# Multi-Objective Configuration Optimization of
## 5 Simulation and Analysis  
Numerical simulations are carried out based on Matlab/Simulink. The allowed depths of discharge of the superconductor (SC) and battery range from 0.25 to 0.95 and 0.2 to 0.9, respectively. Their self-discharge rate is 0, an initial SOC is 0.55, and charge efficiencies are 100% and 80%, respectively. In addition, their unit-rated capacity is 1 MW, and charge/discharge power are 0.1 MW and 1 MW, respectively. The other characteristic parameters are listed in Table 2[16; 17]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **SC** & **Battery** \\ \hline Power rating initial cost \(C_{P}\) (\$/kW) & 366 & 315 \\ Energy rating initial cost \(C_{E}\) (\$/kWh) & 370,000 & 325 \\ Lifespan \(L\) (years) & 50 & 20 \\ Round-trip efficiency \(\eta\) (\%) & 100 & 80 \\ Power conversion system cost \(C_{C}\) (\$/kW) & 153 & 173 \\ Disposal cost \(C_{D}\) (\$/kW) & 1.5 & 1.4 \\ Fixed O\&M cost \(C_{OM}\) (\$/kW) & 13.1 & 17.6 \\ Variable O\&M cost \(C_{OM}\) (\$/kW) & 6.8 & 6.5 \\ \([SO_{Cmin},SOC_{max}]\) & \([0.25,0.95]\) & \([0.4,0.8]\) \\ \(E_{rated\text{-max}}\) (MWh) & 5 & 40 \\ \(P_{rated\text{-max}}\) (MW) & 15 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of supercapacitor (SC) and battery. Figure 4: Scheme of identifying optimal solutions. The wind power is illustrated in Figure 6 that supposes it is of normal distribution with a mean of 50 MW and a variance of 15 MW. Apply BC-MOPSO to determine the rated capacity and power of each ESS, and the configuration solutions and their corresponding objective-function values are listed in Table 3. The distribution of Pareto solutions in the objective-space are demonstrated in Figure 5.  
From Table 3 and Figure 5, it is evident that the rated capacity and power of each ESS increase with increasing satisfaction rate of wind power fluctuation compensation. Especially, when the satisfaction rate is larger than 93.91%, the HESS cost is remarkably increased. To analyze the compensation effect, take the 9 th solution as an example. Figure 6 demonstrates the comparison between the compensated and uncompensated wind power. Investigation from Figure 6, it is clear that HESS dramatically reduces the fluctuation of wind power output, and 94% of \(\mid\eta\mid\) is less than 2%. However, for some period, the difference between the compensated wind power and the reference power is rather large. For example, when \(t\) = 437 s, \(P_{WDnf}\) = 66.25 MW: When \(t\) = 436 s, \(P_{WD}\) is quite large, which leads the SC and the battery to charge and their SOCs to be high. As a result, HESS fails to well compensate the fluctuating wind power that produces a compensated wind power output of 70.63 MW. Figure 5: Distribution of optimal solutions in the objective space. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Solutions**} & \multicolumn{2}{c}{**Objective-Function**} \\ \hline  & \multicolumn{2}{c}{**SC**} & \multicolumn{2}{c}{**Battery**} & \\ \cline{2-7}  & \(E_{SCrated}\) **(MWh)** & \(P_{SCrated}\) **(MW)** & \(E_{Brated}\) **(MWh)** & \(P_{Brated}\) **(MW)** & \(f_{cost}\) & \(f_{prob}\) \\ \hline
1 & 0.1 & 1 & 1 & 2 & 9.79 & \(8.48\times 10^{5}\) \\
2 & 0.1 & 1 & 2 & 4 & 22.28 & \(9.78\times 10^{5}\) \\
3 & 0.1 & 1 & 3 & 5 & 37.86 & \(1.11\times 10^{5}\) \\
4 & 0.1 & 1 & 4 & 9 & 51.75 & \(1.25\times 10^{6}\) \\
5 & 0.1 & 1 & 5 & 13 & 64.24 & \(1.40\times 10^{6}\) \\
6 & 0.1 & 1 & 8 & 14 & 75.82 & \(1.58\times 10^{6}\) \\
7 & 0.1 & 1 & 10 & 18 & 86.51 & \(1.79\times 10^{6}\) \\
8 & 0.1 & 1 & 17 & 20 & 91.15 & \(1.20\times 10^{7}\) \\
9 & 0.6 & 4 & 19 & 20 & 93.91 & \(1.49\times 10^{7}\) \\
10 & 1.8 & 10 & 18 & 20 & 94.81 & \(1.60\times 10^{7}\) \\
11 & 2.2 & 12 & 18 & 20 & 95.7 & \(1.79\times 10^{7}\) \\
12 & 2.9 & 15 & 13 & 20 & 97.4 & \(2.00\times 10^{7}\) \\
13 & 3 & 16 & 14 & 20 & 99.2 & \(2.38\times 10^{7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Pareto solutions and corresponding objectives. Figure 7 depicts the dynamic SOCs of the SC and battery, respectively.