A stability or resonance analysis of a micro-grid consisting of multiple grid-connected-converters (GCC) with LCL filter is important but complicated, because it is influenced by many factors such as LCL filters of the GCC, the grid impedance and various (nonlinear or even time-variable) loads. It is necessary to construct a framework for revealing and analyzing the main unstable factors and then exploring possible approaches for improving the stability. This paper tries to find a framework, in which a linear model of the system is formatted using the impedance based approach. Based on the model, the impacts of some main factors on system stability are explored. Therefore, resonance suppression based on impedance adjusting is presented accordingly. Taking full state feedback control of GCC as an example, simulations of two control cases validate the effectiveness of the current work of the framework.