The use of LCL filter is continuously increasing in AC microgrids because of their good filtering/size ratio and their relative low cost. But, they introduce new resonance modes and may affect the stability of the microgrid, particularly when loads are tightly controlled. This paper deals with a AC network composed of LCL filters and power factor corrector (PFC) rectifiers fed by a grid. First, an average model of the system with two PFC is developed. Then, local stability and resonance phenomena are studied by considering all control loops. It is shown that, under certain conditions, significant oscillations may appear even if the system operating point is in the stable area. More in this case, exciting one of the resonance modes can lead to instability. To improve the stability of the system, we propose to employ local stabilizer agents. They slightly modify the power absorbed the loads by injecting stabilizing powers to the system. Simulations and experimentations confirm the validity of the proposed approach.