This study solves the problem of accurate detection of internal faults and classification of transients in a 5-bus interconnected system for Phase Angle Regulators (PAR) and Power Transformers. The analysis prevents mal-operation of differential relays in case of transients other than faults which include magnetizing inrush, sympathetic inrush, external faults with CT saturation, capacitor switching, non-linear load switching, and ferroresonance. A gradient boosting classifier (GBC) is used to distinguish the internal faults from the transient disturbances based on 1.5 cycles of 3-phase differential currents registered by a change detector. After the detection of an internal fault, GBCs are used to locate the faulty unit (Power Transformer, PAR series, or exciting unit) and identify the type of fault. In case a transient disturbance is detected, another GBC classifies them into the six transient disturbances. Five most relevant frequency and time domain features obtained using Information Gain are used to train and test the classifiers. The proposed algorithm distinguishes the internal faults from the other transients with a balanced accuracy of 99.95%. The faulty transformer unit is located with a balanced accuracy of 99.5% and the different transient disturbances are identified with a balanced accuracy of 99.3%. Moreover, the reliability of the scheme is verified for different rating and connection of the transformers involved, CT saturation, and noise levels in the signals. These GBC classifiers can work together with a conventional differential relay and offer a supervisory control over its operation. PSCAD/EMTDC software is used for simulation of the transients and to develop the two and three-winding transformer models for creating the internal faults including inter-turn and inter-winding faults.