Key Takeaways & Executive Findings
- •• • The WAIES cooperative operation reduced total system cost by 6.58% and carbon trading cost by 1.64% compared to independent operation, while achieving 100% renewable energy consumption. This demonstrates that cross-regional multi-energy sharing can simultaneously improve economic and environmental performance, a critical finding for scaling low-carbon energy networks. • • The asymmetric Nash bargaining model allocates profits proportional to each entity's contribution, with a deliberate bias toward energy suppliers. This design addresses fairness concerns in cooperative games, potentially increasing participation incentives and long-term stability of multi-energy sharing alliances. • • The two-stage robust-Nash optimization method, solved via ADMM and C&CG, ensures reliable decision-making under source-load uncertainty. Out-of-sample validation confirms its strategy adaptability, making it suitable for real-world deployment where renewable generation and demand forecasts are imperfect. • • The framework's scalability to large-scale interconnected energy systems is constrained by potential non-convexity in the bargaining function as the number of members increases, which could lead to negotiation infeasibility. This identifies a key research gap for extending the approach to urban or industrial-scale applications.
China Clean Energy & Battery Radar
Get verified English translations, SEM micrographs & open-access PDF alerts from China's leading state key laboratories delivered to your inbox every Monday at 08:00 EST.
Abstract
This study addresses the cooperative game problem of multi-energy sharing among cross-regional integrated energy systems (IESs) under source-load uncertainty. A wide-area IES (WAIES) multi-energy sharing cooperative operation model is constructed, incorporating electric-thermal-gas coupling, renewable generation, and energy conversion devices. To ensure fair profit distribution among resource-endowed entities, a Nash bargaining model based on asymmetric bargaining is proposed, decomposing the optimization into cooperative cost minimization and profit allocation subproblems. A day-ahead and real-time two-stage robust-Nash optimization method is developed to protect data privacy and mitigate uncertainty, solved via alternating direction method of multipliers (ADMM) and column-and-constraint generation (C&CG). Case studies demonstrate that compared to independent operation, the WAIES reduces total cost by 6.58%, carbon trading cost by 1.64%, and achieves 100% renewable energy consumption. The asymmetric bargaining mechanism correlates profit allocation with contribution, incentivizing cooperation while ensuring fairness. The two-stage robust optimization enhances strategy adaptability under uncertainty, validated through out-of-sample analysis. The framework shows potential for extension to urban agglomeration energy coordination and industrial park cascade optimization, though scalability challenges regarding convexity and negotiation feasibility in large-scale systems remain for future work.
1. Introduction
Existing multi-energy sharing mechanisms are predominantly confined to single integrated energy systems (IESs), failing to address cross-regional energy scheduling and the complex synergies required for wide-area coordination. Traditional cooperative game approaches, such as coalition games, often lack unique optimal solutions and suffer from fairness disputes, while conventional Nash bargaining models inadequately capture contribution disparities arising from heterogeneous resource endowments. Furthermore, source-load uncertainty from renewable generation and stochastic demand introduces dynamic imbalances that compromise the reliability of day-ahead scheduling and real-time operations. These limitations hinder the economic and low-carbon potential of interconnected energy networks.
This study proposes a robust-Nash optimization method based on asymmetric bargaining to overcome these bottlenecks. A wide-area IES (WAIES) cooperative operation model is established, integrating electric-thermal-gas coupling and multi-energy sharing. The asymmetric Nash bargaining model quantifies each entity's contribution, ensuring fair profit allocation and incentivizing cooperation. A two-stage robust optimization framework, solved via ADMM and C&CG, protects data privacy and enhances resilience against uncertainties. Case studies validate that the method reduces total cost by 6.58%, carbon trading cost by 1.64%, and achieves 100% renewable consumption, offering a scalable pathway for urban and industrial energy coordination.
Loading authentic research manuscript (Pages 1–5)...
HUANG Liyan, AI Xin, WANG Zhe (2026). Robust-Nash Optimization Method for Multi-Energy Sharing in Wide-Area Integrated Energy Systems Based on Asymmetric Bargaining. Acta Energiae Solaris Sinica. https://doi.org/10.19912/j.0254-0096.tynxb.202608_9693
Research & Educational Purpose Only: The translations, structured abstracts, analytical annotations, and data reports provided by SinoGreenTechare intended exclusively for academic research, internal corporate R&D, and educational benchmarking. They do not constitute formal engineering, chemical safety, legal, or professional advice.
Copyright & Intellectual Property Notice: Original copyright of the underlying source articles and experimental data remains with the respective authors, institutions, and original publishing journals. SinoGreenTech claims intellectual property only over its proprietary translations, analytical syntheses, and AEO structured enhancements in accordance with international fair use and academic citation principles.
Frequently Asked Questions
What are the failure mechanisms of the proposed robust-Nash optimization under extreme uncertainty scenarios?
The two-stage robust optimization considers worst-case realizations of renewable generation and load, ensuring feasibility within a predefined uncertainty set. However, if actual deviations exceed the set boundaries, the system may incur higher operational costs or violate constraints. The out-of-sample analysis confirms strategy adaptability, but extreme events beyond the uncertainty set could degrade performance. Future work should dynamically adjust uncertainty sets based on real-time data.
How does the asymmetric bargaining model ensure fair profit allocation compared to traditional Nash bargaining?
The asymmetric model weights each entity's bargaining power by its contribution to the coalition, quantified through energy supply, flexibility, or carbon reduction. This creates a positive correlation between contribution and profit share, with a slight bias toward energy suppliers to incentivize participation. In contrast, symmetric Nash bargaining assumes equal bargaining power, which may undercompensate critical contributors and destabilize cooperation.
What are the scalability bottlenecks when extending this framework to large-scale energy systems?
As the number of participating entities increases, the multi-energy coupling constraints grow exponentially, potentially rendering the bargaining function non-convex. This can lead to negotiation infeasibility or multiple equilibria, undermining the uniqueness of the Nash solution. Additionally, computational complexity of ADMM and C&CG escalates, requiring distributed algorithms with convergence guarantees for large-scale deployment.
What is the cost parity of the proposed method against conventional independent operation?
The WAIES cooperative operation reduces total system cost by 6.58% and carbon trading cost by 1.64% relative to independent operation. These savings stem from enhanced renewable utilization (100% consumption) and optimized multi-energy scheduling. The method achieves cost parity with legacy systems while providing additional environmental benefits, making it economically viable for wide-area deployment.
How does the two-stage robust optimization handle data privacy among participating entities?
The ADMM algorithm decomposes the optimization into subproblems solved locally by each entity, exchanging only limited boundary information (e.g., power/heat interchange) rather than full operational data. This preserves privacy while coordinating the coalition. The C&CG algorithm further ensures robust feasibility without centralizing sensitive data, addressing confidentiality concerns in multi-party energy sharing.
Related Chinese Research & Cross-Citations
Wind Turbine Gearbox Fault Diagnosis Method Based on Improved CNN-XGBoost Fusion Model Under Gramian Angular Difference Field
Gearbox failures account for 20–30% of total wind turbine faults and incur maintenance costs equivalent to 10–15% of overall turbine value. Conventional vibration diagnostic pipelines—complementary ensemble empirical mode decomposition with singular value energy spectrum, time-varying filtering empirical mode decomposition, and Teager energy spectrum analysis—remain bounded below 90% accuracy and depend on expert-driven feature engineering that is sensitive to non-stationary operating conditions and noise. This study proposes an intelligent diagnostic architecture that converts one-dimensional gearbox vibration signals into two-dimensional images via Gramian angular difference field (GADF) transformation, preserving intrinsic temporal correlation and time-frequency structure while exploiting matrix sparsity to suppress interference. An improved convolutional neural network (CNN) extracts multi-dimensional features: a convolutional block attention module (CBAM) is embedded in the convolutional layers to weight critical channels and focus on fault-sensitive spatial regions, and a modified βc-ACONC activation function replaces ReLU to mitigate neuron necrosis and enable selective activation. The extracted composite features are then fed into an XGBoost network whose hyperparameters are optimized by an improved sparrow search algorithm (ISSA). Validation on a laboratory wind turbine gearbox dataset yields diagnostic accuracy exceeding 99%, demonstrating robust fault identification capability under complex operating conditions.
Joint Forecasting of Wind and Photovoltaic Power Considering Complementarity
The inherent spatiotemporal complementarity between wind and solar resources offers a theoretical basis for improving renewable power forecasting accuracy. This study proposes a joint wind-photovoltaic (PV) power forecasting strategy that explicitly exploits this complementarity. A bidirectional long short-term memory (BiLSTM) neural network serves as the baseline forecasting model, and a novel sorting and comparative optimization (SCO) algorithm is developed to optimize the model's hyperparameters. The SCO algorithm ranks individuals in ascending order and compares adjacent fitness values to escape local optima, a known deficiency in conventional metaheuristics such as genetic algorithms and particle swarm optimization. For wind farms and PV plants exhibiting significant complementarity, the joint forecasting strategy first aggregates their power outputs, normalizes the combined signal, and then feeds it into the optimized BiLSTM model. Experimental results demonstrate that the proposed SCO-BiLSTM model reduces the eMAPE by 10.313% compared with PSO-BiLSTM. Furthermore, joint forecasting under SCO-BiLSTM lowers the eRMSE by 27.443% relative to standalone PV power forecasting. The study also establishes that forecasting accuracy improves with stronger wind-solar complementarity but degrades as the forecasting horizon extends. These findings confirm that exploiting complementarity in joint forecasting substantially enhances predictive performance for renewable energy integration.
Ultra-Short-Term Wind Power Forecasting Based on Fluctuation Continuation Scenario Identification
Existing ultra-short-term wind power forecasting methods exhibit limited performance due to insufficient extraction of fluctuation information and inadequate analysis of evolution patterns. This paper proposes an ultra-short-term wind power forecasting method based on fluctuation continuation scenario identification. First, the coupling mechanism of wind power fluctuations under multiple turbulence processes is investigated, and historical wind power dynamics are decoupled into a combination of nonlinear and linear fluctuation components. A fluctuation continuation concept is introduced, and the future continuation scale of wind power fluctuations is derived from nonlinear and linear decoupling parameters, thereby classifying fluctuation continuation scenarios. A sparse neural network (SNN) oriented to high-dimensional sparse features is constructed to identify historical fluctuation continuation scenarios, and ultra-short-term power forecasting is conducted separately for each scenario. Validation using measured wind speed and power data from three wind farms shows that, compared with baseline models, the proposed model improves root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) by at least 1.46%, 2.44%, and 14.67%, respectively, demonstrating superior accuracy and stability. The method addresses the limitations of signal decomposition techniques that lack physical interpretability and are sensitive to hyperparameters, and overcomes the high-dimensional sparsity challenges faced by traditional scenario identification models.
Multi-Classifier Open Adversarial Network for Rolling Bearing Fault Diagnosis in Wind Turbine Generator Systems
Rolling bearings in wind turbine generator systems operate under variable speed and load conditions that induce significant data distribution shifts between training and field data, while unknown fault modes absent from the source domain are frequently misclassified as known classes. This study proposes a multi-classifier open adversarial network (MCOAN) for open-set fault diagnosis. Within an adversarial domain adaptation framework, a K-way classifier and an additional K+1-way one-vs-all classifier independently estimate target-sample similarity to the source domain. These similarity scores drive a dynamic weighting mechanism that adaptively reweights target samples during open-set adversarial training and supplies per-sample dynamic thresholds for known/unknown discrimination, thereby promoting cross-domain alignment of shared-class features while suppressing negative transfer from unknown samples. A non-adversarial domain classifier is introduced to stabilize dynamic weight estimation. Validation on two datasets demonstrates high-precision shared-class distribution alignment and unknown-class recognition with favorable robustness. The method removes reliance on empirically preset thresholds that plague conventional open-set back-propagation approaches, where a fixed threshold of 0.5 in the binary cross-entropy adversarial loss provides no per-sample adaptivity. By coupling K-way and K+1-way similarity estimates, MCOAN achieves simultaneous known-class alignment and unknown-class separation without prior knowledge of the unknown-class cardinality, addressing a persistent bottleneck in wind turbine drivetrain condition monitoring where unanticipated bearing failure modes emerge under field conditions.
Unsupervised Automated Identification Method for Abnormal States of Wind Turbine Gearboxes
Addressing the scarcity of labeled data for training classification models in wind turbine planetary gearbox anomaly identification, this study proposes an unsupervised automated detection method. Log Mel-band energy features are extracted from raw vibration signals and fed into an unsupervised anomaly recognition model centered on a U-net autoencoder. A health-state threshold is established based on reconstruction error between model input and output, enabling anomaly identification. The method is validated using factory gearbox test data and operational data from a wind farm in Yangtouya, Shanxi. For factory gearboxes, dual validation is performed using a spectrum amplitude modulation-based signal processing method. Results demonstrate that the proposed method achieves 93.34% recognition accuracy on both factory and wind farm test sets, confirming its capability to automatically and correctly separate abnormal wind turbine gearboxes. The approach eliminates reliance on labeled fault data, offering a scalable solution for full-lifecycle health monitoring, from factory acceptance testing to in-service early anomaly detection, adaptable across different operating conditions and turbine models.
Improved Adaptive Super-Twisting Sliding Mode Control for Permanent Magnet Synchronous Motors
Adaptive super-twisting sliding mode control (ASTSMC) for permanent magnet synchronous motors (PMSM) suffers from prolonged convergence and insufficient disturbance rejection under complex operating conditions. This paper proposes an improved ASTSMC incorporating a fixed-time disturbance observer (FTDO). A power term is introduced into the adaptive super-twisting controller to accelerate convergence far from the origin, while the discontinuous sign function is replaced by a continuous h(s) function to mitigate chattering. The FTDO ensures disturbance estimation converges within a fixed time independent of initial states, overcoming the limitations of traditional and finite-time observers. The estimated disturbance is fed forward to the sliding mode controller for compensation, enhancing robustness. The FTDO design is based on an auxiliary state variable z and its derivative, with error dynamics analyzed via Lyapunov stability. Comparative simulations against conventional disturbance observers and sliding mode controllers validate the proposed strategy. The results demonstrate shorter convergence time, improved dynamic performance, and superior disturbance rejection, making the approach suitable for high-performance servo systems. The method addresses the critical need for robust, fast-response control in electric vehicles, rail transit, and aerospace applications where PMSM drives face significant uncertainties and external disturbances.