In order to maintain optimal load balancing of transformers in the power distribution systems, the hierarchical clustering methods are investigated for phase identification purposes. This method is based on one minus linear correlation and Euclidean pair-wise distance measures to cluster loads that are on the same phase. The phases are assigned to loads based on a majority vote of phase labels within each cluster. The hierarchical clustering methods are compared with other clustering methods such as k-means clustering for various loads connected to different phases. The Electric Power Research Institute's (EPRI) ckt5 test circuit is used to generate a synthetic dataset of single-phase load voltage magnitude measurements. Real power load profiles generated from uniform white noise is used with the OpenDSS software to generate the load voltage magnitude measurements. The accuracy and the running time of the proposed hierarchical clustering are comparable with the k-means algorithm.