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We present a novel model-based approach for parameter identification of a laminated core, such as magnetic permeability and electrical conductivity, of power transformers on the basis of frequency response analysis (FRA) measurements. The method establishes a transformer core model using the duality principle between magnetic and electrical circuits for parameter identification with genetic algorithms. We use reference input impedance frequency responses, calculated by a well-known lumped parameter model of a three-phase transformer and finite-element computations, to analyze identification accuracy of the method. The results verify the ability of the approach to accurately identify the core lamination parameters with respect to the reference values. The approach can be used for parameter identification of a demagnetized core with known geometrical parameters when the core lamination samples are unavailable for experimental tests. The approach can also be employed for transformer core modeling and FRA result interpretation at low frequencies.