Benchmarking of Stability and Robustness against Grid Impedance Variation for LCL-Filtered Grid-Interfacing Inverters

This paper comprehensively analyzes the stability of a grid-interfacing inverter with LCL filter in the discrete domain, where the LCL filter, along with the controller, are modeled in a polar coordinate. System open-loop and closed-loop poles are analytically studied and expressed in the z-domain. Through the poles movement and distribution analysis, the relationship between system stability and the ratio of resonance frequency over sampling frequency is mathematically revealed and calculated as well as the system control gain limit. Moreover, this paper demonstrates that grid-voltage feedforward regulator would significantly alter the inverter stability in a weak power system. By means of Jury stability criterion, the stability status under different filter resonance frequency is given. The selection of resonance frequency and filter parameters makes a considerable difference on system behavior. Finally, to improve the robustness against grid inductance variation, a conservative design recommendation of filter parameters and control gain is given. Through the tests on a laboratory-scale prototype, the theoretical analysis is validated by experimental results.