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Accurate modelling of power transformers is beneficial for fault diagnosis and the health condition assessment of the power transformers. However, measuring the internal parameters of power transformers while they are in operation is not feasible due to the costs involved in interrupting the power supply and dismantling the components. To address this issue, this paper proposes a new method that uses artificial neural networks and genetic algorithms to synthesise the power transformer lumped parameter network based on the frequency response. The proposed methodology can be utilised to model power transformers and obtain lumped parameter values with minimal cost and time. A physically realisable transfer function derived using the sweep frequency response test data of a power transformer is the input of the proposed model. The combined approach of an artificial neural network and genetic algorithms generates the output as resistive, inductive, and capacitive components of the lumped parameter circuit of power transformers. Furthermore, the entire approach is explained using a case study and validated by means of error analysis. The proposed method is an easy-to-implement process to develop in a computer program that can be used effectively for accurate fault identification in power transformers and health assessments. [ABSTRACT FROM AUTHOR]