Three-phase four-wire shunt active power filter based on the SOGI filter and Lyapunov function for DC bus control

The three-phase four-wire shunt active power filter (SAPF) was developed to suppress the harmonic currents generated by nonlinear loads, and for the compensation of unbalanced nonlinear load currents, reactive power, and the harmonic neutral current. In this work, we consider instantaneous reactive power theory (PQ theory) for reference current identification based on the following two algorithms: the classic low-pass filter (LPF) and the second-order generalized integrator (SOGI) filter. Furthermore, since an important process in SAPF control is the regulation of the DC bus voltage at the capacitor, a new controller based on the Lyapunov function is also proposed. A complete simulation of the resultant active filtering system confirms its validity, which uses the SOGI filter to extract the reference currents from the distorted line currents, compared with the traditional PQ theory based on LPF. In addition, the simulation performed also demonstrates the superiority of the proposed approach, for DC bus voltage control based on the Lyapunov function, compared with the traditional proportional-integral (PI) controller. Both novel approaches contribute towards an improvement in the overall performance of the system, which consists of a small rise and settling time, a very low or nonexistent overshoot, and the minimization of the total harmonic distortion (THD).