Stackelberg Game-Based Two-Stage Operation Optimization Strategy for a Virtual Power Plant: A Case Study

With the rapid development of renewable energy technologies, numerous distributed energy resources (DERs) have been integrated into power systems. How to fully exploit renewable energy while maintaining the stable operation of power systems remains an urgent challenge. Furthermore, the diversity of DERs’ ownership requires scheduling approaches that account for the distinct interests and characteristics of multiple stakeholders. To address these challenges, this study introduces a two-stage operational optimization framework for the virtual power plant (VPP), which is grounded in a Stackelberg game model. This strategy innovatively combines two conventional control methods: the day-ahead stage employs direct control for global pre-scheduling, leveraging its cost optimization capability; the intraday stage utilizes dynamic pricing to guide prosumers, tapping into DERs’ flexibility while accommodating their individual energy usage preferences. The Stackelberg game is resolved through a tiered solution methodology employing particle swarm optimization (PSO). To enhance solution efficiency, a Kriging surrogate model is introduced to replace the prosumers’ models, significantly reducing the computational burden of the PSO. Case studies demonstrate that the proposed strategy can balance operating costs and energy usage preferences, and the proposed solution approach can significantly enhance solution efficiency.

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Publication Details

Journal
Energies
Published
2026-02-05
DOI
https://doi.org/10.3390/en19030842
Primary Topic
Smart Grid Energy Management
Type
article
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article

Stackelberg Game-Based Two-Stage Operation Optimization Strategy for a Virtual Power Plant: A Case Study

Boyu Xue, Hongbo Zou, J. H. Chen, Fushuan Wen et al.
Energies
Smart Grid Energy Management
article

Stackelberg Game-Based Two-Stage Operation Optimization Strategy for a Virtual Power Plant: A Case Study

Boyu Xue, Hongbo Zou, J. H. Chen, Fushuan Wen, Yuhong Luo
article en

Abstract

With the rapid development of renewable energy technologies, numerous distributed energy resources (DERs) have been integrated into power systems. How to fully exploit renewable energy while maintaining the stable operation of power systems remains an urgent challenge. Furthermore, the diversity of DERs’ ownership requires scheduling approaches that account for the distinct interests and characteristics of multiple stakeholders. To address these challenges, this study introduces a two-stage operational optimization framework for the virtual power plant (VPP), which is grounded in a Stackelberg game model. This strategy innovatively combines two conventional control methods: the day-ahead stage employs direct control for global pre-scheduling, leveraging its cost optimization capability; the intraday stage utilizes dynamic pricing to guide prosumers, tapping into DERs’ flexibility while accommodating their individual energy usage preferences. The Stackelberg game is resolved through a tiered solution methodology employing particle swarm optimization (PSO). To enhance solution efficiency, a Kriging surrogate model is introduced to replace the prosumers’ models, significantly reducing the computational burden of the PSO. Case studies demonstrate that the proposed strategy can balance operating costs and energy usage preferences, and the proposed solution approach can significantly enhance solution efficiency.

EnergiesVol. 19(3)
China Three Gorges University (CN), Sanya University (CN), Zhejiang University (CN)
Affordable and clean energy
Openalex Percentile: Top 66%
Smart Grid Energy Management
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Stackelberg Game-Based Two-Stage Operation Optimization Strategy for a Virtual Power Plant: A Case Study — Boyu Xue, Hongbo Zou, et al. · Energies (2026) | TGRS Research Map | TGRS