In the modeling process of a unified power quality conditioner (UPQC),a series unit model and a pa- rallel unit model are separately constructed in general,and an idealized series transformer is applied.In addition,the interaction between the series unit and the parallel unit has been rarely analyzed.In this paper,a precise mathematical model of the UPQC is constructed by using an equivalent transformer model,which integrates the se- ries unit with the parallel unit.Then,the interaction between a series inverter and a parallel inverter is analyzed,and the corresponding interaction mechanism is obtained.Furthermore,a coordinate control method of the UPQC is proposed based on the unity power factor (UPF) detection method.Simulation and experimental results prove that the proposed method can help the UPQC achieve a better compensation effect,thus verifying the correctness of the constructed mathematical model and the obtained interaction mechanism.