An nonlinear model predictive controller (NMPC) is proposed in this paper for compensations of single line-to-ground (SLG) faults in resonant grounded power distribution networks (RGPDNs), which reduces the likelihood of power line bushfire due to electric faults. Residual current compensation (RCC) inverters with arc suppression coils (ASCs) in RGPDNs are controlled using the proposed NMPC to provide appropriate compensations during SLG faults. The proposed NMPC is incorporated with the estimation of ASC inductance, where the estimation is carried out based on voltage and current measurements from the neutral point of the distribution network. The compensation scheme is developed in the discrete time using the equivalent circuit of RGPDNs. The proposed NMPC for RCC inverters ensures that the desired current is injected into the neutral point during SLG faults, which is verified through both simulations and control hardware-in-the-loop (CHIL) validations. Comparative results are also presented against an integral sliding mode controller (ISMC) by demonstrating the capability of power line bushfire mitigation.