Electricity grids were designed around large centralized power stations, but the fastest-growing sources of new generation are now scattered across rooftops, substations, and distribution feeders. Solar panels, wind turbines, batteries, and small gas engines each contribute power, yet none behaves like a conventional plant. A team of Egyptian researchers has now tackled one of the least-studied planning questions behind this transformation: where exactly should a virtual power plant begin and end on the map of a real transmission network? Their answer, published in Neural Computing and Applications, shows that getting these invisible borders right can raise operating profits by as much as 85 percent compared with a baseline configuration.
A virtual power plant, or VPP, is a software-defined aggregation of distributed energy resources that are coordinated to act as a single generating unit. Instead of building a new power station, an operator bundles together small generators, controllable loads, and storage systems and schedules them collectively. The concept has split into two operational categories: the commercial VPP, which forecasts production and consumption, submits bids to electricity markets, and organizes daily schedules, and the technical VPP, which continuously monitors the network, detects faults, and pinpoints their locations. Together, these functions allow intermittent renewable resources to participate in markets while shielding the wider grid from their volatility.
The research team, led by Fekry Awad of Benha University together with Ragab A. El-Sehiemy of Kafrelsheikh University and colleagues, focused on a planning problem that most prior studies have sidestepped. While the optimal placement and sizing of distributed generators within a VPP has been examined before, only a handful of papers have addressed how many buses should be included in the VPP and which ones. This matters because the configuration of a VPP directly affects power losses, voltage profiles, power flows through transmission lines, and ultimately the profit the VPP can earn. The researchers framed the task as an optimization problem: maximize total net profit, calculated as revenue from selling power to customers and to the market minus the costs of running conventional and stochastic generators, subject to a set of technical constraints.
Those constraints are demanding. Active and reactive power must balance at every hour, bus voltages must stay within prescribed limits, apparent power through each line cannot exceed thermal capacity, and the number of VPP buses must fall between 10 percent and 35 percent of the total system buses. The team also excluded isolated buses from the candidate set, since they cannot practically serve as VPP boundary buses, which shrinks the search space and prevents infeasible solutions. Uncertainty in market prices, wind and photovoltaic output, and load demand was handled through probability distribution functions, including Gamma, Beta, and Normal distributions, whose outputs feed directly into the optimization routine.
To solve this problem, the researchers deployed the Artificial Hummingbird Algorithm, a bio-inspired metaheuristic introduced in 2022 that mimics three foraging strategies and three flight skills of real hummingbirds. Guided foraging, territorial foraging, and migration foraging correspond to different ways of exploring or exploiting the solution space, while axial, diagonal, and omnidirectional flights describe how candidates move toward food sources. A distinctive feature is the visit table, which mimics the memory-update mechanism of hummingbirds by tracking how often each food source has been visited. Migration foraging drives exploration when a food region suffers from shortage, territorial foraging represents exploitation, and guided foraging balances both in advanced stages. The algorithm has previously proven effective in estimating solar module parameters, optimizing reactive power dispatch, identifying the state of charge of lithium-ion batteries, and improving frequency stability in renewable-rich networks.
The methodology was tested on two standard test systems: the IEEE 57-bus network, a medium-sized system with 80 transmission lines and 7 generators supplying roughly 1250.8 MW of load, and the IEEE 39-bus New England system with 10 generators. For the 57-bus case, the team defined six study scenarios. Case 1 examined normal conditions with 100 percent of base load and 100 percent of grid price. Case 2 removed the generator at bus 12 from service. Case 3 raised the load to 150 percent under the same outage. Cases 4 and 5 progressively increased the price of power sold from the grid to 200 percent and 250 percent of baseline, while Case 6 introduced demand response through a price-elastic demand curve with a dispatchable load of 0.5 at bus 14.
The results reveal a sharp economic logic. When the price of grid power is lower than the cost of distributed generation, profit remains nearly constant across Cases 1, 2, and 3, because the VPP has little incentive to rely on its own generators. But once grid prices exceed generation costs, the picture changes dramatically. In Case 5, profit for hour 2 rose by 78.6 percent from Case 1, hour 7 by 85.2 percent, and hour 21 by 82.7 percent. Power purchased from the grid fell by 75 percent, 66.2 percent, and 47.76 percent for those hours respectively, as the system shifted toward cheaper distributed generators. The number of VPP buses also increased under contingency conditions, and voltage profiles stayed within permissible limits throughout.
Demand response added a further layer of profit. In Case 6, the VPP boundary itself reshaped: buses 15 and 47 entered the boundary at hour 2, while bus 38 exited at hour 7 and buses 38, 48, and 49 exited at hour 21. Total operational profit increased by 14.89 percent at hour 2, 0.63 percent at hour 7, and 7.84 percent at hour 21 compared with the baseline without demand response, driven primarily by peak-shaving and market arbitrage. On the larger IEEE 39-bus system, the VPP border remained remarkably stable across scenarios, concentrating at buses 4, 5, 8, 14, 15, 16, 17, and 27, with distributed generators clustered at buses 14 through 17, even when the generator at bus 30 was removed and the line between buses 16 and 24 was taken out of service.
To validate the robustness of the approach, the researchers benchmarked the Artificial Hummingbird Algorithm against the Grey Wolf Optimizer and a hybrid Grey Wolf–Cuckoo Search variant. AHA outperformed GWO by 0.9 percent, 9.6 percent, and 15 percent in profit for hours 2, 7, and 21 in Case 4, and by 8.4 percent, 15.4 percent, and 13.4 percent in Case 5. Against GWOCS, AHA achieved 6.97 percent, 19.58 percent, and 15 percent higher profit for the same hours. Statistical indicators over 20 independent runs confirmed that AHA reached near-optimal solutions with fewer iterations, although GWO showed slightly better execution time and stability metrics, reflecting AHA’s stronger search capability for the discrete, constrained nature of the VPP border problem.
The implications extend well beyond academic benchmarks. As grids worldwide absorb growing volumes of rooftop solar, wind, batteries, and flexible loads, the question of how to partition them into coherent, profitable, technically sound virtual power plants becomes a central planning challenge. The researchers outline several future directions, including studying VPP schedules under line outages with price uncertainty, minimizing power losses while maximizing profit, managing multiple interconnected VPPs, incorporating FACTS devices when renewables are present, and validating the method with measured electricity prices and wind-photovoltaic datasets from regional distribution networks such as PJM, CAISO, and the Australian National Electricity Market. If those extensions succeed, the invisible borders of virtual power plants may soon be drawn not by intuition but by algorithms inspired by the foraging habits of hummingbirds.
Subject of Research: Robust identifying of VPPs borders with optimal allocation of distributed energy resources for profit maximization by artificial hummingbird algorithm
Article Title: Robust identifying of VPPs borders with optimal allocation of distributed energy resources for profit maximization by artificial hummingbird algorithm
Article References: Awad, F., El-Sehiemy, R. A., Amer, G., Aziz, B. A., & Sakr, W. S. (2026). Robust identifying of VPPs borders with optimal allocation of distributed energy resources for profit maximization by artificial hummingbird algorithm. Neural Computing and Applications, 38(20), Article 818. https://doi.org/10.1007/s00521-026-12617-8
Image Credits: AI Generated
DOI: 10.1007/s00521-026-12617-8
Keywords: Robust, identifying, VPPs, borders, optimal, allocation, distributed, energy, resources, profit, maximization, artificial
News Source: Denise Maddox. (October 17, 2026). Artificial hummingbird algorithm redraws virtual power plant borders to lift grid profits by up to 85 percent. Scienmag.
