Vulnerability of the Largest Normalized Residual Statistical Test to Leverage Points

The largest normalized residual statistical test (LNRT) is claimed to have the ability to detect noncritical single or multiple interacting but nonconforming bad data. However, we show in this letter that this claim does not always hold true for bad leverage points. Specifically, we prove that while a single noncritical and nonleverage measurement that is corrupted by a sufficiently large gross error is likely to be detected, the same measurement in a position of leverage and corrupted by the same gross error is unlikely to be detected. Furthermore, we show that multiple noncritical bad leverage points that are topologically adjacent to each other naturally form one or several groups of interacting bad data, which may cause the LNRT to fail. Since leverage points are common in actual power systems, the LNRT is doomed to frequently fail to detect bad data. Simulation results carried out on IEEE 30-bus system validate our theoretical results.