A fault current compensation technique is proposed in this paper for resonant grounded power distribution systems in bushfire prone areas. Arc suppression devices with residual current compensation inverters are used to compensate fault currents due to single line-to-ground faults in order to mitigate powerline bushfires. The main contribution of this paper is the design of a compensation technique for the T-type residual current compensation inverter using a non-singular terminal sliding mode control scheme. The main objective of the proposed scheme is to reduce the fault current and bring its value to a level so that it cannot ignite fires. The proposed controller is designed based on the selection of a sliding surface in a way the singularity problem can be avoided and chattering effects in existing sliding mode controllers can be eliminated. The desired current injection through the residual current compensation inverter is ensured by enforcing the control law into the terminal sliding surface where the control law is determined by satisfying the Lyapunov stability criteria. The performance of the non-singular terminal sliding mode controller is compared with an integral sliding mode controller by considering different values of fault currents where these values are varied by changing fault resistances. Results for simulation in the software and processor-in-loop simulations are verified against operational standards which are essential for mitigating powerline bushfires. This work focuses to design a non-singular terminal sliding mode controller for the residual current compensation inverter which is used in an arc suppression device to compensate both active and reactive components of the fault current and keeps its value below 0.5 A within 2 s after activating the residual current compensation inverter which is a requirement as per the operational standard. This controller is designed based on the selection of a terminal sliding surface while satisfying the condition for avoiding the singularity problem.