The high-Tc superconducting (HTS) dynamo-type flux pump provides the possibility of charging HTS coils without any electrical contact, removing the need for current leads and their associated thermal loss. Although a number of numerical methods have been proposed for the characterization of the HTS dynamo, the dynamic behavior of the HTS dynamo and its impact on the HTS coils during the charging process has not been deeply studied yet. The crucial point is the parallel dynamic calculation of the HTS dynamo along with the HTS coil. 3D modeling can provide a more precise solution than 2D, but with the cost of massive computation time. In this study, we couple two models of the HTS dynamo and HTS coil together via their lumped parameters to reproduce the dynamic charging process. To predict the AC losses of the whole system during different charging stages, one can first extract the time-dependent DC charging current by pre-calculation for shortening the calculation time. In addition, this methodology has the potential to couple different types of FEM models, including various types of superconducting elements. Moreover, the versatility of this methodology will be validated in our further work.