This paper proposes methods to identify 40 different types of internal faults in an Indirect Symmetrical Phase Shift Transformer (ISPST). The ISPST was modeled using Power System Computer Aided Design (PSCAD)/ Electromagnetic Transients including DC (EMTDC). The internal faults were simulated by varying the transformer tapping, backward and forward phase shifts, loading, and percentage of winding faulted. Data for 960 cases of each type of fault was recorded. A series of features were extracted for a, b, and c phases from time, frequency, time-frequency, and information theory domains. The importance of the extracted features was evaluated through univariate tests which helped to reduce the number of features. The selected features were then used for training five state-of-the-art machine learning classifiers. Extremely Random Trees and Random Forest, the ensemble-based learners, achieved the accuracy of 98.76% and 97.54% respectively outperforming Multilayer Perceptron (96.13%), Logistic Regression (93.54%), and Support Vector Machines (92.60%).