Robust Control of Shunt Active Power Filters: A Dynamical Model-Based Approach with Verified Controllability

Abstract

This paper presents the robust control of Three-Leg Split-Capacitor Shunt Active Power Filters (TLSC SAPFs) by means of structured H∞ controllers for reactive, unbalanced, and harmonic compensation and the DC-link bus voltage regulation. Robust controller synthesis is performed based on the TLSC SAPF dynamical model including power losses in passive elements. Before the control implementation, a systematic procedure for the nonlinear controllability verification of the converter and its quantification using the set-theoretic approach is presented. Controllability verification serves to accurately design the SAPF’s operation region. Thus, a Voltage Oriented Control (VOC) structure is implemented by using two different approaches to determine the PI controller parameters: (1) the traditional Pole-Placement method (PP-PI) and (2) the H∞-PI structured synthesis approach, which leads to PI robust controllers. From the latter approach, two sets of parameters are obtained. The first set considers the nominal model (H∞-PI), and the second one explicitly accounts for the model parametric uncertainties (H∞-uPI). An optimization procedure is presented for obtaining the optimal H∞-PI and H∞-uPI controller parameters where four complementary constrains are defined to establish a trade-off between the controllers performance and robustness. The enforcement of constraints is later evaluated for each of three PI controllers obtained. This work aims to establish a common ground for the comparison of robust control strategies applied to TLSC APFs; therefore, the TLSC SAPF compensation performance is measured and compared with the performance indices: integral of the absolute error (IAE), integral of the time-weighted absolute error (ITAE), integral of the absolute control action (IUA), and maximum sensitivity (Ms).