I. Introduction
With the increase of non-linear loads and impulsive loads in the power grid. For example, large-capacity diodes or thyristor rectifiers, motor variable-speed drive devices, etc [1–3]. Power conditioning is becoming more and more important in high-efficiency and high-reliability power systems. In many cases, harmonic pollution and decaying dc (DDC) components with uncertain amplitude and attenuation rate are not tolerated [4]. The diffusion of nonlinear loads in the power system leads to the generation of p-q theory, which is not only valid in the steady state, but also in the transient process [5]. The p-q theory has been widely used in the design of active power filters (APF) for reactive power and harmonic compensation, but there are few studies on the compensation of DDC components in the transient process.