Power decoupling circuits can compensate the inherent double line frequency ripple power in single-phase systems and greatly facilitate their dc-link capacitor design. Example applications of power decoupling circuit include photovoltaic, light-emitting diode, fuel cell, and motor drive systems. This paper presents the dq synchronous reference frame modeling of single-phase power decoupling circuits and a complete model describing the dynamics of dc-link ripple voltage is presented. The proposed model is universal and valid for both inductive and capacitive decoupling circuits, and the input of decoupling circuits can be either dependent or independent of its front-end converters. Based on this model, a dq synchronous reference frame controller is designed which allows the decoupling circuit to operate in two different modes because of the circuit symmetry. Simulation and experimental results are presented to verify the effectiveness of the proposed modeling and control method.