# Transaction Mechanism Based on Two-Dimensional Energy and Reliability Pricing for Energy Prosumers
## 4 Case Study
### Economic Sensitivity Analysis  
As shown in Figures 8 and 9, the performance under the dynamic price is enhanced by increasing the EES capacity. The EES is a good solution to manage uncertainty, but increasing the EES capacity reduces the revenue by growing the EES cost. In this section, we evaluated the net revenue considering the EES cost.  
The net revenue is calculated as:  
\[\text{Net }\textit{revenue}=PW(\chi)\times Annual\textit{revenue}-EES\textit{ cost}, \tag{10}\]  
where \(PW(\chi)\) is the current worth factor that fairly adjusts the revenue to accommodate future timeframes into the present value. Assuming the service time \(\chi\) = 10 (year) of EESs, a price escalation rate \(r_{e}\) = 2.5 (%/year), and a discount rate \(r_{d}\) = 10 (%/year), the worth factor is calculated as [30]:  
\[PW(\chi)=\sum_{i=1}^{\chi}\frac{(1+r_{e})^{i-0.5}}{(1+r_{d})^{i-0.5}}. \tag{11}\]  
The EES cost is constructed from the power-subsystem capacity cost and the energy-subsystem capacity cost. Based on the corresponding capacity costs of Li-ion batteries, it was estimated as $240/kW and $360/kWh, respectively [27].  
Figure 11 shows the net revenue per year. Under the proposed ERT case illustrated as a solid line with square markers, the net revenue is greater than that without EES over the entire range, and the maximum net revenue enhancement achieved is about 6.6% when the EES capacity applied is 7% of installed generation. However, under the conventional price presented as a solid line with circle markers, the net revenue is greater than that without EES only when the EES capacity is less than 10% of the installed generation, and the maximum net revenue enhancement is about 1%, with 2% EES capacity of installed generation. As such, the proposed ERT is economically efficient and adaptively manages the uncertainty, and the conventional pricing is inefficient.  
Figure 10: The change in band hit ratio under the conventional pricing mechanism and the proposed ERT with varying EES capacity. (**a**) Conventional price case; (**b**) Proposed ERT.  
In Case 1, the prosumer realizes more revenue than under the conventional price every day. The average prosumer revenue improvement has the same value under both the conventional pricing and the ERT in Case 2, but the prosumer revenues under the ERT in Case 2 have a higher or lower value than under the conventional price. This is because the proposed ERT varies according to the daily generation characteristics. However, in Case 2, the utility has more MAE improvement, 25.1%, versus 19.0% for the conventional system, as presented in Table 3. In addition, the MAE change also shows a similar pattern as presented in Figure 10b. These results verify that the proposed ERT is an effective way to manage grid reliability without loss of prosumer benefits.  
Comparing the results of Case 1 and Case 2 in Table 3, the greater revenue enhancement case yields less MAE improvement. Revenue and MAE are the performance metrics of the prosumer and the utility, respectively. Thus, the trade-off between revenue enhancement and MAE improvement can be used as the band design strategy.