# Modeling and Simulation of Autonomous DC Microgrid with Variable Droop Controller
## 4 Results and Discussion  
Table 1 includes the system parameters for MATLAB simulation. With \(V_{NL}-V_{min}\) set as 10 V and \(P_{DCmax}\) as 5 kW, the P-V droop coefficient was obtained as 0.002. The nominal DC bus voltage was 300 V. The droop resistor was designed for \(r_{d}=0.588\). The voltage regulation subject to varying load was primarily investigated with the variable droop control and compared with the fixed droop control. The current sharing was also compared for different load cases. The load transients of 1.5 KW were introduced at 0.25 s, 0.5 s, and 0.8 s, respectively.  
Waveforms in Figures 7 and 8 shows the DC bus voltage, the current shared by the two parallel connected converters, and the load transients with both fixed and variable droop control. With the fixed droop control, the bus voltage drops quickly in response to the transients which will in turn affect the stability of the microgrid. With the variable droop control, the bus voltage obtained for the first load transient is 297.4756 Volts, while for the fixed droop control it is 295.2776 Volts. For a total load current of 15 amperes, the total source current must add up to 45 A. Hence, the current shared by each source is 22.5 A. Since the converter transformation ratio is 3, the total source current is higher than the load current thereby maintaining a power balance in the system.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**System Parameters** & **Values** \\ \hline \(V_{NL}\) & 305 V \\ \(V_{min}\) & 295 V \\ \(V_{\text{DC}}\) nominal value & 300 V \\ \(P_{\text{DC}max}\) & 5 kW \\ P-V droop coefficient, \(k\) & 0.002 \\ Source side inductor & 0.763 \(\times\) 10\({}^{-4}\) H \\ DC bus capacitor & 0.01 \(F\) \\ Initial value of \(R_{d}\) & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: System parameters.  
Figure 7: Wave forms of the DC bus voltage, current sharing by the sources, and the load transients obtained with fixed droop control. (**i**) DC bus voltage, (**ii**) source current 1, (**iii**) source current 2, (**iv**) load current.  
With variable droop control, the droop resistor adjusts its value according to the change in load and thus eliminates sharp deviations. The value of \(r_{d}\) changes to a lower value at the instant of load switching and then gradually varies to produce a smooth voltage deviation instead of a sudden fluctuation, which is not desirable for the stability of the microgrid.  
The droop resistor adjusts its value according to the change in load and thus eliminates sharp deviations. The value of \(r_{d}\) changes to a lower value at the instant of load switching and then gradually varies to produce a smooth voltage deviation instead of a sudden fluctuation that leads to unstable microgrid operation. The voltage regulation achieved with fixed droop control is 1.57 %, while with variable droop it is 0.84 %. The results indicate the supremacy of the variable droop controller in maintaining the voltage regulation in comparison to the fixed droop controller. The waveforms that confirm these results are shown in Figures 9 and 10. Figure 11 shows the variation in the droop resistor subject to load change. At 0.25 seconds, when the load transient of 2.5 kW is introduced, the droop resistor changes its value from 0.1651 to 0.1642. Figure 12 illustrates the variation in \(r_{d}\) for a randomly varying load current.  
Figure 8: Wave forms of the DC bus voltage, current sharing by the sources, and the load transients obtained with variable droop control. (i) DC bus voltage, (ii) source current 1, (iii) source current 2, (iv) load current.  
Figure 9: DC bus voltage for a load transient of 1.5 kW at 0.25 s with fixed droop (zoomed from Figure 6).