Due to the existence of grid impedance, the grid transformer leakage reactance have to be taken into account. The point of common coupling (PCC) is a common point of weakness in the grid [1]–[2]. This may lead to stability and power quality problems of grid connected converter. Namely, the low-order harmonics generated by a non-linear load leads to the background voltage harmonics at the PCC due to the grid impedance, which further affects the connection between the grid and converter. In addition, the high-order switching harmonics generated by the operation of the equipment connected to the power electronic grid further degrade the grid power quality [3]–[4]. The LCL-type converters have been widely used in renewable energy grid-connected systems due to their excellent performance in high-frequency harmonic attenuation [5]. However, the phenomenon of resonance exists due to the circuit structure of the LCL-type converters. The active damping method can be employed to avoid these problems such as high hardware cost and reduced power transmission efficiency caused by passive damping method [6]–[15]. Besides, the performance of the control system should be studied considering the digital delay, which causes a phase lag in the control system and threatens system stability and anti-disturbance ability. For the converter-side current feedback (CCF) and grid-side current feedback (GCF), stability can be achieved without using a damping strategy if specified digital delay requirements are met [8],[16]. Many measures have been proposed by scholars to reduce the delay, including the double sampling method, the impedance reshaping method and the pole-zero delay compensation method [14]–[17]. An improved sampling technique is proposed in [14], which can reduce the delay time by sampling the signal twice in each carrier cycle. By adopting the state observer, the signal of the previous cycle can be used to predict the signal of the next cycle, so as to reduce the sampling delay caused by digital delay. However, this method requires additional computing resources, and the observer is extremely sensitive to the small range variation of parameters. For example, the parameter values of resistance and inductance will change with the length of current passing time, which may lead to estimation or prediction error [15]. The delay effect can also be effectively reduced by adding low-pass filter [5] and sampling reconstruction [14]. In addition, there are many researches on