The high-Tc superconducting (HTS) dynamo exploits the nonlinear resistivity of an HTS tape to generate a DC voltage when subjected to a varying magnetic fie ld. This leads to the so-called flux pumping phenomenon and enables the injection of DC current into a superconducting coil connected to the dynamo without current leads. In this work, the process of charging a coil by an HTS dynamo is examined in detail using two numerical models: the Minimum Electromagnetic Entropy Production and the segregated H-formulation fi nite element model. The numerical results are compared with an analytical method for various airgaps and frequencies. Firstly, the I-V curves of the modeled HTS dynamo are calculated to obtain the open-circuit voltage, short-circuit current and internal resistance. Afterward, the process of charging a coil by the dynamo including the charging current curve and its dynamic behavior are investigated. The results obtained by the two models show excellent quantitative and qualitative agreement with each other and with the analytical method. Although the general charging process of the coil can be obtained from the I-V curve of the flux pump, the current ripples within a cycle of dynamo rotation, which can cause ripple AC loss in the HTS dynamo, can only be captured via the presented models.