## 4 Economic Analysis
### Cost Comparison (Economic Analysis)
The cost of a system without a base power source is expressed as \(C_{1}\), and the cost of a system with a base power source is expressed as \(C_{2}\). Using the variables defined above, (12), (13), and \(C_{1}\) can be expressed as (14). Here, \(\alpha\) is a value  
Figure 6: Cost comparison according to the presence or absence of a base power source. for correcting A and B, defined as a ratio, and is an arbitrary constant to determine the actual capacity of A and B.  
\[C_{1}=(\mathrm{A}+\mathrm{B})\alpha\cdot\mathrm{y}+2.96(\mathrm{A}+\mathrm{B}) \alpha\cdot\mathrm{z} \tag{14}\]  
The cost of a system with a base power source \(C_{2}\) can be expressed as (15). \[C_{2}=A\cdot\alpha\cdot x+B\cdot\alpha\cdot\mathrm{y}+2.96\mathrm{B}\cdot \alpha\cdot\mathrm{z} \tag{15}\]  
To analyze the economic feasibility according to the presence or absence of a base power source, we attempted to find a branch point where the two systems have the same cost; that is, \(C_{1}\) and \(C_{2}\) are the same. \[C_{1}\ =C_{2}\]  
This can be expressed as follows from (14) and (15). \[(\mathrm{A}+\mathrm{B})\alpha\cdot\mathrm{y}+2.96(\mathrm{A}+ \mathrm{B})\alpha\cdot\mathrm{z}\ =A\cdot\alpha\cdot x+B\cdot\alpha\cdot\mathrm{y}+2.96\mathrm{B}\cdot\alpha \cdot\mathrm{z}\] \[(\mathrm{A}+\mathrm{B})\mathrm{y}+2.96(\mathrm{A}+\mathrm{B}) \mathrm{z}\ =A\cdot x+B\cdot\mathrm{y}+2.96\mathrm{B}\cdot\mathrm{z}\]  
The above equation can be summarized simply as (16). \[x=\mathrm{y}+2.96\mathrm{z} \tag{16}\]  
From (16), it can be seen that when the unit cost of a base power source (fuel cell) is equal to the sum of the unit cost of the PV and 2.96 times the unit cost of ESS, the costs of adopting and not adopting the base power source are the same. Because it is advantageous to adopt a base power source for the stability of the system's power supply, it is recommended to adopt a base power source if the unit cost of the base power source is equal to or less than \(\mathrm{y}+2.96\mathrm{z}\). In other words, when a base power source is adopted, the criterion for securing the system power supply stability and economic efficiency can be presented as (17). \[x\ \leq\mathrm{y}+2.96\mathrm{z} \tag{17}\]  
The value of \(C_{0}\), 2.96, is a variable value depending on the characteristics of the system components (inverter, ESS, cable, etc.). However, it can be treated as a constant figure because the efficiency of the inverter and the characteristics of the ESS are generally set as generalized and leveled values. If there is a problem when this constant value is applied as 2.96, owing to technological or environmental changes in the future, then it can be corrected by modifying the value of the constant (\(C_{0}\)) using (11). To visually see the condition of (17), a random variable was put into (17) and illustrated as a graph, as shown in Figure 7. Because the \(x\) value must be smaller than \(\mathrm{y}+2.96\mathrm{z}\) or the same in the equation, the area under the group consisting of multiple points corresponds to the criterion. The base power source has an advantageous condition in terms of economics when the \(x\), \(\mathrm{y}\), and \(\mathrm{z}\) values are located within this area.