## 4 Simulation Results
### Market Price
During these hours, while KY's market price was set by the LNG plants, NKY's marginal unit shifted to coal plants owing to the influx of solar PV generation. This shift in marginal units within each zone explains the significant price disparity observed in the 2-zonal pricing scheme. In 2023, an exceptionally large gap between coal and LNG fuel costs led to a significant price divergence; however, the magnitude of this effect may vary annually based on fuel costs and changes in the merit order. We now examine the market prices resulting from the 5-zonal pricing schemes categorized as 5-Zonal (ATC, ZMP) and 5-Zonal (FBMC, ZMP). Table 7 presents a comparative analysis of the pricing outcomes across the five designated zones. \begin{table}
\begin{tabular}{c c c} \hline
**Category** & **Capital (KY)** & **Non-Capital (NKY)** \\ \hline Demand (TWh) & 219.9 (38.6\%) & 349.5 (61.4\%) \\ \hline Generation (TWh) & 118.3 (20.1\%) & 455.0 (79.9\%) \\ \hline \end{tabular}
\end{table} 
Table 6: Regional distribution of electricity demand and generation. Figure 5: Annual hourly average solar PV generation and market price gap between KY and NKY zones under the 2-Zonal (SMP). Our analysis of the 5-zonal pricing schemes revealed noteworthy insights. As evidenced in Table 7, the price differentials among the four zones within NKY (CC, JL, KW, YN) were notably small, in the range 0.81-1.46 KRW/kWh, regardless of application of the 5-Zonal (ATC, ZMP) or 5-Zonal (FBMC, ZMP) scheme. This holds true even though the FBMC model, which incorporated the zonal PTDF matrix and marginal loss factors, tended to reflect the network characteristics more accurately than the ATC model. The consistently small price differences across both schemes indicated to the occurrence of minimal congestion between the four zones within NKY, even when considering more precise network modeling. By extending this analysis, we observed that the 5-zonal pricing schemes effectively replicated the market price levels of the previously discussed 2-Zonal (ZMP) scheme. This similarity in outcomes can be attributed to two key factors: negligible price differentiation within the NKY zone (discussed earlier) and the persistence of the binding transmission flow constraint between the NKY and KY zones. Essentially, the absence of significant congestion within NKY, coupled with the dominant congestion between NKY and KY, resulted in price patterns that closely mirrored those observed in the simpler 2-Zonal (ZMP). Finally, we present the nodal pricing results, categorized as Nodal (LMP) and Nodal (ELMP), in Table 8 and Figure 6. Table 8 lists the average market prices for the load and generation nodes across the entire Korean power market, calculated as load- and generation-weighted averages, respectively. Figure 6 offers a visual representation of these weighted average market prices for nodes within each subregional administrative division, providing a detailed geographical perspective on the price distribution under nodal pricing. Nodal (ELMP) yielded higher prices than Nodal (LMP) owing to the partial incorporation of the FSR's no-load and start-up costs into market prices based on allowance for their partial commitment. Regardless of the specific nodal pricing scheme, the nodal pricing results maintained the trend observed in zonal pricing, with the KY zone generally exhibiting higher market prices than the NKY zone. Furthermore, the results aligned with the typical expectation that load nodes experienced higher prices than generation nodes owing to transmission losses and network congestion [45]. Consequently, this detailed nodal pricing reflected the local network constraints and delivery costs across the network, offering precise economic signals for market participants.