This paper presents a nonlinear extended state observer (NLESO)-based nonlinear model predictive controller (NMPC) design for resonant grounding devices called rapid earth fault current limiters (REFCLs) to compensate arc faults in power distribution networks covering bushfire prone areas. The proposed NLESO is designed to estimate disturbances which are represented through changes in the neutral voltage due to unknown faults and changes in leakage parameters of distribution networks during hot summer days. The NMPC in this work compensates the fault current and subsequently, the faulty phase voltages irrespective of fault impedances. The dynamical model of REFCLs is transformed into a suitable model to design NLESO and nonlinearities are modeled in such a way that these fall within different sectors depending on the value of the observer gain and estimation errors while ensuring the desired recovery of states during severe transients. The estimated disturbances are then incorporated into the NMPC to achieve the expected compensation level for both fault current and faulty phase voltage. The proposed NLESO-based NMPC’s stability is analyzed by representing the whole system in form of a Lure system. Finally, the performance of the proposed scheme is evaluated through simulations using MATLAB/Simulink and OPAL-RT real-time simulator following the Victorian regulatory impact statement for reducing powerline bushfires.