## 4 Results
### Performance Analysis  
Figure 3 shows the average net benefit and return of investment (ROI) of the participants by the VESS operation with varying VESS capacity. The average net benefit is measured as the average value of the net benefit of the participants in Equation (6) with the billing period of 1 month. The ROI shows that the economic efficiency of service participation is calculated using Equation (12). Moreover, changes in VESS capacity show the effect of changes in service cost of the VESS. In Figure 3a,b the line with circles represents the results of the VESS operation using **P0**, and the lines with squares and diamonds present the results of applying the VESS operation of **P1** considering the usage factors as \(\beta=1\) and \(\beta=2\), respectively. As shown in Figure 3a, the net benefit of the participants increases as the VESS capacity increases. This is because the unit cost of the VESS reduces with the increment in the VESS capacity using Equation (1). Therefore, the capacity of the VESS allocated to the participants increases. In the case of the VESS operation by **P0**, in which the operation is limited according to the allocated capacity, the net benefit increases significantly as the VESS capacity increases. The results of the VESS operations by **P1** \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Demand Price** & \multicolumn{3}{c}{**Energy Price (USD/kWh)**} \\
**(USD/kW)** & **Off-Peak** & **Mid-Peak** & **On-Peak** \\ \hline
7.4818 & 0.0476 & 0.0942 & 0.1146 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Time-of-use tariff of Korea electric power company [35]. Figure 2: Comparison of the virtual energy storage system (VESS) operation according to **P0** and **P1**: (**a**) VESS operation for participants 1 and 2 by **P0**; (**b**) VESS operation for participants 1 and 2 by **P1**. with one cycle and two cycles achieve much higher net benefit than by **P0**. This verifies that the proposed VESS operation of managing the usage is more effective than the VESS operation, which limits the allocated capacity. In the case of the VESS operation by **P1** with one cycle, the increment of the net benefit exhibits marginal change when the implemented VESS capacity is varied. In this case, the usage factor restricts the VESS operation, and the participants achieve the benefit by reducing the unit VESS only. The result obtained by **P0** has the ROI of slightly greater than 1. However, when the VESS capacity is 100 kWh, the ROIs of 2.0 and 2.7 are achieved according to the results of the proposed VESS operations with one and two cycles, respectively. This means that the proposed VESS operations using **P1** are more than twice as cost-effective as the existing operation using **P0**. Increasing the implemented VESS capacity reduces the ROIs of the proposed VESS operations. This is because the participants use more VESS capacity to achieve benefits by increasing the implemented VESS capacity as depicted in Figure 3a, but the increase in benefit is less than the increase in cost. Figure 4 shows how savings on the electricity bill are achieved by applying the VESS operation. The electricity bill consists of a demand bill and energy bill as shown in Equation (3). In Figure 4, the blue bar, red bar, and yellow bar represent savings on the demand bill, energy bill, and total electricity bill, respectively, compared with the electricity bill without the VESS operation in Equation (3). The proposed VESS operation achieves more total savings on the electricity bill compared with that of the VESS operation by **P0**. Particularly, the VESS operation for reducing the demand bill is to lower the peak demand by charging operation. The savings on the demand bill are highly related to the maximum allocated VESS capacity. Therefore, the proposed VESS operation provides more savings on the demand bill in comparison to VESS operation by **P0**. The VESS is charged and discharged to shift the demand from high price times to other times for reducing the energy bill.