Day-ahead Coordination of Virtual Power Plants within Active Distribution Networks using Deterministic Bi-Level Optimization
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.
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BibTeX
@misc{barajasarguello2026dayahead,
title = {{Day-ahead Coordination of Virtual Power Plants within Active Distribution Networks using Deterministic Bi-Level Optimization}},
author = {Laura M. Barajas-Arguello and Rafael A. Núñez-Rodríguez and Daniel Gebbran and Clodomiro Unsihuay-Vila},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17927},
eprint = {2609.17927},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17927},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Day-ahead Coordination of Virtual Power Plants within Active Distribution Networks using Deterministic Bi-Level Optimization
AU - Laura M. Barajas-Arguello
AU - Rafael A. Núñez-Rodríguez
AU - Daniel Gebbran
AU - Clodomiro Unsihuay-Vila
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17927
UR - https://arxiv.org/abs/2609.17927
AB - 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.
ER -