Based on EEMD and RMS, a method of abnormal power consumption detection by using a high-dimensional statistical index was proposed. Firstly, power users were divided into typical load types based on the density space clustering algorithm. For each load type, EEMD was used to transform the energy consumption curve into the high-dimensional empirical mode function group, and then Chebyshev polynomial index in the random matrix theory was used to monitor the abnormal behavior. The high-dimensional statistical index was constructed to judge abnormal power consumption. The algorithm in this paper has general applicability to multi-source load and a good discriminating effect.