DSP-Based Implementation of an LQR With Integral Action for a Three-Phase Three-Wire Shunt Active Power Filter

Abstract

This paper presents the design and implementation of a Linear Quadratic Regulator (LQR) with Integral action (LQRI) for a three-phase three-wire shunt active filter (SAF). 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 dc bus voltage regulation and harmonics and reactive power compensation. The converter model is set in the d−q rotating reference frame. The latter is augmented with the integral of the q component of the SAF currents and dc bus voltage to achieve integral action. The controller's performance depends on the weighting matrix, which is chosen to ensure satisfactory response. The converter is controlled as a whole, i.e., a multi-input-multioutput system and a fixed pulsewidth modulation at 10 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 experimental results obtained with a digital signal processor-based implementation of the controller on the DS1104 of dSPACE show good performance in terms of dc bus voltage regulation (small overshoot and very fast time response) and a low total harmonic distortion of ac line currents.Index Terms-Digital signal processor (DSP), linear quadratic regulator (LQR), optimal control, shunt active power filter.

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