## 3 Simulation Results
### Simulation Results for the Jeju Island System  
Figure 7 shows the configuration of the Jeju Island power network [42]. There are four generators and three HVDC systems, i.e., two LCC HVDCs and one VSC HVDC. The first LCC HVDC is a 180 kV/300 MW system constructed in 1998, and the second LCC HVDC is a \(\pm\)250 kV/400 MW system constructed in 2013. The VSC HVDC considered in the simulation is a planned installation with a capacity of \(\pm\)150 kV/200 MW. The base of complex power is 100 MW, and the base voltage is 154 kV. The active power of generators, line impedance, and data of the shunt compensator in the test system are represented in Appendix A. The actual load data from Jeju Island at peak time is utilized, as illustrated in Figure 8. The simulation scenarios are similar to those with the IEEE 14-bus test system. Only one generator at Jeju 3C/S controls the voltage magnitude at 1.04 p.u., and the other generators only regulate active power, which means that the reactive power of these generators is zero. The output of the conventional method is determined proportional to capacity. Table 3 shows the results of steady-state analysis using the conventional and proposed methods. As the outputs of multiple HVDCs are determined proportional to their capacity in the conventional method, the active power ratio of Jeju #1, #2, and #3 is 3:4:2. On the other hand, the results of the proposed method determine the operating points of the HVDCs using an op \begin{table}
\begin{tabular}{c c c} \hline  & **Conventional** & **Proposed** \\ \hline Deviation of LCC HVDC’s output (\(\Delta P_{LCC}\)) & \(-\)0.32 MW & \(-\)0.28 MW \\ Deviation of VSC HVDC’s output (\(\Delta P_{VSC}\)) & \(-\)0.32 MW & \(-\)0.35 MW \\ Deviation of power loss & \(-\)36.41 kW & \(-\)36.74 kW \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of power loss between randomly sampled load profiles. Figure 6: Graphical coefficient determination method applied to the IEEE 14-bus test system. Figure 7: Configuration of the Jeju Island network with multiple HVDCs. power loss in the system was reduced 13.82% from that of the conventional method. The results suggest that operation with the proposed optimization problem would reduce power loss. In the second case, Jeju #1 and Jeju #3 are connected to same bus. Among two HVDC systems, the ratio of active power is not significant, because they are connected to same bus. However, the references to them are determined because LCC HVDC absorbs reactive power different from the VSC HVDC. Therefore, the proposed optimization problem considers not only active power but also optimal reactive power flow. Figure 9 presents a graphical analysis of droop coefficient determination. To verify the droop coefficient determination method, 1000 randomly extracted scenarios were utilized. Equivalent droop coefficients \(R_{eq}\) and \(D\) were assumed to be identical to the previous case study. As a result, we could derive the droop coefficients, \(R_{LCCI}\), \(R_{LCC2}\), and \(R_{VSC}\), as 0.298, 0.233, and 0.426, respectively. The droop coefficients derived from Figure 9 are verified by comparison with the conventional case, in which the steady-state system is determined by an optimization problem. The only difference between the conventional and proposed methods is that the droop coefficients are proportional to capacity in the conventional method. Table 4 shows the average loss deviation from the power loss at steady-state for 1000 random cases. Power loss deviation is reduced 0.48% using the proposed droop coefficients. The difference is very small because the droop coefficient in the conventional method is very similar to that of the proposed method; however, the power loss is successfully reduced using the proposed method.