## 1 Introduction  
Due to the fast-growing energy demand and environmental problems related with the conventional fossil fuel, the renewable energy sources from wind turbine or photovoltaic system are considered as promising alternatives for power generation in the global energy market. The progress of distributed power generation systems based on renewable energy sources is mainly facilitated by the development of power electronics technology. In general, in order to connect different kinds of renewable energy sources to the point of common coupling (PCC), power electronics converters should be employed as the interface between the renewable sources and main grid [1, 2]. Commonly, the pulse width modulation (PWM) grid-connected inverters with a high switching frequency are widely used to deliver the power from the renewable energy resources to the grid. To achieve high-quality grid-injected currents which meet the stringent harmonic standard, harmonics around the switching frequency should be effectively filtered out. For this purpose, an inductive (L) filter with high inductance value can be used at the inverter output, providing the easiness in control design [3]. On the other hand, compared with an L filter, inductive-capacitive-inductive (LCL)-type filters are more attractive due to smaller physical size and better harmonic attenuation capability of high-order harmonics [4, 5]. Nevertheless, the LCL filter introduces a resonant peak into the system, which may cause an output resonance problem [6; 7; 8; 9]. To ensure a stable and reliable operation of the inverter system, a proper damping method should be considered either by the passive or active method. The study in [8] focuses on the stability problem of the LCL-filtered grid-connected inverters for a large set of grid impedance value, in which the inverter-side current is controlled by means of a proportional resonant (PR) control scheme. As discussed in this paper, the conventional active damping, which highly depends on the knowledge of hardware system, is ineffective under the grid inductor variation in weak grid condition. In addition to the resonance problem, other issues such as the grid harmonic distortion and grid impedance at PCC should be addressed to produce high-quality grid-injected inverter currents [10]. A passive method to damp the resonance peak caused by the LCL filter is to insert a resistor in series with the filter capacitor. This solution is simple and highly reliable, regardless of the change in the resonance frequency. However, the power dissipation in resistor is unavoidable and the high-frequency attenuation is affected [11]. To overcome this limitation, various active damping methods have been presented to ensure the system stability, which include the indirect current control, the partial-state feedback (e.g., capacitor current and capacitor voltage) control, and the full-state feedback control [12; 13; 14; 15; 16; 17; 18]. Generally, the current controllers are constructed by two typical approaches: the classical control approach (i.e., by transfer function) [12; 13; 14] and modern control approach (i.e., by state-space model) [15; 16; 17]. In the work of [12], the active damping based on the indirect current control method is achieved by the inverter-side current feedback with notch filter. In this study, the effectiveness of the notch filter-based active damping is investigated in detail by considering the control delay, filter parameters' variation, and grid impedance. However, in indirect current control method, the dynamic tracking performance is degraded due to the filter delay and small phase margin [19]. In the studies of [13; 14], the virtual resistance is realized by partially feeding back the capacitor current and voltage, respectively. Then, the digital filters are brought in to enhance the system stability. However, the high-pass filter with the approximate derivative characteristic in [13] may amplify high-frequency noise, and the notch filter proposed in [14] is quite sensitive to the resonance frequency variation.