Hysteresis describing method for control of an active power filter

A hysteresis describing method is proposed to control and design an active power filter. The describing function used to develop this method consists of the linearisation of the non-linear current control loop. The linearisation is done by deriving the hysteresis complex describing function to find the stability condition of the closed-loop current. Under this condition, the frequency and amplitude values of the error signal correspond to the maximum switching frequency and the current ripple, respectively. The proposed method permits calculation of these parameters in a simple algebraic equation as a function of the hysteresis band, dc bus voltage and inductive filter value. Moreover, the compromise between the dc bus voltage and inductor value can be evaluated easily as a function of both switching frequency and ripple requirements. Two design examples are worked out. Experimental results validate the theory.