## 5 Numerical Results
### Case 2--Profit Maximization with Reliability Constraints by the Commission without Incentive  
Figure 12 illustrates operations of the BESS coordinated with the renewables, considering the reliability constraints imposed by the reliability commission without additional incentives for energy discharged from the BESS. As presented in Figure 12d, after implementation of the reliability constraint, the BESS discharged the energy, considering a 70% reliability constraint on the output. In the figure, it can be observed that the BESS tended to charge the discharge energy more frequently throughout the charging periods, forcing the BESS to discharge greater energy during the off-peak periods, as intended. Compared to the energy charged and discharged \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Resource**} & **Revenue from** & **Revenue from** & **Revenue from** & **Total Revenue** \\  & **SMP** & **REC1** & **REC5** & **(KRW/USD)** \\ \multirow{2}{*}{PV-BESS} & KRW 572,670 & KRW 329,411 & KRW 569,239 & KRW 1,471,319 \\  & USD 480.71 & USD 276.52 & USD 477.83 & USD 1235.06 \\ \hline \multirow{2}{*}{WPG–BESS} & KRW 3,205,115 & KRW 2,543,911 & KRW 42,878 & KRW 5,791,904 \\  & USD 2690.46 & USD 2135.43 & USD 35.99 & USD 4861.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Intraday revenue generated from the prior operating method. Figure 12: Operation of the BESS and the PV in coordinated with profit maximization, with reliability constraints, without the incentive: (**a**) intraday operation of the BESS with WPG with profit maximization; (**b**) intraday operation of the BESS with the PV with profit maximization; (**c**) intraday operation with the reliability constraint of the BESS with WPG; (**d**) intraday operation with profit maximization and the reliability constraint of the BESS with the PV. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Resource**} & **Revenue from** & **Revenue from** & **Revenue from** & **Total Revenue** \\  & **SMP** & **REC1** & **REC5** & **(KRW/USD)** \\ \multirow{2}{*}{PV–BESS} & KRW 572,670 & KRW 329,411 & KRW 569,239 & KRW 1,471,319 \\  & USD 480.71 & USD 276.52 & USD 477.83 & USD 1235.06 \\ \hline \multirow{2}{*}{WPG–BESS} & KRW 3,205,115 & KRW 2,543,911 & KRW 42,878 & KRW 5,791,904 \\  & USD 2690.46 & USD 2135.43 & USD 35.99 & USD 4861.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Intraday revenue generated from the scheduling methods with profit maximization. in the former case, the total energy from both operations was the same, calculated to be 128.64 kWh and 1707.81 kWh, despite the reliability criteria limiting the output at the PCC by 70% of the nominal capacity of the PV, and the fact that the schedule for the charging operation was shifted backwards for the periods with lower SMP. Figure 11(c) presents the scheduling result from the coordination between the WPG and the BESS. As also presented in Tables 11 and 12, without and with implementation of the reliability constraints, there is virtually no difference in the revenue between the operating schedules from the perspective of the revenue streams. The revenues generated from the intraday operations represented in Tables 11 and 12 without and with the reliability constraints. Despite the reliability constraint limiting the output measured at the PCC by 70%, the revenue from REC1 and REC5 virtually did not differ. The revenue from SMP was the only stream which exhibited differences, because the imposed constraint and decreased revenue by 0.16%. Furthermore, from the perspective of increasing the total revenue, even though reliability constraints on the output were imposed, compared to the former scenario, the total revenue of the portfolio with the PV and the BESS from SMP and varied only 0.16% and 0.062% compared to the former revenue, implying that the reliability constraint does not significantly influence the revenue, unless the utilization factor of the PV itself in the site continuously exceeds 70% and the SMP is greater than prices of the REC.