## 4 Simulation Results
### Power Flows  
While Sections 4.2 and 4.3 primarily focus on the results dominated by pricing mechanisms, power flow is an aspect strictly related to the market-clearing model. Consequently, the power flows for the Uniform (SMP), 2-Zonal (SMP), and 2-Zonal (ZMP) zones, which shared common market-clearing results, were identical. Within the nodal pricing, Nodal (LMP) and Nodal (ELMP) shared the same market-clearing results. Notably, the power flow resulting from nodal pricing can be considered to align with the actual power flows, that is, power system operations. Only the 5-zonal pricing yielded different market-clearing results depending on whether the ATC or FBMC model was used. The results for uniform pricing and 2-zonal pricing, which stem from the imbalance between the capital and non-capital regions mentioned in Table 6, indicated an annual average flow of 11,661 MW from NKY to KY, with transmission congestion occurring for 4376 h annually. Our primary focus was on the 5-zonal pricing. Figure 9 illustrates the power flow between each zone when adopting the ATC and FBMC model in 5-zonal pricing. In Figure 9, the red lines represent identical flows in the ATC and FBMC models, whereas the blue lines indicate different flows. Specifically, the flows differed in the two transmission interfaces: KY\(\rightarrow\)GW and CC\(\rightarrow\)JL. Table 11 presents the annual average power flow and congestion hours between the zones. To compare the results of the 5-zonal pricing with the actual power flows, we must consider that the actual power flows were derived from nodal pricing. Therefore, for a direct comparison with the 5-zonal pricing, we aggregated the power flow results from nodal pricing into the zones defined in the 5-zonal pricing scheme. The aggregated results, reflecting the zonal grouping of power flows from the nodal pricing, are presented in Table 11 for comparison. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Pricing Scheme**} & \multicolumn{2}{c}{**5-Zonal (ATC, ZMP)**} & \multicolumn{2}{c}{**5-Zonal (FBMC, ZMP)**} & \multicolumn{2}{c}{**Nodal Pricing**} \\ \cline{2-7}  & **Average Flow** & **Congestion** & **Average Flow** & **Congestion** & **Average Flow** & **Congestion** \\  & **(MW)** & **Hours (h)** & **(MW)** & **Hours (h)** & **(MW)** & **Hours (h)** \\ \hline KY\(\rightarrow\)GW & 4423 & 4374 & \(-\)4491 & 3665 & \(-\)5619 & 1457 \\ \hline CC\(\rightarrow\)KY & 16,083 & 4374 & 7615 & 3665 & 6947 & 1457 \\ \hline GW\(\rightarrow\)CC & 14,996 & 5275 & 2347 & 0 & 1697 & 0 \\ \hline CC\(\rightarrow\)JL & 1814 & 8083 & \(-\)2865 & 431 & \(-\)2280 & 86 \\ \hline JL\(\rightarrow\)YN & 4802 & 568 & 166 & 1 & 34 & 0 \\ \hline YN\(\rightarrow\)CC & 875 & 8612 & 184 & 2 & 174 & 0 \\ \hline YN\(\rightarrow\)GW & 5065 & 0 & 1310 & 0 & 1691 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison of annual average power flows and congestion hours between zones in 5-zonal pricing and aggregated nodal pricing results. Two significant implications can be drawn from these results. First, the ATC model, which disregards physical laws, produced interzonal flows that deviated from actual power flows. Consequently, if redispatch, which was not considered in this study, were to be considered, it is anticipated that the ATC model would facilitate a substantial increase in side payments. In contrast, the FBMC model demonstrated reasonable interzonal power flows compared to the actual flows. Although the FBMC model necessitates accompanying processes such as system reduction, it is expected to necessitate less redispatch than the ATC model, which is a commonly observed advantage in previous studies [27]. Second, this analysis elucidated why the SMP mechanisms could not be applied to 5-zonal pricing in the Korean power system. As illustrated in Figure 9, Korea's power system forms a loop network. The SMP mechanism is based on the rule of separating market prices when transmission lines between adjacent zones are congested.