This paper proposes a new adaptive nonlinear extended state observer-based model predictive controller (ANLESO-MPC) for residual current compensation (RCC) inverters to compensate fault characteristics in resonant grounded power systems (RGPSs). In the proposed scheme, the adaptation feature is used to adapt the adjustable inductor appearing in the dynamical model of RGPSs by satisfying the desired fault current compensation requirement which in turn will ensure the resonance condition. Since the adapted parameter is used in the control signal, the ANLESO-MPC offers robustness against parameter sensitivity. The neutral voltage is considered as a disturbance and the change in this voltage as an extended state to estimate this disturbance while incorporating the adapted parameter so that the adaptive nonlinear extended state observer (ANLESO) provides robustness against disturbances. Finally, the model predictive controller (MPC) is designed for the RCC inverter utilizing estimated disturbances and adapted parameters to fully achieve the fault current compensation. The performance of the controller is evaluated using simulations in MATLAB/Simulink and OPAL-RT real-time platforms under varying fault impedances as the fault characteristics change with variations in the fault impedance. Results are also compared with a conventional MPC where the proposed ANLESO-MPC seems more effective to compensate fault characteristics.