Clodomiro Unsihuay-Vila

arXiv2026

Day-ahead Coordination of Virtual Power Plants within Active Distribution Networks using Deterministic Bi-Level Optimization

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.

math.OC↗

arXiv2026

Fair Dynamic Operating Envelopes using Distributed Multi-Period Optimal Power Flow and Jain Index for Active Distribution Networks

Dynamic operating envelopes (DOEs) are increasingly used to publish time-varying export limits that keep distribution networks within operational limits. Purely technical DOE allocation, however, can systematically privilege electrically favorable prosumers, while embedding fairness directly into a single-period optimal power flow (OPF) objective mixes network feasibility, equity and efficiency in a way that obscures the cost of fairness. This paper proposes a two-stage, multi-period framework that addresses both of these. Initially, a technical distributed OPF computes network-feasible export envelopes. The subsequent stage then applies a dynamic aggregate export budget and redistributes capacity through cumulative proportional fairness, limiting the additional curtailment by an admissible efficiency budget. The resulting fair DOEs are treated as first-stage decisions, while battery storage provides scenario-dependent recourse under demand and renewable uncertainty. The operational problem is solved by a calibrated regional alternating direction method of multipliers (ADMM) on a lossless LinDistFlow model and independently validated using AC power flow. On the IEEE 33-bus feeder over a 24-hour horizon, the technical benchmark yields 2.1097 MWh of renewable curtailment, whereas the fairness-constrained allocation increases curtailment to 5.7216 MWh but caps the maximum cumulative curtailment ratio at 11.20% and raises Jain fairness indices close to unity, with AC voltage deviations below 0.01 p.u. and no voltage or thermal violations under the adopted 0.90-1.05 p.u. limits. Results show that considering both storage (which alleviates curtailment impact) and multi-period fairness (which increases curtailment) is an interesting approach for modern DOE design, which in turn requires a multi-period, co-designed approach.

eess.SY↗