Robust Admittance Shaping Approach to Grid Current Harmonic Attenuation and Resonance Damping

This paper presents a novel grid current control of a grid-connected voltage source converter with an LCL filter. The proposed control method uses an $\mathcal {H}_\infty$ synthesis method to shape the input admittance of the converter, to track a given current reference, and/or to limit the controller actuation at different frequency ranges. The converter admittance is shaped, both in magnitude and phase, following a model reference defined by the designer in the frequency domain. By specifying a low admittance magnitude reference, the optimization algorithm will obtain a controller that actively damp the filter resonance and attenuate/reject the grid voltage oscillations, either in a wide frequency range or concentrated at the main harmonic frequencies. Additionally, the proposed controller design methodology takes advantage of its admittance phase shaping capability to improve the system robustness in front of grid uncertainties and minimizing converter impact over grid stability due to its positive-real nature. The synthesized controller only measures the grid current and voltage to achieve the aforementioned results, reducing the number of sensors (and their associated cost) required for its implementation. Experimental results illustrate the correct behavior of the closed-loop system with the designed controller in time and frequency domain.