Modeling and control of three-phase four-leg split-capacitor shunt active power filter

This paper deals with the modeling and control of a 3-phase 4-leg split-capacitor shunt active power filter (APF) topology. The APF is aimed to compensate harmonic phase currents, harmonic neutral current, reactive and unbalanced nonlinear load currents in 4-wire distribution systems. In addition, the dc-link capacitor voltages are regulated and equalized to eliminate the imbalance problem which is due to the presence of dc component in the neutral wire current. The capacitor voltage imbalance is a major problem for conventional 4-wire split-capacitor topology as it degrades significantly the performance of the compensator. For the sake of the control, the multivariable state space model of the APF is developed in the synchronous dq0 frame. The model is used to obtain the desired closed loop dynamics and to select the converter switching states by applying a sliding mode control strategy. The control law has a switching component forcing the system's trajectory to the sliding surface and a continuous component valid on the sliding surface. The stability of the closed loop system is proved by means of Lyapunov stability criterion. The robustness over a wide range of operation is another property of the control. Simulations are conducted to verify the analytical analysis of the control.