## 4 Calculation of Generation Time for Energy Self-Sufficiency of 90% with PVs and ESSs  
\(\bullet\)\(C_{0}\) = \((\text{Se}\times 2)-100\)  
\(\bullet\)\(C_{0}\) = Correlation coefficient  
\(\bullet\)\(Se\) = self-sufficiency (%)  
\[A_{p}=\frac{\left(\left(C_{0}+100\right)/2\right)\times 12\right)\ -\ \left(100\times O_{p}\right)}{\sum_{k=1}^{12}E_{k}- \left(100\times O_{p}\right)} \tag{4}\]  
\(\bullet\)\(A_{p}\) = Application coefficient  
\(\bullet\)\(O_{p}\) = Number of households that had over a 100% generation time efficiency per month  
\(\bullet\)\(E_{k}\) = Sum of efficiency from January to December  
The following equation used to set the energy self-sufficiency of the target household as 90%. \(\bullet\)\(C_{0}\) = \((90\times 2)-100\) = 80  
\[A_{p}=\frac{\left(\left(80+100\right)/2\right)\times 12\right)\ -\ \left(100\times 5\right)}{1116.19\ -\ \left(100\times 5\right)}=\frac{580}{616.19}=0.9412651 \tag{5}\]  
As shown in Table 4, for those months when the self-sufficiency was over 100%, the values were limited to 100%. Under this condition, by using the derived application coefficient, a 90% energy self-sufficiency could be verified. In the case of households that used an average of 250 kWh per month in the last year, the energy self-sufficiency increased from 73% to 93%, and the optimized capacity of the PVs increased from 1.65 to 2.82 kW, which is an approximately 71% rise. For households with 350 and 450 kWh energy usages, the capacities of the PV facilities increased from 2.32 to 3.95 kW, and 2.98 to 5.28 kW, respectively. Both cases showed an approximately 70% rise in PVs capacity, as presented in Figure 5.  
According to the results of the research and the simulations, when the energy self-sufficiency of a household exceeds 93%, errors are inevitable; therefore, the optimum capacity of the PVs and ESSs must be selected in the limited condition of a below 93% energy self-sufficiency. As shown in Figure 5, the optimum capacity of the ESS for a household using 250 kWh per month is approximately 7.15 kWh, and does not change, as the energy self-sufficiency varies between 70% and 90%. For households with an average power usage of 350 and 450 kWh, the optimum capacities of the ESS are 10.01 and 12.87 kWh, respectively. When energy self-sufficiency is set between 70% and 100%, hourly increases are generated as the capacity of the PVs decreases, resulting in a steady value for the capacity of the ESS. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Category** & \begin{tabular}{c} **Average Generating** \\ **Hour per Day (h)** \\ \end{tabular} & \
\begin{tabular}{c} **Calculation** \\ **Method (A\({}_{\text{p}}\) = 0.9412651)** \\ \end{tabular} &
\begin{tabular}{c} **Average of Self-Sufficiency Set** \\ **to 90% (\%)** \\ \end{tabular} \\ \hline January & 3.15 & \((3.15/3.56)\times 0.9413\times 100\) & 83.40 \\ February & 3.47 & \((3.47/3.56)\times 0.9413\times 100\) & 91.83 \\ March & 4.23 & 100.00 & 100.00 \\ April & 4.23 & 100.00 & 100.00 \\ May & 4.52 & 100.00 & 100.00 \\ June & 4.11 & 100.00 & 100.00 \\ July & 3.27 & \((3.27/3.56)\times 0.9413\times 100\) & 86.35 \\ August & 3.44 & \((3.44/3.56)\times 0.9413\times 100\) & 90.95 \\ September & 3.72 & 100.00 & 100.00 \\ October & 3.52 & \((3.52/3.56)\times 0.9413\times 100\) & 93.11 \\ November & 2.55 & \((2.55/3.56)\times 0.9413\times 100\) & 67.41 \\ December & 2.53 & \((2.53/3.56)\times 0.9413\times 100\) & 66.92 \\ Average & 3.56 & - & 90.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average power generated by 3-kW PVs per day for each month over the last eight years. Figure 5: PVs and ESSs capacity change graph with a 70–100% self-sufficiency. With Equations (1)-(3) used to derive the optimum capacities of the PVs and ESS, a large range of errors were found. Further analyzation was conducted, and when the energy self-sufficiency increased from 70% to 94%, the capacity of the ESS was shown to be 267.74% of the capacity of the PVs at a whole range.