Active power filter (APF) is widely used in distribution network because of its fast tracking and harmonic elimination function. Among them, LCL type APF has better ability to suppress high frequency harmonics. With the increasing number of APF connected to the grid, the interaction between the APFs can not be ignored. For the problem of interaction among multiple APFs, firstly, the equivalent model of multi APF grid connection is derived based on Norton theorem. Secondly, the interaction is quantitatively analyzed by using the generalized dynamic relative gain array (GDRGA). Finally, the suppression of interaction is transformed into a multi-objective optimization problem. In view of the defects of traditional sparrow algorithm, such as poor global optimization ability and easy to fall into local optimization, tent chaos and dynamic random Cauchy mutation are introduced to improve, and the improved sparrow algorithm is used to coordinate and optimize the control parameters of APF. The results show that the improved sparrow algorithm can get pareto solution sets with better distribution and better performance. After multi-objective optimization, the interaction between APFs can be effectively suppressed, which verifies the effectiveness of the proposed method.