Resilient distributed economic dispatch for cyber–physical power systems considering carbon emissions trading and false data injection attacks

The credible intermediate exchange data are the cornerstone of solving distributed low-carbon economic dispatch (ED) optimization problems for cyber–physical power systems (CPPSs). Unfortunately, the intermediate exchange data easily suffer from false data injection attacks (FDIAs), which will inevitably undermine the authenticity of the computation results, producing an inaccurate distributed dispatch strategy and further having adverse effects on both carbon emissions and operating costs. To address the problem, this paper proposes a novel resilient distributed ED model considering carbon emissions trading (CET) for CPPSs under FDIAs. First, before analyzing the impact of intermediate exchange data compromised by FDIAs on distributed ED, an attack-free ED model with CET is established by combining carbon incentive into the existing multi-period time-coupled models, which is solved by a fully distributed algorithm to produce the normal intermediate exchange and observation data. Second, to address the incorrect compensation data problem from the existing single-layer detection mechanism based on the assumption of completely credible observation data, a double-layer detection mechanism and the corresponding data compensation strategy are designed, while the convergence of fully distributed algorithm based on the correctly compensated data is theoretically proved. Third, to achieve stable operation of CPPSs under frequent FDIAs, a credibility-based isolation mechanism is proposed, in which agent credibility is quantified by a state health score within the closed interval [0,1], instead of the existing credibility evaluation methods (i.e., binary logic). Consequently, after isolating low credibility agent, a reconfiguration-based response strategy is proposed to maintain stable operation of CPPSs. Finally, the experimental results confirm the feasibility and effectiveness of the proposed method.