False data injection attacks (FDIAs) can bypass conventional bad data detection methods. Recently developed FDIA detection methods based on statistical consistency of measurement values may not work effectively when false data do not significantly deviate from historical trends. They may also mistakenly treat actual power grid events as FDIAs. In this paper, a highly discriminative FDIA detector named the ${k}$ -smallest residual similarity ( ${k}$ SRS) test is proposed. The method is based on the rationale that perfect FDIAs can hardly be achieved in AC state estimation, and real-world imperfect FDIAs always lead to subtle changes in the probability distributions of measurement residuals. Therefore, the statistical consistency of measurement residuals can be carefully portrayed to detect practical FDIAs in AC state estimation. Herein, the Jensen-Shannon distance (JSD) is used to precisely quantify the similarity of measurement residual distributions. Simulations on the IEEE 30-bus system demonstrate that the proposed method can achieve high detection rates and low false alarm rates under a variety of conditions where existing methods do not yield satisfactory results.