Abstract
The rapid proliferation of renewable energy sources has introduced multi-layered uncertainty into modern power system operation, challenging conventional deterministic and stochastic optimization frameworks. To address this complexity, this study proposes a deep learning–assisted distributionally robust optimization (Deep-DRO) framework designed to enhance both economic efficiency and operational reliability under uncertainty. The model integrates a hierarchical coordination architecture, wherein deep learning modules infer the probabilistic structure of uncertain variables–such as solar irradiance, wind availability, and load fluctuation–while the DRO layer enforces system-wide robustness through an adaptively reshaped ambiguity set. The learning-assisted ambiguity reconstruction enables the optimization to dynamically adjust conservativeness, improving the tradeoff between cost, reliability, and renewable utilization. Methodologically, the proposed framework employs a multi-agent dispatch structure consisting of three decision layers–county, feeder, and distributed energy resource (DER)–each learning distinct policy mappings through reinforcement-guided coordination. Deep networks trained on high-resolution meteorological and operational data estimate scenario distributions, while the robust optimization core minimizes expected cost and reliability penalties under distributional ambiguity. The resulting hybrid system seamlessly couples data-driven forecasting and model-based optimization, bridging the gap between predictive intelligence and operational robustness. To ensure scalability and interpretability, convergence diagnostics, sensitivity analyses, and cost decomposition studies are performed across multiple test systems and uncertainty scenarios. Simulation results on a benchmark multi-region distribution network demonstrate substantial performance gains. Compared to conventional DRO, the Deep-DRO model reduces total operational cost by 11.0–13.5%, improves reliability indices from 0.864 to 0.911, and raises renewable utilization from 85.6% to 89.7%. The integrated deep learning mechanism effectively captures latent correlations among stochastic parameters, enabling the system to maintain resilience even under 30% higher uncertainty variance. Furthermore, carbon emissions decline by 28.6% relative to baseline, confirming that the proposed method achieves an intrinsic balance between economic optimization and environmental sustainability. The analysis reveals that hierarchical learning fosters adaptive coordination among agents, while the robust layer guarantees performance consistency across uncertain conditions. The study thus advances a generalizable paradigm for intelligent, risk-aware energy management, offering theoretical and practical implications for future power system restoration, smart grid autonomy, and sustainable dispatch design.
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Data availability
The datasets generated during and/or analysed during the current study are not publicly available due to conflict of interest but are available from the corresponding author on reasonable request.
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Funding
This work was supported by the 2025 Science and Technology Project of State Grid Henan Electric Power Company (5217L0250006).
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Yongle Zheng conceived the study, designed the overall Deep-DRO framework, and supervised the methodological development and system modeling. Huixuan Li developed the deep learning modules, including the GNN–Transformer hybrid forecasting model, and contributed to the uncertainty analysis and data preprocessing. Shiqian Wang implemented the hierarchical multi-agent reinforcement learning architecture and carried out the training, convergence analysis, and robustness evaluation. Zhongfu Tan contributed to the mathematical formulation of the distributionally robust optimization layer and supported theoretical validation and sensitivity studies. Xiaoliang Jiang conducted the case studies, prepared simulation datasets, and performed comparative experiments across Baseline, Stochastic, DRO, and Deep-DRO models. Peng Li assisted in the design of numerical experiments, result interpretation, and the development of reliability and emission-related performance indicators. Yijun Jiang (corresponding author) coordinated the project, refined the optimization strategy, guided the integration of learning modules with robust optimization, and provided overall technical supervision. Hongkai Zhang contributed to manuscript writing, figure preparation, and revisions, and supported the interpretation of technical findings and their practical implications. All authors reviewed and approved the final manuscript.
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Zheng, Y., Li, H., Wang, S. et al. Multi-agent coordination and uncertainty adaptation in deep learning–assisted hierarchical optimization for renewable-dominated distribution networks. Sci Rep (2026). https://doi.org/10.1038/s41598-026-35945-0
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DOI: https://doi.org/10.1038/s41598-026-35945-0
