## 4 Results and Analysis
### Trading Results for Interval I  
Figure 10 shows the trading results of the different trading strategies for Interval I. Prosumers were able to sell the majority of their PV energy to the P2P customers because of their lower generation and the high demand of the customers (see Figure 10b). Contrarily, due to the relatively lower PV generation of the prosumers, the customers were only able to trade a small amount of their demand from the P2P market (Figure 10a). Figure 10c shows the Interval I welfare metrics using different trading strategies. Because the prosumers sold the majority of their PV energy via the P2P trading platform, their welfare was relatively higher compared to the customers' welfare, as is evident in Figure 10c. The low welfare of the customers was due to their limited participation in the market because of the relatively lower PV generation of the prosumers. Figure 11 shows the convergence of the Stackelberg  
Figure 8: Simulation test case with a set of 10 customers and 5 prosumers located at different nodes in a radial network based on [34].  
Figure 9: P2P input data for the suggested trading platform. The data is shown as the double axis graph, where the aggregated PV power of the prosumers is shown in the form of the bar graph with respect to the power axis.  
game for one of the samples of the market. In this particular sample, the matched orders were (P1-C1, P2-C1, P3-C2, and P4-C3), where P represents the prosumer number, and C represents the customer number. As is evident from Figure 11, the proposed GT approach found the optimal solution while maximizing the utility function of the prosumers' and the customers' savings.  
Another important aspect for Interval I was that the amount of P2P energy traded using the GT approach was lower compared to the ZI strategy. This resulted in lower welfare for the market participants using GT compared to the rule-based determination. This was due to the fact that the prosumers will have some reluctance (\(\alpha_{j}>0\)) when determining their utility function, which limits their participation in the P2P market. In an ideal case where the prosumers have zero reluctance (\(\alpha_{j}=0\)), both the ZI and GT methods will yield approximately the same trading results. However, the reluctance parameter \(\alpha_{j}\) is imperative to model the individual preference of the participants under the heavy losses/a network fee, which will be depicted at the later portion of the Section 4. Additionally, to avoid the singularity for the optimization function of the prosumers given in Equation (15), the problem will be solved for \(\alpha_{j}>0\). Note that the clearance mechanism (gray portion of the bar graphs) in the results shows the unmatched orders of the P2P market. For customers, the clearance amount is the energy bought from the market operator at the utility real-time price (RTP). Similarly, the prosumers sell any remaining excess PV energy to the operator as a FIT for clearance purposes.  
Figure 10: Comparison of P2P trading results for Interval I for different trading strategies. (**a**) Customers’ trading pattern for Interval I. (**b**) Prosumers’ trading pattern for Interval I. (**c**) Welfare metrics for Interval I.