{
  "abstract": "This paper proposes a deterministic bilevel optimization framework for the coordinated operation of Virtual Power Plants (VPPs) embedded in an active distribution network. The Distribution System Operator (DSO) acts as the upper-level leader, minimizing a weighted combination of expenditure, active losses and voltage deviation subject to nonlinear AC power flow constraints, while each VPP operates as a lower-level follower that maximizes its profit under the uniform price signal issued by the DSO. Unlike most existing formulations, which linearize the lower-level subproblem to obtain a Mixed-Integer Linear Program (MILP), the proposed model retains the full AC Optimal Power Flow (AC-OPF) equations, producing a bilevel Mixed-Integer Nonlinear Program (MINLP). The lower-level problem is replaced by its Karush-Kuhn-Tucker (KKT) optimality conditions and the Strong Duality Theorem, yielding a single-level Mathematical Program with Equilibrium Constraints (MPEC). Complementarity conditions are then linearized via the Fortuny-Amat big-M transformation. The framework is validated on the IEEE 33-bus feeder over a 24-hour horizon, with four distributed resources aggregated into a single VPP. Compared with individual dispatch against a regulated time-of-use tariff, aggregation reduces active losses by 10.5 %, the accumulated voltage deviation by 18.3 %, and the bus-hours below 0.95 p.u. from 132 to 29. These gains cost 0.31 % in social cost and 0.26 % in DSO expenditure, while the rent of the aggregator is preserved.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17927",
  "author_total": 4,
  "authors": [
    {
      "name": "Laura M. Barajas-Arguello"
    },
    {
      "name": "Rafael A. Núñez-Rodríguez"
    },
    {
      "name": "Daniel Gebbran"
    },
    {
      "name": "Clodomiro Unsihuay-Vila"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5c7224qqzpwhr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17927",
  "fulltext_url": null,
  "id": "5c7224qqzpwhr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17927",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CE"
    ],
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2208|Optimal Power Flow Distribution"
    ]
  ],
  "openalex": "W7213498144",
  "pdf_url": "https://arxiv.org/pdf/2609.17927",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5c7224qqzpwhr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.17927",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17927"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Day-ahead Coordination of Virtual Power Plants within Active Distribution Networks using Deterministic Bi-Level Optimization",
  "title_text": "Day-ahead Coordination of Virtual Power Plants within Active Distribution Networks using Deterministic Bi-Level Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/5c7224qqzpwhr",
  "venue": "arXiv",
  "versions": []
}