In order to further improve the user experience of power system customers, and aiming at the problems of poor optimization ability, lack of compactness and difficulty in solving the optimal number of clusters, a Gaussian mixture clustering algorithm combining elbow method and Expectation-Maximization (EM) was proposed, which can mine the potential information in a large number of customer data. The good clustering results were obtained by EM algorithm iteration. Aiming at the shortcoming of the traditional Gaussian mixture clustering algorithm that needs to obtain the number of user clusters in advance, the number of customer clusters was reasonably found by using elbow method. The case study shows that compared with hierarchical clustering algorithm and K-Means algorithm, the proposed algorithm has the increase of both FM (Fowlkes-Mallows) and AR (Adjusted-Rand) indexes more than 10%, and the decrease of Compactness Index (CI) and Degree of Separation (DS) less than 15% and 25% respectively. It can be seen that the performance of the algorithm is greatly improved.