A convex-relaxation based method for optimal water-power flow. (November 2022)

• Record Type: Journal Article
• Authors: Li, Xinyi; Wu, Zhenyu; Yang, Lun; Sun, Mingyi; Zhao, Xia
• Is Part Of: Energy reports. Volume 8(2022)Supplement 13
• Page Start: 973
• Page End: 983
• Publication Date: 2022-11
• Subjects: Water network -- Optimal water-power flow -- SOC relaxation -- Convex envelope -- Sequential convexification; Power resources -- Periodicals; Energy industries -- Periodicals; Power resources; Periodicals; Electronic journals; 621.04205
• DOI: 10.1016/j.egyr.2022.08.031
• Languages: English
• ISSNs: 2352-4847

Abstract

Abstract: 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.