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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.
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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Header DbId: enr
DbLabel: Energy & Power Source
An: 191973429
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  Label: Title
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  Data: An Exact Spectral Refinement Method for Nonconvex Branch-Flow Feasibility in Active Distribution Networks.
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  Data: <searchLink fieldCode="AR" term="%22Dang%2C+Laite%22">Dang, Laite</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ni%2C+Ming%22">Ni, Ming</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Song%2C+Xiaochuan%22">Song, Xiaochuan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yuan%2C+Yi%22">Yuan, Yi</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ding%2C+Tao%22">Ding, Tao</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> tding15@mail.xjtu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Energies+%2819961073%29%22">Energies (19961073)</searchLink>. Feb2026, Vol. 19 Issue 4, p1009. 31p.
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  Data: *<searchLink fieldCode="DE" term="%22Semidefinite+programming%22">Semidefinite programming</searchLink><br />*<searchLink fieldCode="DE" term="%22Power+distribution+networks%22">Power distribution networks</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br />*<searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br />*<searchLink fieldCode="DE" term="%22Photovoltaic+power+systems%22">Photovoltaic power systems</searchLink><br />*<searchLink fieldCode="DE" term="%22Quadratic+programming%22">Quadratic programming</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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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        Value: 10.3390/en19041009
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 31
        StartPage: 1009
    Subjects:
      – SubjectFull: Semidefinite programming
        Type: general
      – SubjectFull: Power distribution networks
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Optimization algorithms
        Type: general
      – SubjectFull: Photovoltaic power systems
        Type: general
      – SubjectFull: Quadratic programming
        Type: general
    Titles:
      – TitleFull: An Exact Spectral Refinement Method for Nonconvex Branch-Flow Feasibility in Active Distribution Networks.
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            NameFull: Dang, Laite
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            NameFull: Ni, Ming
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            NameFull: Song, Xiaochuan
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            NameFull: Yuan, Yi
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            NameFull: Ding, Tao
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            – D: 15
              M: 02
              Text: Feb2026
              Type: published
              Y: 2026
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              Value: 19
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            – TitleFull: Energies (19961073)
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