# Risk-Based Virtual Energy Storage System Service Strategy for Prosumers
## 4 Results and Discussion  
In this section, to verify the effectiveness of the proposed VESS service strategy, the benefits to the SP and units are measured, and the effects of the characteristics of the system parameters are discussed. To perform simulations, the ESS cost parameters were set as \(\alpha_{1}=0.6\), \(\alpha_{2}=0.000032\), and \(\alpha_{3}=0.19\), fitting the value in [28]. The experimental environment presented in [26] was used as the P2P energy transaction for prosumers. The prosumers traded energy using the central P2P energy transaction mechanism in [26]. The daily energy transaction was the prosumer-traded energy within the same pair for a day. The transaction was measured every half hour. The prices for buying from and selling to the grid were assumed to be \(p_{B}=0.15\) $/kWh and \(p_{S}=0.10\) $/kWh, which are the average electricity prices in the U.S. [33]. The P2P energy transaction price was set to \(p_{T}=0.125\) $/kWh. The average daily demand and uncertainty of the prosumers were uniformly distributed in the range of \((20,30)\) kWh and \((0,30)\)%, which is the reference case in [26].  
Figure 3 shows the monthly benefit of SP according to the VESS installation capacity and service price, with eight prosumer pairs in Figure 3a, and 16 pairs in Figure 3b, by applying the proposed VESS service strategy. To evaluate the effectiveness of the proposed VESS service strategy, the results using the VESS service strategy without considering VaR are compared in Figure 3c,d with eight pairs and 16 pairs, respectively. In the figures, the points marked as X are the optimal points for maximizing the benefit to the SP when the SP is profit-seeking. As mentioned above, the operational point of the non-profit SP is expressed as the line where the benefit to the SP is 0, as shown in the figures. The points marked as diamonds are the optimal points for maximizing the benefit of units in a non-profitable service operation.  
In the case of a profit-seeking SP, when comparing the benefits to the SP considering VaR and without considering VaR, the values are $28.8 and $30.2 monthly for the eight pairs and $66.5 and $81.0 for the 16 pairs, respectively. The results show that the SP can achieve more benefit using the proposed VESS service strategy considering VaR compared with not considering VaR. The absolute benefit to the SP is low. This is because the ESS cost is still high, even if a VESS is applied. However, the benefit to the SP applying the proposed VESS service strategy considering VaR compared with that without considering VaR increases with the number of prosumer pairs, as shown in Figure 4.  
Figure 4 presents the benefit enhancement of the SP applying the proposed VESS service strategy compared with not considering VaR. It is shown that increasing the number of prosumer pairs, the benefit enhancement by the proposed VESS service strategy is increased. This is because by increasing the number of prosumer pairs, the unit ESS cost can be reduced with increasing serving capacity compared with the results in Figure 3a,b. Moreover, owing to multi-user diversity, the cost reduction according to the consideration of VaR is increased. The benefit enhancement ratio is saturated when the number of  
prosumer pairs is larger than 32. This means that the VESS service strategies considering VaR and without considering VaR have the similar benefit enhancement ratio. However, even in this case, using the proposed VESS service strategy, the SP achieves more than 30% additional benefit. To check the effect of VaR, Figure 5 shows the VESS installation capacity and serving capacity purchased by units when the proposed VESS service strategy is used. In fact,  
Figure 4: Benefit enhancement of the SP after applying the proposed VESS service strategy considering VaR compared with not considering VaR. Figure 3: Monthly benefits of SP as a function of VESS installation capacity and service price when varying prosumer pairs and VaR consideration; **(a)** Results for eight pairs considering VaR.