The model of a grid-connected inverter used for the corresponding controller design depends on the equivalent resistance and inductance between the inverter and the grid. These parameters are not fixed and change with operating conditions, temperature, and age. This paper analyses the effectiveness of the application of the model reference adaptive control (MRAC) approach in obtaining an accurate model of a grid-connected inverter system. Active and reactive power based MRAC approaches are used to estimate the equivalent resistance and reactance between the inverter and the grid. Detailed stability analysis of the MRAC approach is presented. The system models for the MRAC controller design are derived and guidelines on the controller parameters selection are proposed. Experimental results validate the feasibility of the proposed scheme.