LQ control of a three-phase four-wire shunt active power filter based on three-level NPC inverter

This paper presents the design and implementation of a linear quadratic regulator (LQR) with Integral action (LQIR) for a three-phase four-wire shunt active power filter using a three-level neutral point clamped inverter (SAF-NPC). The integral action is added so as to cancel the steady state errors for reference tracking or disturbance rejection knowing that the standard LQR provides only proportional gains. The controller is designed to achieve overall DC bus voltage regulation, unbalance voltage between the upper and lower capacitors, harmonics, reactive power and loadpsilas neutral current compensations. The converter model is set in the d-q-o rotating reference frame. The latter is augmented with the integral of the q component of the SAF-NPC currents, DC bus voltage unbalance and overall DC bus voltage to achieve integral action. The controllerpsilas performance depends on the weighting matrix, which is chosen to ensure satisfactory responses. The converter is controlled as a multi-input multi-output (MIMO) system and a fixed PWM at 2.34 kHz is used to generate the gating signals of the power devices. The system is tested for harmonics, reactive power and load unbalance compensation for balanced/unbalanced loads. The simulation results obtained with SPS and Simulink of Matlab show good performance in terms of overall DC bus voltage regulation, DC bus voltage unbalance compensation (small overshoot and very fast time response) and a low total harmonic distortion (THD) of ac line currents.