Simplified Model and Sliding Mode Control Method of Active Power Filter

For the theoretical validation of the sliding mode control method's stability in active power filters, given that the alteration in DC side voltage is significantly less than the variation in compensation current, the DC side voltage is considered a fixed value to streamline the mathematical representation of the parallel three-phase active power filter in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha-\beta$</tex> coordinate framework. Utilizing the streamlined model, a sliding mode control technique is suggested, applying the constant velocity asymptotic law to demonstrate the method's stability. Results from the simulations indicate that this technique guarantees not just the system's steadiness but also the stability of the control approach in response to load variations. If the Total Harmonic Distortion (THD) of the grid current reaches 21.54 %, the THD of the adjusted grid current drops to 3.54 %. Therefore, this method is effective and feasible.