This paper presents the authors’ multi-channel measurement systems designed and built to conduct research on partial discharge phenomena using the acoustic emission method. The systems provide real-time monitoring, recording of signals and analysis of recorded signals. The analysis is carried out in time, frequency, time-frequency and discrimination threshold domains. In particular, a descriptor with the ADC acronym is defined, which ranks the signals according to the so-called degree of advancement. Studies have been carried out, showing that for a single partial discharge source, when tested in parallel, using the electrical and acoustic emission methods, the ranking of the signals using this descriptor is identical to the ranking according to the value of the apparent charge introduced by sources. This paper presents the authors’ patented method of partial discharge location and identification in power oil transformers. The results of tests of power oil transformer at the test station, conducted in parallel with the electric method and the authors’ method, and the results of tests in three selected transformers carried out during ongoing in-situ operation using the authors’ method are presented. Based on these results, the authors make diagnoses of the condition of the insulation systems in the tested transformers. The inspections of these transformers confirm the diagnoses.