I. Introduction
In recent years, distributed renewable power generation systems have been integrated to power networks to address the environmental concerns due to greenhouse gas emission from power generation and achieve carbon neutrality targets, [1] . Comparing with traditional grid, inverter-based sources integrated with power system is increasing the vulnerability for the system at weak grid case [2] – [4] . Non-ideal grid impedance decreases control efficiency in a weak grid and can also affect system stability due to load variation. When the inverter current is distorted for several cycles during the operation, the effective weak grid impedance will have a critical role in distortion. [5] . A synchronization system such as a phase-locked loop (PLL), is fundamentally needed with other grid-connected inverters to provide references to controllers. PLL is designed for low grid impedance conditions which is not the case in weak grid [6] – [8] . The controller technique reported in [9] reveal the risk of the non-linear nature of PLL and show the absentees of the requirement of PLL at controller approach enhanced the stability boundary. Further study mentioned in [10] the control method will enhance the PLL stability through the injection of reactive current and reducing the gain of current controller. The controller approach in [11] robustness the system through the active damping of capacitor-current-feedback.