Half-quadratic criterion-based continuous-time adaptive control for robust LCL-filtered grid-tied inverter

Grid-tied inverters are essential for seamlessly integrating sustainable energy resources into the electrical grid, yet they also introduce harmonics due to the inherent switching operations of power electronics. While inductance-capacitance-inductance (LCL) filters effectively limit these harmonics, enhancing overall system performance, they come with their own set of challenges. These include design complexity, potential resonance at high frequencies leading to system instability, and variations in grid impedance. This paper addresses the design complexities by employing a circle search algorithm to optimize the LCL filter and control system parameters. Additionally, a continuous time-based adaptive filtering algorithm, the half-quadratic criterion, is implemented to dynamically adjust the gain of the inner capacitor current feedback damping loop and the gains of a proportional resonant controller to address the resonance and grid impedance variation issues. These algorithms aim to minimize a constrained multi-objective optimization function based on total harmonic distortion, including high-frequency harmonic distortion and the absolute amplitude error between the measured and reference currents. The system is tested using MATLAB/SIMULINK and real-time Typhoon HIL simulations. The findings illustrate that the proposed control scheme significantly enhances the damping region by suppressing the resonance frequency in the higher frequency band. Furthermore, the results demonstrate that the proposed control loop maintains robustness against fluctuations in grid-side impedance, accommodating increases up to 400% and decreases down to 75%. The system achieves a nearly negligible steady-state error and maintains a transient error below 0.1% throughout step changes in reference current.