Power transformers are important electrical machines that allow power flow in the transmission and distribution energy systems. Therefore, condition monitoring and fault diagnosis applied to power transformers are crucial in order to guarantee high levels of energy supply to the whole world. In this scenario, one of the most common failures is the discharge activities in the dielectric components due to insulation degradation caused by overload operation, moisture, overheating, as well as manufacturing flaws such as conductor tilting, conductor bending, the deposition of dirt in bushings, etc. In this context, it is important to develop systems that allow the type of failure to be classified since different flaws require different maintenance actions. Hence, this article presents a new approach to classify three operational conditions: surface discharges on bushings, electric arcs inside the transformer, and machines without flaws. An acoustic sensor was attached to the machine wall and the 100 acoustic signals per operational condition were acquired with a frequency rate of 1 MHz. After that, signal processing analysis based on the spectrum content was carried out. The results indicated that skewness combined with the average frequency and equivalent bandwidth statistics is a promising tool to assess the operational conditions and classify the type of failure. Therefore, this work contributes to the improvement of power transformer maintenance systems.