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This paper investigates the performance of differential protection of power transformers in the presence of internal faults, external faults, and cross-country faults in the presence of current transformers saturation, which is one of the main innovations of this study. Today, detection and discrimination of cross-country faults from other disturbances are one of the most important challenges facing protection engineers. Therefore, in this study, maximum overlap discrete wavelet transform has been used in order to accurately detect and classify these disturbances based on the extraction of energy coefficient indices of superior features. First, the cross-country faults, internal faults and external electrical faults, and inrush current phenomenon on the system under study in the EMTP software are simulated and differential current is sampled in different disturbances. Then, the mean indices of the sum of energy coefficient each level are calculated by MODWT by MATLAB software, and based on the values of indices, discrimination and classification of events are done. The results obtained from the simulations confirm that the proposed protection algorithm can detect and classify cross-country faults from other disturbances. Also, this method will improve the differential protection performance in different operating conditions and increase the reliability of power systems.