As a kind of non-stationary signal, the electrical load curve can be regarded as composed of a wide-stationary low-frequency component and a non-stationary high-frequency component. Aiming at the temporal multi-granularity characteristics of load data, a controllable clustering model of the electrical load curve based on variational mode decomposition and fast search of the density peak is proposed. The original load curve is decomposed into three modal components of low-, intermediate-, and high-frequency by variational mode decomposition. First, the low-frequency modal components of the load curve are used to achieve coarse-grained clustering among clusters. Then, the intermediate-frequency components are superimposed on the subclasses to achieve fine-grained clustering within the cluster. The validity of the proposed model is verified using the OpenEI data set and compared with different clustering algorithms for the direct clustering of the original load data. The experimental results show that the model can achieve reasonable clustering at different time granularities. This work is supported by the National Natural Science Foundation of China (No. 61763049) and the Key Project of Applied Basic Research of Yunnan Province (No. 2018FA032).