## 4 Simulation Results  
The sample microgrid used in simulation for a PB is shown in Figure 3. Three sources are included; one is a solar resource, one is a conventional resource such as a diesel generator, and one is an energy storage source such as a battery. In the simulation, these sources are modeled as variable voltage sources, and droop control is implemented for each. The numeric values used for this microgrid model are shown in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Value** & **Unit** \\ \hline \(R_{1B}\) & 0.1 & \(\Omega\) \\ \(L_{1B}\) & 1 & mH \\ \(R_{2B}\) & 0.2 & \(\Omega\) \\ \(L_{2B}\) & 2 & mH \\ \(R_{3B}\) & 0.12 & \(\Omega\) \\ \(L_{3B}\) & 1 & mH \\ \(C_{load}\) & 1 & mF \\ \(k_{p}\) & 1 & \\ \(k_{i}\) & 10 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Patrol base microgrid parameter values. Figure 2: Solar irradiance measured each minute on 1 June 2012. A simulation was completed to represent one full day at the PB. The power available from solar energy at each minute of the day is shown in Figure 4a. The data described in the previous section is used, assuming that there are 4 square meters of solar panels available. The required load at each minute is shown in Figure 4b, with the three load tiers described above added together to form the total required load. The system was first simulated using traditional, linear droop control for each of the three sources, where the reference current is defined as  
\[i_{\mathit{ref}}=\frac{V_{\mathit{ref}}-V_{\mathit{bus}}}{R_{d}} \tag{3}\]  
The droop control settings for each of the three sources are shown in Table 5.  
Figure 4: (**a**) Solar power available and (**b**) load profiles for simulated 1440 min period. Figure 3: Example microgrid used in simulation for patrol base (PB) demonstration of droop control methods. The power supplied by each of the three sources during the simulated one day period is shown in Figure 5. When it is sunny during the day, the solar source operates with traditional droop control, and does not use all of the available power. The conventional source is required to meet most of the load demand. The storage source supplies and absorbs power throughout the day as the load changes. The simulation was then repeated using optimal high dimension droop control for the solar resource. Its reference current is defined as [12]  
\[i_{ref1}^{*}=\frac{-V_{bus}+\sqrt{4\hat{P}(s)R_{1B}+V_{bus}^{2}}}{2R_{1B}} \tag{4}\]  
where \(s\) is the solar irradiance in W/m\({}^{2}\) multiplied by the 4 m\({}^{2}\) of panels. The conventional and storage sources kept the same droop settings as in Table 5 for the second simulation. The power supplied by each of the three sources during the simulated one day period is shown in Figure 6. With optimal high dimension droop control, all of the available power from the solar resource is utilized. This means that the conventional source is required to provide less power to the system. The storage source changes during the sunny part of the day, and supplies power as needed during the night. A comparison of Figures 5 and 6 shows that the use of traditional linear droop control limits the amount of power that can be utilized from the solar resource, while the use of optimal high dimension droop control allows all of the available power from that resource to be utilized. This also means that the conventional source is needed less, and the storage source is able to charge during times of high irradiance, and use that stored energy during cloudy periods or at night. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Source** & \(V_{ref}\) & \(R_{d}\) \\ \hline Solar & 300 & 2.5 \\ Conventional & 300 & 0.4 \\ Storage & 295 & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Traditional droop control settings for patrol base (PB) simulation. Figure 5: Power supplied by solar, conventional, and storage sources when traditional droop control is used.