## 1 Introduction
Hybrid microgrids connected with the primary grid can regulate bidirectional power transfer (production/consumption) by employing AC/DC VSC for battery energy storage setups. It is necessary to highlight that hybrid microgrids can be scaled with ease. Moreover, the implementation of such microgrids may be performed at several levels using different configurations. These microgrids can be integrated with a Low-Voltage (LV) residential-scale grid or a Medium Voltage (MV) distribution-level grid [21]. The literature has several references for Grid-Connected Inverters (GCI) using PR controllers. Few studies specify the process of designing the PR controller [22; 23; 24]. All specified research is appropriate and highlights PR efficacy. Nevertheless, most research focuses on the PR controller being used in continuous-time. In contrast, a major proportion of the GCI applications require a digital setup. In such cases, the task of using the PR controller digitally is something the reader should ascertain. The main unique contributions of the approach recommended in this paper can be summed up as shown below:  
1. This work aims to formulate a model that can assess the behaviour of distributed energy resources in 14-node IEEE systems that stem from the change in the opening protocol of the disconnector, which establishes a power generating island. The stability analysis it exposes makes it possible to determine the performance of a radial distribution power system given various disturbances. Results have relevance in the operation and planning phases of a distributed generation system. 2. As a renewable energy interface, numerous control technologies can be used to operate controlled inverters or rectifiers. In this study, some converters operated in an open-loop control strategy while others operated in a closed-loop control strategy. Furthermore, pulse width modulation techniques at varying carrier frequencies were utilised by these rectifiers or inverters. 3. The main contribution of this paper the proposed method not only focused on the transient response but also improve the steady-state response which smooth the voltage, furthermore all inverters are effectively involved to increase capacity of the microgrid for better power management. 4. The hybrid microgrid was equipped with nonlinear and linear loads, typical energy storage systems, and balanced and unbalanced loads. Moreover, this paper thoroughly describes the model with all the data needed to tackle the abovementioned studies. 5. This paper offers a design process for the digital PR current controller implemented to a GCI. The procedure describes a step-by-step method for calculating the resonant and proportional gains, as well the resonant path's coefficients. Its main contribution is helping facilitate and providing support to researchers who are tasked with designing GCI that incorporates present control strategies in a digital environment. The paper will also present an analysis of the frequency domain of a digital PR controller. This analysis utilised the fictitious w-domain. The case-study demonstrated the efficacy of GCI that uses a digital PR current controller, which was designed with the help of the proposed procedure. The paper also demonstrates how the proposed procedure has validity for a number of resonant path PR controllers.