| Summary: | This paper proposes a convex reformulation for the non-linear optimal water-power flow (OWPF) problem to optimize the operation cost of the integrated electricity–water network (IEWN). Due to the significant challenge in seeking the optimal solution of non-convex problems, the original OWPF problem is reformulated as a tractable mixed-integer second-order cone programming (MISOCP) problem. For the power distribution network, a second-order cone (SOC) relaxation is employed to address the non-linear branch power flow equation. For the water distribution network, a big-M trick is introduced to handle the unknown direction of water flow, then SOC relaxations and convex envelopes are employed to deal with quadratic and bilinear terms in non-convex constraints, respectively. To enhance the approximation accuracy of the proposed MISOCP model, a convex combination method and a sequential convexification approach are developed. Numerical results demonstrate that the proposed method outperforms the original non-linear formulation and linearized reformulation in accuracy, efficiency, and robustness.
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