This paper develops a robust tool for handling ac side stability issues occurring in $LCL$-filter-based grid-connected converters. $LCL$ filters give advantages in cost and dynamic as smaller inductors employed compared with $L$ filters for the same required damping of the switching harmonics. Nevertheless, the additional poles introduced by the $LC$ part induce resonance in the system leading to stability problems. To deal with this stability issue, a new damping method based on the generalized circle criterion is proposed in this paper. The large signal nature of the applied theory allows obtaining high damping efficiency and robustness under large variations of the grid impedance. A theoretical analysis and the experimental results are presented to show the effectiveness of the proposed compensating method.