Under normal operation, insulation systems of high voltage electrical devices, like power transformers, are constantly subjected to multiple types of stresses (electrical, thermal, mechanical, environmental, etc) which can lead to degradation of the machine insulation. One of the main indicators of the dielectric degradation process is the presence of partial discharges (PD). Although it starts due to operational stresses, PD can cause a progressive insulation deterioration since it is characterized by localized current pulses that emit heat, UV radiation, acoustic and electromagnetic waves. In this sense, acoustic emission (AE) transducers are widely applied in PD detection. The goal is to reduce maintenance costs by predictive actions and avoid total failures. Due to the progressive deterioration, the assessment of the PD evolution is crucial to improve the maintenance planning and ensure the operation of the transformer. Based on this issue this article presents a new wavelet -based analysis to characterize the PD evolution. Three levels of failures were carried out in a transformer and the acoustic signals captured by a lead zirconate titanate piezoelectric transducer were processed by discrete wavelet transform. Experimental results revealed that the energy of the approximation levels increased with the failure evolution. More specifically, levels 4 and 6 presented a linear fit to characterize the phenomena, enhancing the applicability of the proposed approach to transformer monitoring.