Distributed electricity–carbon co-optimization of hydrogen energy storage microgrids with dynamic laplace perturbation and model predictive control

Zhongzheng Li, Mengke Liao, Yan Wang, Ruixuan Zhang, Jiawen Sun and Hua Zheng

PLOS ONE, 2026, vol. 21, issue 9, 1-51

Abstract: Hydrogen energy storage microgrids can improve renewable-energy accommodation and cross-energy flexibility, while repeated boundary-variable exchange in distributed scheduling may expose private operating information. This paper develops a privacy-aware electricity–carbon co-optimization framework that integrates day-ahead distributed clearing with intra-day model predictive control (MPC). The day-ahead model coordinates electricity, heat, hydrogen conversion, battery storage, and thermal storage while accounting for direct gas-boiler emissions and indirect emissions associated with imported electricity. A dynamically decaying Laplace mechanism is incorporated into the alternating direction method of multipliers (ADMM), and privacy performance is evaluated through finite-transcript privacy-budget accounting and reconstruction-based leakage analysis. Compared with fixed Laplace noise, the dynamic mechanism exhibits a higher baseline mean leakage-risk score (0.67 versus 0.58), but reduces the centralized cost gap from 2.85% to 0.94% and the number of iterations from 50 to 38. Matched-condition tests further show lower cost gaps at equal leakage risk and lower leakage risk at equal cost gap. An inverse-variance reconstruction attack reveals increased information exposure during later iterations. Meanwhile, the intra-day MPC maintains feasible multi-energy operation under the tested forecast errors. The base-case operational emissions are 2.09 t CO2, and the carbon-parameter sensitivity analysis shows a smooth variation in cleared cost. The results demonstrate the coordinated economic, privacy, and convergence characteristics of the proposed scheduling framework.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0350884

DOI: 10.1371/journal.pone.0350884

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