An Exact Spectral Refinement Method for Nonconvex Branch-Flow Feasibility in Active Distribution Networks.
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| Title: | An Exact Spectral Refinement Method for Nonconvex Branch-Flow Feasibility in Active Distribution Networks. |
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| Authors: | Dang, Laite1 (AUTHOR), Ni, Ming1,2 (AUTHOR), Song, Xiaochuan1 (AUTHOR), Yuan, Yi2 (AUTHOR), Ding, Tao2 (AUTHOR) tding15@mail.xjtu.edu.cn |
| Source: | Energies (19961073). Feb2026, Vol. 19 Issue 4, p1009. 31p. |
| Subject Terms: | *Semidefinite programming, *Power distribution networks, *Mathematical optimization, *Optimization algorithms, *Photovoltaic power systems, *Quadratic programming |
| Abstract: | High penetration of distributed photovoltaics (PV) makes hosting-capacity assessment and active distribution network operation challenging, primarily due to the need to accurately restore nonconvex branch-flow equalities rather than relying on relaxations that may produce physically inconsistent solutions. This paper develops an ADMM-coordinated framework with an exact spectral refinement for QP1QC subproblems, which converts the semidefinite characterization into a tractable one-dimensional refinement over a generalized-eigenvalue-defined interval and enables reliable primal recovery of the original equality constraints. Numerical tests on modified IEEE 33-, 792-, and 1137-bus feeders show that the proposed method substantially improves equality restoration: the normalized mismatch of nonconvex equalities is reduced from 82–108% under SOCP/SDP relaxations to 0.004% on the 33-bus system, and from 94–98% to 0.67% on the 792-bus system; on the 1137-bus system, the mismatch remains 6.4%, still far below the relaxation baselines. Compared with an SDP-based hidden-convex benchmark, the proposed approach preserves essentially the same optimization outcomes while achieving 7–16× lower runtime and converging in 8–13 ADMM iterations. [ABSTRACT FROM AUTHOR] |
| Database: | Energy & Power Source |
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| Abstract: | High penetration of distributed photovoltaics (PV) makes hosting-capacity assessment and active distribution network operation challenging, primarily due to the need to accurately restore nonconvex branch-flow equalities rather than relying on relaxations that may produce physically inconsistent solutions. This paper develops an ADMM-coordinated framework with an exact spectral refinement for QP1QC subproblems, which converts the semidefinite characterization into a tractable one-dimensional refinement over a generalized-eigenvalue-defined interval and enables reliable primal recovery of the original equality constraints. Numerical tests on modified IEEE 33-, 792-, and 1137-bus feeders show that the proposed method substantially improves equality restoration: the normalized mismatch of nonconvex equalities is reduced from 82–108% under SOCP/SDP relaxations to 0.004% on the 33-bus system, and from 94–98% to 0.67% on the 792-bus system; on the 1137-bus system, the mismatch remains 6.4%, still far below the relaxation baselines. Compared with an SDP-based hidden-convex benchmark, the proposed approach preserves essentially the same optimization outcomes while achieving 7–16× lower runtime and converging in 8–13 ADMM iterations. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 19961073 |
| DOI: | 10.3390/en19041009 |
