Multi-Objective Evolutionary Optimization for Worst-Case Analysis of False Data Injection Attacks in the Smart Grid

False data injection attacks (FDIA) have drawn significant interests recently after the discovery of vulnerabilities of bad data detectors (BDD) deployed in the smart grid. While most FDIA analyses focused separately on the aspects of stealthiness, knowledge, resources, or expected consequences of the attack, few have evaluated the relationship and tradeoffs among these factors to identify the worst-case scenario in realistic operations. To fill the gap, this paper investigates a strictly stealthy FDIA scheme with multi-objective evolutionary optimization, which could compromise a small set of meters to inflict large impacts on the smart grid in realistic scenarios. Compared with existing attack schemes that relax the problem with the l(1)-norm, the paper introduced the Improved Strength Pareto Evolutionary Algorithm (SPEA2) as the solver to directly obtain the l(0)-sparse attack vector. Meanwhile, the unobservability is ensured by not only bypassing the BDD but also satisfying the physical and operational constraints. A three-step constraint handling technique is also proposed for the SPEA2 to ensure the stealthiness and improve the efficiency of attack vector identification in the worst-case scenario. Simulation results on the IEEE 14-bus and 30-bus systems demonstrate that the new multi-objective formulation discovers highly sparse attack vectors with significant impacts on the system without triggering immediate emergency responses. The influence of alternative objectives and constraints has also been evaluated to reveal the trade-offs among the attack's stealthiness, sparsity, and impact. The results are expected to facilitate better-informed risk assessment and mitigation with refined worst-case understandings.