## 2 Design of a System without Base Generation (Referenced Study)
### Capacity Design of the ESS Systems  
The capacity of the ESS was first calculated by considering the daily power generation of the PV system, inverter efficiency, depth of discharge (\(E_{DOD}\)), and state of charge (\(E_{SOC}\)) of the ESS. These were calculated by excluding the amount of set-off power (\(P_{CT}\)). Therefore, the final equation for the ESS capacity calculation can be expressed as (4) [9].  
\[ESS_{0}=\frac{PV_{E}\times T_{as}}{I_{eff}\times E_{DOD}\times E_{SOC}}-P_{CT} \ [kWh] \tag{4}\]\[C_{CTP}=\frac{P_{CT}}{P_{day}} \tag{5}\]  
In (4), the set-off power (\(P_{CT}\)) is calculated by subtracting the amount of power generated by photovoltaic power from the amount of power consumed during the same period of the day. The set-off power (\(P_{CT}\)) refers to the amount of PV generated power that is directly supplied to customers (target area) as it is generated. It could be expressed as (5), which also refers to the self-sufficiency rate of the PV power generation system built in the target area. In addition, it is advantageous in terms of cost reduction because it is possible to reduce the capacity of the ESS as much as the amount of set-off power (\(P_{CT}\)).  
Figure 1 shows the daily load pattern and daily PV power generation in the targeted region of this study. \(P_{CT}\) is illustrated as the yellow area where the two graphs overlap. The \(P_{CT}\) is 1038 kWh, which is calculated as 47% of the total load amount of 2197 kWh. In this study, when the actual calculation is done with \(C_{CTP}\), it would be substituted as 0.47.  
\(C_{CTP}\) would be further applied to the equations as 0.47 in this study.  
\[\begin{split} ESS_{0}=\frac{PV_{E}\times T_{as}}{I_{eff}\times E _{DOD}\times E_{SOC}}-C_{CTP}\cdot P_{day}\left[kWh\right]\\ ESS_{0}=\frac{PV_{E}\times T_{as}}{I_{eff}\times E_{DOD}\times E _{SOC}}-0.47P_{day}\left[kWh\right]\end{split} \tag{6}\]  
Equations (1)-(6) are the results of the referenced study, but we would like to summarize some equations once again for the economic analysis in this study. This is not a new calculation or analysis of the existing equation but a brief reorganization of the relationship between the capacity of the PV power generation system and the capacity of the ESS system. First, (3) is reorganized for the average daily power consumption (\(P_{day}\)) using (2), as shown in (7) [9].  
\[P_{day}=PV_{E}\Big{[}T_{as}\times I_{eff}\times(1-C_{L})\times(1-E_{CL})\times (1-E_{DL})\Big{]}\left[kWh\right] \tag{7}\]  
Figure 1: The set-off power in a day.  
Equation (6) is rearranged to (8) using (7). The relationship between the capacity of the ESS system and the capacity of the solar power generation system can be summarized as (9). The remaining, excluding \(ESS_{0}\) and \(PV_{E}\) in (9), are treated as an arbitrary constant (\(C_{0}\)), which can be organized as (10) in which \(C_{0}\) could be defined as (11).  
Equations (9) and (10), which reorganize the capacity of the ESS system (\(ESS_{0}\)) using the capacity of the PV power generation system (\(PV_{E}\)), are used in the economic analysis in Section 4.  
\[ESS_{0}=\frac{PV_{E}\times T_{as}}{I_{eff}\times E_{DDO}\times E_{SOC}}-C_{CTP }\cdot PV_{E}\Big{[}T_{as}\times I_{eff}\times(1-C_{L})\times(1-E_{CL})\times( 1-E_{DL})\Big{]}\left[KWh\right] \tag{8}\]  
\[ESS_{0}=\bigg{\{}\frac{T_{as}}{I_{eff}\times E_{DDO}\times E_{SOC}}-C_{CTP} \cdot T_{as}\times I_{eff}\times(1-C_{L})\bigg{\}}PV_{E}\left[KWh\right] \tag{9}\]  
\[ESS_{0}=C_{0}\cdot PV_{E}\left[KWh\right] \tag{10}\]  
\[C_{0}=\bigg{\{}\frac{T_{as}}{I_{eff}\times E_{DDO}\times E_{SOC}}-C_{CTP} \cdot T_{as}\times I_{eff}\times(1-C_{L})\bigg{\}} \tag{11}\]