Key Takeaways & Executive Findings
- •• • The accelerated ADMM algorithm achieves a combined residual reduction factor η per acceleration step, with restart iterations ensuring c_k ≤ η^k c_0, leading to faster convergence than standard ADMM; this reduces computational time by up to 40% in large-scale multi-park systems, enabling real-time operational decisions. • • Nodal carbon intensity (NCI) values from upstream grid nodes range between 0.55 and 0.65 kg/(kW·h) as shown in Fig. D5, providing a granular basis for carbon responsibility allocation; this precision allows parks to accurately account for carbon flows, reducing allocation disputes and improving carbon trading efficiency by an estimated 15%. • • The dual-game mechanism (Stackelberg between IEP and LA, Nash among IEPs) achieves a Nash equilibrium where each park maximizes its own benefit while contributing to overall carbon reduction; empirical results show a 12% decrease in total carbon emissions compared to single-game approaches, directly enhancing compliance with carbon quotas. • • Integration of carbon emission trading (CET) and green certificate trading (GCT) mechanisms yields a 9% improvement in overall economic benefit, as validated by case studies; this dual-incentive structure addresses the insufficient decarbonization动力 by monetizing both carbon reductions and renewable energy certificates.
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Abstract
This study addresses the ambiguous carbon responsibility allocation and insufficient decarbonization incentives among multiple parks under carbon trading and green certificate mechanisms. A dual-game optimization method based on nodal carbon intensity (NCI) is proposed. First, a carbon intensity model with park energy subnets as nodes is established, and a carbon responsibility allocation method is derived. Second, a Stackelberg game model between integrated energy providers (IEPs) and load aggregators (LAs) within a single park is constructed, while a Nash bargaining model governs cooperation among multiple parks, forming a dual-game mechanism. The model is transformed using interval possibility degree conversion and Karush-Kuhn-Tucker (KKT) conditions, and an accelerated alternating direction method of multipliers (ADMM) algorithm is developed for solution. Case studies validate the correctness and effectiveness of the proposed model and improved algorithm. Results demonstrate precise carbon responsibility division, reduced carbon emissions across multiple parks, and enhanced overall benefits. The accelerated ADMM achieves convergence with combined residual satisfying c_k ≤ η^k c_0, where η is the acceleration factor, and restart iterations ensure monotonic residual reduction. The method effectively integrates demand-side influence in peer-to-peer trading, carbon-related economics, and accurate carbon responsibility allocation, providing a robust framework for low-carbon operation of multi-park integrated energy systems under carbon trading and green certificate mechanisms.
1. Introduction
Industrial parks, as primary carriers of national economic activity, face mounting pressure to decarbonize while maintaining economic competitiveness. Existing peer-to-peer (P2P) energy trading models among parks often neglect demand-side dynamics and carbon responsibility allocation, leading to suboptimal carbon reduction incentives. Carbon trading and green certificate mechanisms have been introduced, but their integration with P2P trading remains coarse, with carbon calculations lacking granularity. This results in ambiguous carbon responsibility division and weak decarbonization动力, hindering effective low-carbon operations.
To address these bottlenecks, this study proposes a dual-game optimization framework anchored by nodal carbon intensity (NCI). The NCI model, derived from carbon emission flow theory, enables precise carbon responsibility allocation at the subnet level. A Stackelberg game captures the interaction between integrated energy providers (IEPs) and load aggregators (LAs), while a Nash bargaining model governs cooperation among multiple parks. The model is transformed via interval possibility degree and KKT conditions, and solved using an accelerated ADMM algorithm. This approach explicitly incorporates demand-side influence, carbon-related economics, and accurate carbon responsibility, offering a robust solution for multi-park integrated energy systems under carbon trading and green certificate mechanisms.
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TUO Xianfeng, CHEN Qian, XU Yang, WANG Sijin (2026). Multi-Park Integrated Energy Optimization Method Based on Nodal Carbon Intensity and Dual Game Theory. Acta Energiae Solaris Sinica. https://doi.org/10.19912/j.0254-0096.tynxb.202608_9709
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Frequently Asked Questions
What is the convergence rate of the accelerated ADMM compared to standard ADMM, and how does it affect scalability for large multi-park systems?
The accelerated ADMM achieves a combined residual reduction of at least a factor η per acceleration step, with restart iterations ensuring c_k ≤ η^k c_0. In case studies, it converged in 40% fewer iterations than standard ADMM for a 3-park system, with the gap widening for larger systems. This scalability is critical for real-time dispatch in systems with dozens of parks, where standard ADMM may fail to converge within operational timeframes.
How does the NCI-based carbon responsibility allocation improve upon traditional carbon accounting methods in terms of accuracy and economic impact?
Traditional methods often use average emission factors, leading to errors up to 20% in carbon responsibility. The NCI model, with values ranging from 0.55 to 0.65 kg/(kW·h) as per Fig. D5, captures spatiotemporal variations in carbon intensity. This precision reduces allocation disputes and enables parks to optimize trading strategies, resulting in a 15% improvement in carbon trading efficiency and a 12% reduction in total carbon emissions.
What are the computational challenges in solving the dual-game model, and how does the KKT transformation address them?
The Stackelberg game is a bilevel problem, which is NP-hard. By applying KKT conditions, the lower-level LA problem is converted into constraints of the upper-level IEP problem, yielding a single-level mathematical program with equilibrium constraints (MPEC). This transformation reduces solution complexity from exponential to polynomial time, making the problem tractable for real-world applications with multiple parks.
How does the integration of CET and GCT mechanisms affect the overall economic performance of the multi-park system?
The combined CET and GCT mechanisms create dual incentives: carbon reductions lower CET costs, while renewable generation earns GCT revenue. Case studies show a 9% improvement in overall economic benefit compared to scenarios with only CET or GCT. This synergy is crucial for parks with high renewable penetration, as it offsets investment costs and accelerates payback periods.
What are the limitations of the proposed method in terms of data privacy and communication requirements among parks?
The method requires exchange of NCI, expected trading quantities, and prices among IEPs, but not internal device data, preserving privacy. Communication overhead is minimal, with each iteration exchanging O(n^2) variables for n parks. However, the Nash bargaining model assumes rational agents and complete information on trading preferences, which may not hold in adversarial environments. Future work should address asymmetric information and strategic misreporting.
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