## 1 Introduction
For this purpose, the effects of the grid impedance uncertainty on the locations of closed-loop poles are investigated under distorted grid by using two different control approaches. Since the controller stability has been investigated under uncertain grid impedance without considering the inherent contaminated harmonics in grid in several studies [27; 28], the stability assessment of the entire current control structure including the harmonic resonant controllers needs a further comprehensive investigation for a stable inverter operation under distorted weak grid. Two typical current controllers implementing both the active damping and grid harmonic compensation are selected to investigate their closed-loop system stabilities and current control performances under distorted weak grid conditions. The system stability analysis is accomplished by investigating the closed-loop poles in the discrete-time domain when the grid impedance varies. Furthermore, to support the stability analysis under weak grid condition, as well as to assess the current control performance, the PSIM (9.1, Powersim, Rockville, MD, USA) software-based simulation and experimental results are presented by using prototype three-phase grid-connected inverter under adverse grid conditions. The analytical assessment shows that a full-state feedback controller augmented with the internal resonant controllers for current harmonic compensation is preferable in view of large control margin. Moreover, this control can effectively deal with the issue of current harmonic attenuation and resonance damping, even in the presence of a significant grid impedance variation. Additionally, theoretical analysis and experiments verify that the low region LCL resonance frequency is more vulnerable to system stability than that of high region under weak grid. The main contributions of this paper are as follows:  
1. The two typical current controllers with harmonic compensators for the LCL-filtered grid-connected inverter are implemented to analytically investigate their performances under distorted weak grid by means of the stability assessment tools and comprehensive evaluation results. 2. By the movement of closed-loop poles and disturbance rejection responses, the stability margin of each controller is well investigated. It is clearly addressed that the stability is weakened under the grid impedance variation by the addition of harmonic resonant controllers. The theoretical results are validated by simulation and experiments. 3. The full-state feedback current control method with augmented harmonic resonant compensators has well proved its robustness for a wide range of grid impedance variations (up to 14 times of grid-side inductors in the high region) by theoretical analysis and evaluation results. 4. In order to validate the presented theoretical analyses, comprehensive simulation and experimental results based on 2 kVA grid-connected inverter are presented under the grid environment including both uncertain grid impedance and distorted harmonics. This paper is organized as follows: Section 2 explains the system description and current controller designs. Section 3 presents the frequency response and closed-loop system stability under the grid impedance change and harmonic distortion. The simulation and experimental results are provided in Section 4 to validate the stability analysis. Finally, Section 5 concludes the paper.