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Power transformers are considered as one of the essential elements in electrical networks. Any failure in these equipments directly reduces network reliability and increases maintenance costs. Consequently, the preventive maintenance techniques are increasingly developed. In this regard, frequency response analysis is an appropriate method in order to diagnose any change which occurs in transformer physical construction. This contribution has been concentrated on the low frequency range of the Frequency Response Analysis (FRA) measurements. The effects of core magnetization, core grounding condition, terminal connections and etc on transformer frequency response are shown and discussed. Also, practical measurements performed on faulty power transformers are represented. The obtained results are very interesting and applicable for maintenance engineers to find the occurred fault.