Sustainable Energy Systems Through Fair Carbon Pricing: A Shapley Value-Based Optimization Framework

Jiyong Li (), Huang Hao, Xiaoping Xiong, Jiajia Chai, Hanzhong Cui, Haoyuan Li, Zhiliang Cheng and Chen Ye
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Jiyong Li: School of Electrical Engineering, Guangxi University, Nanning 530004, China
Huang Hao: School of Electrical Engineering, Guangxi University, Nanning 530004, China
Xiaoping Xiong: School of Electrical Engineering, Guangxi University, Nanning 530004, China
Jiajia Chai: China Resources New Energy (Tengxian) Co., Ltd., Wuzhou 543300, China
Hanzhong Cui: China Resources New Energy (Tengxian) Co., Ltd., Wuzhou 543300, China
Haoyuan Li: China Resources New Energy (Tengxian) Co., Ltd., Wuzhou 543300, China
Zhiliang Cheng: School of Electrical Engineering, Guangxi University, Nanning 530004, China
Chen Ye: School of Electrical Engineering, Guangxi University, Nanning 530004, China

Sustainability, 2025, vol. 17, issue 22, 1-38

Abstract: Sustainable energy systems necessitate an equitable distribution of carbon burdens among stakeholders. This paper proposes a Shapley value-based carbon pricing mechanism embedded in a dual-layer Stackelberg framework, where the upper layer optimizes generation schedules and carbon prices, while the lower layer coordinates demand response strategies. The approach introduces several key innovations, including a Shapley allocation method that enhances fairness (achieving a Jain index of 0.94 compared to 0.78 in baselines), multi-dimensional dynamic pricing, and an improved ADMM algorithm that reduces computational demands by 34.2%. Validation on the IEEE 33-node test system yields a 27.5% reduction in operational costs (from USD 1.952 M to 1.415 M), a 17.8% decrease in emissions, and 97.8% integration of renewable energy sources. Overall, this framework promotes the transition to sustainable energy systems while upholding principles of equity.

Keywords: integrated energy system; two-tier optimization; Stackelberg game; carbon trading; dynamic carbon pricing; Shapley value; demand response; improved ADMM (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2025
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