Predictive diagnostics of the health status of electrical components subject to partial discharge still appears to be challenging to implement. The determination of residual life, especially, is often highly uncertain in many cases. In various high-value components such as cables and joints, precise localization of partial discharge events can be a valuable tool for estimating the progression of degenerative processes such as electrical treeing. This study focuses on certain new techniques used to determine the position of moving charges using induced currents measured across a suitable set of electrodes. These techniques have been developed in the field of radiation detectors. Specifically, we developed and analyzed the performance of three different localization algorithms based on induced current measurement and tailored for the localization of internal discharges in axisymmetric components. Moreover, these algorithms are capable of determining the real charge exchanged by a discharge. Therefore, this technique provides a measurement of greater physical relevance compared to the concept of apparent charge defined in international standards. The performance of the methods was evaluated using data from detailed numerical simulations of the discharge process, providing a feasibility analysis for the practical implementation of these techniques and the development of associated electronics.