A coupled field-circuit formulation and a duality based approach for analysis of low-frequency response of transformers

Frequency response analysis (FRA) is a well accepted condition monitoring technique for power transformer windings. The low-frequency region (generally, below 10 kHz) of the response is governed by the magnetic circuit. It is generally observed that the shape of frequency response in terms of the driving point impedance for the central phase and the end phases is inverted `V´ and inverted `W´, respectively, in the low-frequency region. A qualitative explanation for the above phenomenon is presented in this work. A step-by-step calculation of core parameters and their variation with frequency for different phases have been explained. Two different approaches, viz. a coupled field-circuit approach based on finite element formulation and a method based on duality principle, are employed for modeling. Results of the two methods have been verified with experimental data.