In this paper, the challenge of harmonic injection mitigation becomes critical with the massive use of inverters in electrical distribution systems that has been discussed and analyzed. Currently, between the inverter and the grid, L, LC or LCL filters is often used to mitigate the current harmonic. Further, filter connection in both delta-to-star or star-to-delta transformer for state space model of LC filter couplings with impedance is obtained in this paper and it also talked about the different passive damping techniques that been used to suppress the resonance effect on the filter. The effect of series and parallel damping resistor techniques that impact filtering and stability are also been analyzed and discussed. At the end, the simulation results show that LCL filter with parallel damping resistor achieves best performance compared on those for L, LC, or LCL with series damping resistor while at the same time enhancing the smoothness of the signal output while at the same time reducing the percentage of total harmonic distortion between inverter-grid connection.