respective operators. The merits of the Benders decomposition-based solver are demonstrated on the IEEE 4-bus PDN coupled with a 3-node WDN and the IEEE 123-bus PDN coupled with the 36-node WDN.