High steady-state control accuracy and fast dynamic performance are crucial technical characteristics for hybrid active power filter（HAPF）

therefore

according to the topological structure of transformerless hybrid active power filter（TLS-HAPF）

an improved control strategy based on fast repetitive control（RC） is proposed in this paper

which includes proportional-integral（PI） and fast RC. The controller is implemented in a positive-rotating synchronous frame

where all6 n±1 order harmonics of nonlinear loads can be well suppressed

meanwhile

fast dynamic response is achieved and minimal storage space is occupied. Based on the time domain method

the control parameters of the compound controller are designed; its steady state performance and dynamic performance are analyzed in detail. Compared with the traditional compound control

the proposed control strategy on improving RC is of excellent steady-state tracking performance and faster transient response

which is verified by simulation and experimental results.