In this paper, a discrete sliding mode control scheme is developed for the residual current compensator (RCC) inverter in a arc suppression coil (ASC) which is used for eliminating the fault current in resonant grounded power distribution networks to eliminate the impacts of powerline bushfires. The proposed discrete sliding mode controller (D-SMC) is designed based on the dynamical model of the ASC where the model is first represented in the d q -frame and then discretized. The D-SMC ensures the injection of the desired current through the RCC inverter so that the current flowing through the neutral reduces to zero which in turn reduces the phase-to-ground voltage of the faulty phase and hence, mitigates the adverse effects of powerline bushfires. A discrete sliding surface is selected to determine the switching control inputs for the RCC inverter and the stability of the proposed D-SMC is also analyzed to ensure the injection of the desired current to the neutral point under any operating conditions while satisfying operational standards. The effectiveness of the proposed D-SMC is evaluated through simulation results in terms of minimizing the fault current through the injection of the current to the neutral point and comparisons are made with existing proportional integral (PI) controller through simulations as well as other control strategies.