An approach for estimating a virtual power plant's energy-regulation feasible region showed its clearest numerical advantage when operating constraints on individual resources were coupled, according to a simulation. Here, a feasible region means the set of energy and regulation schedules the model treats as possible. In that comparison, the proposed I=2 version had a normalized mean absolute error of 7.5%, compared with 13.6% for an outer-approximation method and 13.4% for the proposed I=1 version.
The authors report that aggregate feasible-region error was reduced by over 40% in cases with coupled DER operating constraints. They also state that the proposed method was at least not inferior to typical feasible-region approximation methods in the tests and performed better in some scenarios.
Learning the region from dispatches
The paper uses a virtual-battery representation, a battery-like mathematical description, together with inverse optimization to approximate the aggregate region. In plain terms, the procedure works backward from dispatch decisions: the original VPP model generates optimal dispatch results under different scenarios, and those results are used to fit the parameters of the approximate feasible region.
During fitting, the generated scheduling results are treated as optimal solutions for the approximate model, with noise allowed in that relationship. The fitting formulation uses strong duality, primal feasibility, dual feasibility and stationarity conditions.
A structured simulation
The numerical case study modeled a virtual power plant aggregating 4,000 electric vehicles. Scenarios from July 1 to July 20 were used for fitting, while July 21 to July 30 were used for testing. Each scenario contained two-by-T matrices, with T equal to 16 time intervals.
The evaluation compared the proposed approach with an outer-approximation method under two DER regulation-operation models: one decoupled and one coupled.
The easy case looked different
In the decoupled model, the results were close across methods. Normalized mean absolute error was 1.8% for outer approximation, 1.6% for proposed I=1 and 1.7% for proposed I=2.
That pattern changed in the coupled model. Error was 13.6% for outer approximation and 13.4% for proposed I=1, while proposed I=2 recorded 7.5%, the lowest reported figure.
What the percentages mean
The paper calculates feasible-region error as mean absolute error divided by the maximum true value from the original model. Mean absolute error is the average size of the absolute differences, so the reported percentage is scaled against the largest value in the original model.
The reported evaluation used the numerical case study described above: a 4,000-EV virtual power plant, July scenarios for fitting and testing, and the two regulation-operation formulations. The authors' broader accuracy statement is framed around these tests: they say the method was at least not inferior to typical approaches and better in some scenarios.
The document is an arXiv version 1 preprint dated 26 Aug 2026. Its front matter also states that the work was accepted by PESGM2024.
The work was supported by the National Natural Science Foundation of China under Grant 52107102 and by the Major Smart Grid Joint Project of the National Natural Science Foundation of China and State Grid under Grant U2066205.
Paper data and sources
Original title: Approximating Energy-Regulation Feasible Region of Virtual Power Plants: A Data-driven Inverse Optimization Approach
Authors: Ruike Lyu, Hongye Guo, Qixin Chen
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: 10.1109/pesgm51994.2024.10689111
Original paper · Full text