This paper presents a novel method based on sparse representation classification (SRC) and random dimensionality reduction projection (RDRP) to classify electric power system fault types in real time. Each testing fault sample is firstly represented as an overcomplete sparse linear combination of training fault samples. Then RDRP is applied to extract fault features with reduced dimensionality and construct the sensing matrix of the sparse representation. Next, L1 minimization is used to calculate the sparse representation of the testing sample so that the fault type can be determined according to the minimum residual between the testing sample and its sparse representation. Simulation results show that RDRP is efficient to extract fault features and reduce dimensionality, and SRC achieves a high classification accuracy and a strong robustness to noise and disturbance, guaranteeing that this method can be used for on line fault detection and classification in large electric power systems.