**2. System Description**

Microgrid is defined as one or more DG units connected closely with loads through coupling inductance and LC filter [3]. DGs such as PV generate DC power therefore; they usually utilize an inverter to convert the DC power to AC. Microgrid operates in two different modes; island and grid-connected modes. In the island or autonomous mode, maintaining the voltage and frequency of the system and supporting the required active and reactive powers is the main task [27–31]. In the grid-connected mode, the main target is to control the delivered DGs powers into the grid. In this paper, to control a predefined real and reactive powers to the grid, two cases are considered. In the first case, an inverter-based DG is delivering power to the grid through a coupling inductance and LC filter as shown in Figure 1. While in the second case, two inverter-based DG units are sharing their powers to the grid at the point of common coupling (PCC) through a coupling inductance and LC filter as shown in Figure 2.

**Figure 1.** Grid-connected microgrid (One distributed generation's (DGs) case).

**Figure 2.** Grid-connected microgrid (Two DGs case).

From Figures 1 and 2:

*Cf*, *Lf* and *Rf* are the capacitance, inductance and resistance of the LC filter,

*Lc* and *Rc* are the inductance and resistance of the coupling inductor,

*Rd* is the damping resistance,

*iL* is the coupling inductor current,

*io* is the inverter output current,

*ic* is the capacitor current,

*VI* is the inverter output voltage,

*Vo* is the PCC voltage,

*Vg* is the grid voltage.

*Cf1*, *Lf1* and *rf1* are the capacitance, inductance and resistance of the LC filter for DG1,

*Cf2*, *Lf2* and *rf2* are the capacitance, inductance and resistance of the LC filter for DG2,

*iL1* and *iL2* are the coupling inductor currents of DG1 and DG2 respectively,

*ic1* and *ic1* are the capacitor currents of DG1 and DG2 respectively,

*VI1* and *VI2* are the inverter output voltages of DG1 and DG2 respectively,

*rd1* and *rd2* are the damping resistances.

In both cases, it is worth mentioning that each DG inverter is assumed to be connected to a constant DC power source, so there no need to regulate the DC-link voltage otherwise, a controller should be introduced to regulate the DC-link voltage [13]. Meanwhile, our main objective in this paper is to study the AC side dynamic performance of the inverter-based DG in the grid-connected mode.
