A novel mesh-free methodology for the coupled magnetic field-circuit simulation of power transformers is presented in this paper. The proposed methodology employs equivalent models for the conductors and the iron core, which are based on the field produced by elementary geometric configurations and boundary conditions derived from Ampere's and Faraday's laws. Power losses in the windings due to circulating currents are calculated with the proposed method and the Finite Element Method (FEM). A 25 MVA transformer is investigated as a case study and the effect of the conductor connections within the windings is considered through its incidence matrix. The windings losses obtained by applying the proposed methodology are compared with the losses estimated from the short circuit test showing an excellent agreement. The computational performance is also compared with FEM. It has been found that the proposed method is about 9 times faster than FEM retaining the level of precision required for transformer design purposes.