## 5 Simulations Results  
The proposed control strategy has been implemented on the MG shown in Figure 6, including two DGs with two local loads and one AC load connected to the PCC. Both DGs have to procure the active and reactive demands, required by the local loads and the AC load, which is assumed to be supplied according to their nominal capacity. This results in there not being overloading for all the DGs contributed to the power sharing issue. The system specifications and control parameters are represented in Tables 1 and 2, respectively. The root locus map of the transfer function of proposed control system is presented inFigure 7, which implies on the system stability based on roots movement in terms of \(\xi_{gc}\) variation in grid-connected operation mode. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline AC grid voltage (\(V_{AC}\)) & 400 (V, rms) \\ AC grid frequency (\(f_{AC}\)) & 50 (Hz) \\ Switching frequency (\(f_{sw}\)) & 15 (kHz) \\ Input DC voltage (\(V_{dc}\)) for both DGs & 500 (V) \\ Filter resistance (\(R_{f}\)) for DG1 & 62 (mf\(\,\)) \\ Filter resistance (\(R_{f}\)) for DG2 & 48 (mf\(\,\)) \\ Filter inductance (\(L_{f}\)) for DG1 & 2.2 (mH) \\ Filter inductance (\(L_{f}\)) for DG2 & 2.1 (mH) \\ Filter capacitance (\(L_{f}\)) for DG1 & 220 (μF) \\ Filter capacitance (\(L_{f}\)) for DG2 & 220 (μF) \\ Rated Power (\(S_{nominal}\)) for DG1 & 4 (kVA) \\ Rated Power (\(S_{nominal}\)) for DG2 & 8 (kVA) \\ Feeder impedance (\(Z_{feeder}\)) for DG1 & 35 + j10 (m\(\,\)\(\Omega\,\)) \\ Feeder impedance (\(Z_{feeder}\)) for DG1 & 44 + j16 (m\(\,\)\(\Omega\,\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System specifications. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Active droop coefficients (m) for DG1 & 4.26 \(\times\) 10\({}^{-4}\) (V/W) \\ Active droop coefficients (m) for DG2 & 7.63 \(\times\) 10\({}^{-4}\) (V/W) \\ Reactive droop coefficients (n) for DG1 & 3.04 \(\times\) 10\({}^{-4}\) (rad/s/Var) \\ Reactive droop coefficients (n) for DG2 & 6.08 \(\times\) 10\({}^{-4}\) (rad/s/Var) \\ Cut-off frequency (\(\omega_{c}\)) for both DGs & 10 (rad/s) \\ \(\xi_{gc}\) & 1000 \\ \(\xi_{isl}\) & 800 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Control parameters. Figure 6: The MG under consideration. The simulation results are conducted out in three scenarios. In all of scenarios, the proposed control approach is applied to the system at \(t=1\) s to \(t=9\) s, where the accurate power sharing is obtained. The total load connected to the MG is 900 W - j750 Var, in which the two DGs are arranged to supply it. Since the apparent power of DG2 is twice than DG1, it is expected that the power sharing is achieved with ratio of 2:1. It means that if the total load is divided into three parts, two of them should be procured by DG2 and the remained load has to be supplied by DG1. Due to the significant effect of feeder impedance in power sharing issue, there are three different feeder impedances considered in the MG for both DGs. At the first scenario, it is assumed that the feeder impedance is completely inductive and the resistive part is neglected. The results of this scenario are represented in Figure 8, where in Figure 8a, the active powers are shared in the aforementioned ratio of 2:1, as well as the reactive powers shown in Figure 8b. The frequency of each DG and their terminal output voltages are represented in Figure 8c,d, that they are kept constant in their permissible range. As soon as the feeder impedance are varied to totally resistive, the results are obtained in Figure 9, where the accurate power sharing without no errors is achieved. Even if the impedance feeder is assumed to be complex, the results do not change any more as shown  
Figure 8: Power sharing in the first scenario considering inductive feeder impedance; (**a**) output active powers of DGs, (**b**) output reactive powers of DGs, (**c**) output frequencies of DGs, (**d**) terminal DGs voltage.