Simple Hysteresis Describing Technique to Control a Non-Active Power Compensator

A hysteresis control analysis technique to control an active power filter is proposed in this paper. This technique settles the maximum switching frequency of the inverter and the ripple of the compensated current as conditions for continuous cycling of the system. The describing function method is used to develop this technique that consists of the linearization of the current non-linear feedback loop. The linearization is made by deriving the hysteresis complex describing function and then applying the stability limit cycle condition to the current closed-loop to determine the frequency and amplitude values of the error signal. These values are the maximum switching frequency and the current ripple, respectively. A new "describing technique" method is proposed, which permits calculation of these parameters in a simple algebraic equation as a function of the hysteresis band, dc bus voltage and inductive low pass 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 current ripple requirements. This technique is applied to design a single-phase non-active power compensator. Simulation results have shown that the predicted values are very close to the values obtained by simulation