Asymmetric Nash Bargaining Optimizes Energy Sharing and Benefit Allocation for Building Clusters

Coordinating distributed energy resources across urban architectures has long presented complex engineering and economic hurdles, particularly when balancing fluctuating renewable generation against the distinct daily consumption habits of different building types. In a study published in Results in Engineering, an engineering research team led by Liting Zhang, Jiang Li, Fanyue Qian, Yongwen Yang, Hanling Zhao, Xiaochen Lu, and Hongbo Ren investigated an inter-building energy-sharing and cooperative benefit-allocation architecture designed for virtual power plants aggregating residential, commercial, and office facilities. The investigators demonstrated that establishing physical electricity exchanges between complementary buildings, paired with incentive-based demand response and cooperative game theory, drastically cut simulated net operating expenditures while establishing an equitable distribution of financial rewards among all participants.

The physical foundation of the investigated virtual power plant connects heterogeneous building structures across a local distribution grid to exploit temporal mismatches in power consumption. In standalone operations, individual facilities frequently endure severe operational penalties, suffering from localized photovoltaic curtailment when generation exceeds immediate internal needs or being forced to procure high-priced electricity from the main utility grid during regional peak demand hours. By establishing formal energy-sharing protocols, the researchers structured a two-layer control hierarchy where local building loads hold first priority for any on-site solar generation, followed immediately by mutual-aid transfers to deficit buildings, local battery storage charging, external storage charging, and only finally main grid exports. Conversely, shortfalls draw progressively from local photovoltaic panels, local battery reserves, external peer storage, and lastly the external utility grid.

To rigorously examine this multi-facility framework, the authors formulated a comprehensive two-stage mathematical optimization scheme. Stage I establishes an optimal inter-building energy-sharing scheduling model over a discrete scheduling horizon, explicitly formulated to minimize the net operating expenses of the aggregated cluster. This objective function incorporates electricity purchasing and selling costs under seasonal time-of-use tariffs, photovoltaic operation and maintenance expenses, electrochemical energy storage system degradation penalties, and carbon-emission compliance costs calculated using a carbon-trading price of 50 CNY per metric ton of carbon dioxide alongside regional baseline grid-emission factors of 0.5703 metric tons of carbon dioxide per megawatt-hour. In addition, physical electricity transfers across the cluster account for a five percent intra-cluster transmission loss, modeled as an inter-building transmission efficiency of 0.95.

Crucially, Stage I departs from rigid, top-down curtailment strategies by explicitly embedding user comfort and convenience directly into mathematical operational constraints and economic penalty functions. The optimization accounts for flexible thermal loads governed by the Predicted Mean Vote index, a standard thermal comfort metric spanning from negative three for cold sensation to positive three for hot sensation, with zero denoting neutral thermal equilibrium. Indoor temperatures are allowed to vary within an acceptable deadband of plus or minus one degree Celsius without incurring penalty costs, whereas departures beyond this threshold generate monetary discomfort charges proportional to occupancy counts and calculated willingness-to-pay parameters. Simultaneously, schedulable electric vehicles, modeled with 80-kilowatt-hour battery packs and maximum charging limits of 8 kilowatts per time step, are governed by strict user-requirement constraints guaranteeing that departure states of charge reach at least 80 percent of maximum capacity while penalizing time and energy deviations.

Building upon the physical dispatch established in Stage I, Stage II resolves the complex problem of dividing the resulting financial gains through an asymmetric Nash bargaining framework. Traditional cooperative approaches frequently allocate revenues strictly according to gross power output or static baseline asset sizes, an approach that systematically undervalues active operational flexibility provided during critical peak-pricing intervals. To overcome these deficiencies, the investigators introduced a Composite Contribution Coefficient that quantifies three distinct behavioral dimensions: a baseline-contribution share reflecting long-term mutual-aid capability, a real-time energy-sharing contribution capturing dynamic kilowatt-hour transfers, and a demand-response performance share evaluating load curtailment and load shifting. In the baseline weighting structure, these components received weights of 0.4, 0.3, and 0.3, respectively, establishing the normalized bargaining power of each facility over their non-cooperative disagreement points.

The quantitative performance of the framework was evaluated using empirical electrical load datasets collected from three representative buildings in Shanghai, China, encompassing comprehensive 30-day observations across both summer and winter operational conditions. Photovoltaic output and baseline building electrical demands were predicted using bidirectional long short-term memory neural networks, achieving mean absolute percentage errors of 4.15 percent and 2.85 percent, respectively. Meanwhile, electric vehicle charging demands across fleets of 20 vehicles per building were forecast utilizing a spatio-temporal graph convolutional recurrent network, which exhibited a mean absolute percentage error of 6.23 percent. The underlying building profiles demonstrated substantial operational diversity: commercial buildings exhibited average demands of 841.76 kilowatts in summer and 1,344.28 kilowatts in winter, whereas office buildings averaged 179.29 and 218.93 kilowatts, and residential buildings averaged 236.86 and 296.31 kilowatts across the respective seasonal observation periods.

Simulation of the system-level operational scenarios revealed dramatic cost differentials across cooperative dispatch modes. Under Scenario 1, representing completely independent standalone facility operations without coordinated dispatch, the total virtual power plant operating cost reached 12,792.00 CNY per day. Transitioning to Scenario 2, which implemented centralized virtual power plant scheduling and demand response without inter-building energy sharing, reduced the daily cost to 8,728.19 CNY, representing a 31.77 percent reduction. When inter-building energy sharing was fully integrated alongside demand response in Scenario 3, the total daily cluster operating expense plummeted to 3,768.77 CNY per day. This achieved an aggregate cost reduction of 70.54 percent relative to independent operation and a 56.82 percent reduction compared to demand response alone, confirming the substantial economic value unlocked by peer-to-peer power transfers.

The evaluation of electric vehicle flexibility confirmed that actively integrating mobile battery storage yields substantial economic advantages provided that travel convenience remains safeguarded. Across three evaluated vehicle participation cases, operating without vehicle flexibility generated an electric-vehicle-related cost of 120.00 CNY per day, leaving user net profits at negative 2.00 CNY per vehicle. Enabling managed charging while meeting target satisfaction levels lowered fleet operating costs to 86.50 CNY per day, producing user net profits of 3.70 CNY per vehicle and generating 78.00 CNY per day in indirect utility purchase savings. Deeper participation accepting greater charging schedule and state-of-charge deviations further decreased vehicle operating expenses to 72.80 CNY per day and increased user profits to 19.25 CNY per vehicle, generating 195.00 CNY in indirect savings while illustrating the trade-off between user satisfaction and power system arbitrage.

When dividing the cooperative surplus generated by energy sharing, the proposed asymmetric Nash bargaining strategy significantly improved fairness and contribution alignment compared to conventional bargaining benchmarks. In a representative case distributing 2,007.18 CNY of cooperative revenue, traditional Nash bargaining allocated 749.06 CNY to the commercial building, 689.06 CNY to the office building, and 569.06 CNY to the residential building. Under the proposed asymmetric framework incorporating the Composite Contribution Coefficient, the commercial facility received 881.61 CNY—an uplift of 132.55 CNY reflecting its superior baseline and real-time mutual-aid support—while the office and residential structures received 640.34 CNY and 485.23 CNY, respectively. Despite reallocating payoffs toward higher contributors, the overall distribution fairness evaluated via Jain’s Fairness Index increased from 0.938 under traditional Nash bargaining to 0.986 under the proposed framework, closely approaching the ideal fairness ceiling of 1.000.

Computational testing demonstrated that the proposed two-stage framework scales efficiently for practical operational deployment. Evaluated across synthetic clusters scaling from 3 to 15 buildings using the Gurobi solver, the total optimization variables expanded from 504 to 2,520 while constraints increased from 171 to 759. Across this range, Stage I solution runtimes scaled in an approximately linear fashion from 0.0042 seconds to 0.0378 seconds with a verified 0.00 percent optimality gap. Meanwhile, because Stage II resolves cooperative revenue allocation via analytical formulations derived from Karush-Kuhn-Tucker optimality conditions without requiring exponential coalition enumeration, its execution consistently required less than 0.001 seconds. These runtimes comfortably satisfy the computational requirements necessary for hourly rolling dispatch in district-scale virtual power plant management.

Despite these robust operational gains, the authors highlighted key boundaries and simplifications governing the present study. The scheduling framework relies on an incentive-based demand response formulation with prescribed compensation parameters and thermal penalty functions rather than modeling consumers’ endogenous, behavioral price elasticities to retail time-of-use tariffs. Furthermore, intra-cluster electrical transmission losses were represented through a lumped 95 percent efficiency baseline rather than explicit physical power-flow modeling across verified distribution feeder line impedances and spatial distances. Future research is planned to expand the architecture by embedding both own-price and cross-period demand elasticity formulations, evaluating multi-year meteorological variations, and incorporating distributed optimization techniques suitable for very large, decentralized multi-energy networks.

Subject of Research: Virtual power plant optimal scheduling and cooperative revenue allocation in building clusters

Article Title: A Study on Energy-Sharing based Optimal Scheduling and Benefit Allocation for VPP Building Clusters via Asymmetric Nash Bargaining

Article References: Zhang, L., Li, J., Qian, F., Yang, Y., Zhao, H., Lu, X., & Ren, H. (2026). A Study on Energy-Sharing based Optimal Scheduling and Benefit Allocation for VPP Building Clusters via Asymmetric Nash Bargaining. Results in Engineering, 32, Article 113846. https://doi.org/10.1016/j.rineng.2026.113846

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113846

Keywords: virtual power plants, energy sharing, Nash bargaining, demand response, distributed energy resources, building energy management, electric vehicles, smart grids, Energy-Sharing, based, Optimal, Scheduling