With the wide application of smart meter, the power grid has accumulated a large number of original power consumption data. However, data loss still exists in power consumption information acquisition equipment under complex working environment. This article fills in the missing original electricity consumption data while fully considering the influence of Gaussian noise. Firstly, the original electricity consumption data matrix is obtained by rearranging the independent user data sequence, and the ideal electricity consumption data matrix is replaced by nonnegative matrix factorization; Secondly, F norm and kernel norm are selected to regularization Gaussian noise and ideal power consumption data with low rank characteristics to build optimization models; Finally, based on the block coordinate minimum algorithm framework, the matrix factors obtained from non negative matrix factorization are alternately updated using EM algorithm and direct method, effectively achieving accurate interpolation of data. Simulation analysis and experimental results have verified the effectiveness and accuracy of the algorithm.