Reputation-Based Optimization for Distributed Energy Management Under Persistent DoS Attacks

The distributed energy management (DEM) is of significance for smart grids due to the growing concern over potential cyber threats. This study delves into a multiobjective DEM problem that encompasses economic and environmental costs, as well as transmission losses, while also considering the impact of persistent Denial-of-Service (DoS) attacks. To tackle this challenge, a novel distributed optimization algorithm over a digraph is proposed, leveraging a zeroth-order scheme to handle unavailable gradients and incorporating momentum terms to provide accurate descent directions. The theoretical analysis demonstrates the algorithm's ability to achieve a linear convergence rate while ensuring real-time maintenance of decision variables within the feasible domain. Building on this, a novel reputation-based resilient DEM framework is introduced to address scenarios involving persistent DoS attacks. This framework calculates a reputation index for each communication link to monitor its reliability. Considering the impact of attacked links on network connectivity and their reputation indexes, corresponding strategies are devised. Specifically, if an attacked link disrupts network connectivity and its reputation index falls below the threshold, a connectivity restoration optimization algorithm is activated to reconstruct links, minimizing communication costs and alleviating information congestion. Finally, the effectiveness of the proposed algorithm and framework is validated through numerical simulations.