Lyapunov-Function-Based Control Approach for Three-Level Four-Leg Shunt Active Power Filters with Nonlinear and Unbalanced Loads

Abstract

This paper presents a control method for three-level four-leg shunt active power filters (SAPFs) based on Lyapunov's stability theory. The dynamic equations of the SAPF will be achieved and then transformed into the dq0 frame. By considering the nonlinearity of the obtained equations, the Lyapunov technique is used in order to find a solution to enhance the system stability. The design in this approach is to define an energy function in terms of the system states and after that ascertain the control rule that makes the considered function derivative always negative under all conditions. By the use of the proposed method and determining the appropriate reference currents, the SAPF provides compensation for reactive, harmonic, neutral and unbalanced current components generated by grid-connected loads. The accuracy of the proposed control approach is validated via MATLAB/Simulink software.