Secure Consensus-Based Resilient Distributed Energy Management With Privacy Preservation of Cyber-Physical Micro-Grid

Abstract

Due to privacy preservation and cyber attack, it brings a great challenge to energy management of cyber-physical micro-grid. To address those issues, this paper proposes a privacy preservation based resilient consensus algorithm (PPRCA). To avoid privacy disclosure, a privacy mechanism is developed by integrating dimension expansion with time-varying noise injection. Unlike traditional methods that sacrifice optimality for privacy, this approach strictly satisfies the ( $\epsilon, \sigma $ )-data-privacy standard while theoretically guaranteeing convergence to the exact global optimum. To defend against dishonest nodes without relying on trusted nodes, a distributed detection mechanism is designed based on the algebraic conservation and statistical consistency of the consensus states. By establishing a dual-validation protocol that cross-checks the sum of decomposed sub-states and the statistical decay properties of injected noise, nodes can identify and isolate dishonest nodes. Additionally, the theoretical analysis confirms the convergence and consensus of the algorithm, and the error bounds in the presence of undetectable dishonest nodes are rigorously analyzed. Comprehensive simulation evaluations on the IEEE 39-bus system and 118-bus system further validate the significant performance in terms of convergence and optimality. Note to Practitioners—This paper is motivated by the practical security challenges in the energy management of cyber-physical micro-grid, specifically regarding privacy leakage and influence of dishonest nodes. Existing solutions often face a trade-off between privacy and optimality or rely on trusted nodes. This paper proposes a privacy preservation based resilient consensus algorithm. It employs a dimension expansion and noise injection mechanism to ensure strict privacy without compromising the exact global optimum. Furthermore, a distributed detection protocol is designed to identify dishonest nodes based on algebraic conservation, eliminating the need for trusted reference nodes. Experimental results on the IEEE 39-bus system and 118-bus system validate the effectiveness of the algorithm in maintaining system stability and optimality under attacks. This approach offers a robust solution for secure smart grid operations, and future work will extend this framework to asynchronous communication environments.