Privacy-Preserving Distributed Optimal Economic-Emission Dispatch Over Directed Graphs

Distributed dispatch algorithms offer robustness and flexibility but also elevate the potential for privacy disclosure when addressing various economic dispatch problems. To address such a concern, one introduces a privacy-preserving distributed optimization algorithm in this paper, specifically tailored for solving the economic-emission dispatch (EED) problem over directed graphs. The EED algorithm aims to minimize operating costs and carbon emissions of distributed generators (DGs) while ensuring the balance between power supply and demand. Specifically, a new kind of distributed EED algorithms incorporating the state decomposition mechanism to protect local outputs and cost coefficients is developed and utilized. Moreover, the convergence of the algorithm is rigorously demonstrated by using tools from eigenvalue perturbation theory. The privacy-preserving performance is confirmed by calculating the gap between the actual value and the inference value by external eavesdroppers. Furthermore, the existence of this gap ensures the preservation of both outputs and cost coefficients, which indicates that the privacy information of each node is protected. Finally, simulation experiments on the IEEE 39-bus system illustrate the effectiveness of the designed algorithms.