## 5 Simulations and Discussions
### Simulations Results  
Figure 9 shows the WF output. It is clear that the WF output is smoothed by the KE control. Especially, the proposed optimal KE control mitigates the WF output only when the fluctuation becomes large. Therefore, the generating efficiency of WF with the optimal KE controller is kept higher than that of the MA KE controller. By contrast, \(L^{\text{YC}}\) can be large, and the charge/discharge loss of ESS is reduced by the MA KE control, because the stress of ESS is reduced. Figure 10 shows the ESS output. The peak of ESS output in the proposed systems is smaller than that in the conventional system. It implies that the technical requirement can be satisfied by an ESS with smaller rated power (small rated capacity). Figure 11 shows the combined output. It can be seen from Figures 9 and 11 that the fluctuation of WF output is smoothed by the ESS. Although the KE control cannot satisfy the technical requirement by itself, as shown in Figure 12, the proposed system with the KE control and the ESS guarantees the requirement (Figure 13). Figures 14 and 15 show the SOC of Li-ion battery and NaS battery, respectively. The SOC of the ESS in the proposed/conventional systems is maintained within the proper range. The fluctuation of the SOC of Li-ion battery is larger than that of NaS battery, because the C-rate of Li-ion battery is bigger than that of the NaS battery, although these batteries have the same rated power. Table 6 summarizes the simulation results. Rated power (rated capacity) of ESS is estimated from Table 6. The rated output power of the ESS in the proposed systems are approximately 45% less than that of the ESS in the conventional system. It is evident from these results that the technical requirement \(\Delta F_{\text{g}}(t)\leq 10\%\) is satisfied while maintaining a lower charge/discharge loss of the ESS while using the KE control. Table 6 lists the SD of \(P_{\text{WF}}\) and \(P_{\text{g}}\). These values is related to power quality, such as frequency in the power system. It is clear that the WF with KE control can mitigate not only 1-Min. fluctuation of \(P_{\text{WF}}\) (\(P_{\text{g}}\)) but also SD of WF output \(P_{\text{WF}}\) (\(P_{\text{g}}\)) without increasing \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Li-Ion Battery** & **NaS Battery** \\ \hline C-rate & 3 & 0.13 \\ Price [JPY/kWh] & 200,000 & 25,000 \\ Efficiency \(\eta\) [\%] & 85 & 85 \\ \(L^{\text{cal}}\) [y] & 10 & 15 \\ PCS price [JPY/kW] & 28,800 & 28,800 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of energy storage systems (ESSs). \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Con. (MPPT)** & **Pro. (MA)** & **Pro. (Opt.)** \\ \hline Sampling period [s] & 0.5 & 0.5 & 0.5 \\ Number of Steps for MA & – & 1200 & 1200 \\ \(K_{\text{q}}\) & – & 120 & – \\ \(\alpha\) & – & 5 & – \\ \(K_{\text{p}}\) & 0.65 & 0.5 & 0.5 \\ \(a_{0}\) & \(9\times 10^{-6}\) & \(9\times 10^{-6}\) & \(9\times 10^{-6}\) \\ \(a_{1}\) & \(6\times 10^{-3}\) & \(6\times 10^{-3}\) & \(6\times 10^{-3}\) \\ \(A\) & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Controller parameters of wind generator (WG) and ESS. the rated power of ESS. Moreover, the proposed optimal KE control can reduce the \(E_{\text{WF}}^{\text{loss}}\), not requiring ESS with a high rated power. However, the Li-ion battery lifespan of the proposed system with the optimal KE controller is shorter than that with the MA KE controller because the MA KE controller removes the fluctuation of the WF output, regardless of whether the WF has large fluctuations or not. Therefore, the cycle life of the Li-ion battery in the proposed system with the MA KE control is longer than the proposed system with the optimal KE control. Note that the Li-ion battery lifespan of the ESS in the conventional system is larger than that of the proposed systems, because the ESS has large rated capacity. For the same reason, the lifespan of the NaS battery is determined by the calendar life, since the C-rate of the NaS battery is small.