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

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