Distributed electricity–carbon co-optimization of hydrogen energy storage microgrids with dynamic laplace perturbation and model predictive control
- 1Economic and Technical Research Institute of State Grid Xinjiang Electric Power Co., Ltd., Urumqi, Xinjiang, China
- 2School of Electrical and Electronic Engineering, North China Electric Power University, Beijing, China
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.
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BibTeX
@article{li2026distributed,
title = {{Distributed electricity–carbon co-optimization of hydrogen energy storage microgrids with dynamic laplace perturbation and model predictive control}},
author = {Zhongzheng Li and Mengke Liao and Yan Wang and Ruixuan Zhang and Jiawen Sun and Hua Zheng},
journal = {PLOS One},
year = {2026},
month = sep,
doi = {10.1371/journal.pone.0350884},
url = {https://doi.org/10.1371/journal.pone.0350884},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Distributed electricity–carbon co-optimization of hydrogen energy storage microgrids with dynamic laplace perturbation and model predictive control
AU - Zhongzheng Li
AU - Mengke Liao
AU - Yan Wang
AU - Ruixuan Zhang
AU - Jiawen Sun
AU - Hua Zheng
PY - 2026
DA - 2026/09/23
JO - PLOS One
DO - 10.1371/journal.pone.0350884
UR - https://doi.org/10.1371/journal.pone.0350884
AB - 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.
SN - 1932-6203
ER -