Hysteresis describing method for control of an active filter

A hysteresis describing method is proposed to control and to aid in the design of an active power filter. The describing function is used to develop this method. It consists of the linearization of the non-linear current control loop and determines the maximum switching frequency and the maximum ripple of the compensated line current in the limit cycle point: the stability condition. The proposed method permits calculation of the switching frequency and current ripple in a simple algebraic equation as a function of the hysteresis band, dc bus voltage and inductive output filter value. Moreover, the compromise between the dc bus voltage and the inductor value can be easily evaluated as a function of both switching frequency and ripple requirements. From this last point of view, this method makes the active power filter design more facile and attractive. Two design examples are worked out. The experimental results validate the theory.