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

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.