<p>Comparison with representative studies.</p>

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.