## 4 Simulation Results
### Market Price  
In this section, we analyze and compare the market prices resulting from the different pricing schemes: current uniform, 2-zonal, 5-zonal, and nodal pricing. Our analysis begins by examining the differences between the currently adopted Uniform (SMP) and the 2-zonal pricing schemes, which include both 2-Zonal (SMP) and 2-Zonal (ZMP) schemes, as illustrated in Table 5.  
When analyzing the 2-Zonal (SMP), we observed that the KY zone maintains a price level nearly identical to the current Uniform (SMP). However, the NKY zone exhibited a significant market price decrease of \(11.4\%\). In contrast, the 2-Zonal (ZMP) facilitated an average price reduction of approximately \(8.2\%\) for both the KY and NKY compared to the 2-Zonal (SMP). This price reduction is attributed to the fundamental difference between the SMP and ZMP mechanisms in their treatment of the no-load and start-up costs. The SMP compensates for these costs; however, the ZMP does not. The dramatic price divergence between the KY and NKY zones under the 2-Zonal (SMP) scheme may raise questions. This phenomenon is rooted in the imbalance between the electricity demand and supply in the Korean power system. Table 6 summarizes the demand and generation for the capital (KY) and non-capital (NKY) regions for 2023. As illustrated in Table 6, although the KY zone accounted for approximately \(40\%\) of the total demand, it contributed to only approximately \(20\%\) of the total generation. This imbalance resulted in a significant power flow from NKY to KY. Moreover, the distribution of generation sources was exacerbated the price divergence. Low-cost generation and renewable energy sources, particularly solar PV, were predominantly located in the NKY zone, whereas high-cost generation sources were concentrated in the KY zone. Consequently, under the current Uniform (SMP), price-setting units were mostly situated in the KY zone. Figure 4: Comparison of daily simulated Uniform (SMP) and actual market prices for 2023. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Pricing Scheme**} & \multirow{2}{*}{**Uniform (SMP)**} & \multicolumn{2}{c}{**2-Zonal (SMP)**} & \multicolumn{2}{c}{**2-Zonal (ZMP)**} \\ \cline{3-6}  & & **KY** & **NKY** & **KY** & **NKY** \\ \hline Market Price & & & & & \\ (KRW/kWh) & 164.75 & 164.76 & 146.05 & 153.07 & 132.47 \\ \hline \hline \end{tabular} Note: KY refers to the capital region and NKY to the non-capital region.  
\end{table} 
Table 5: Comparison of market prices under Uniform (SMP) and 2-zonal pricing schemes. This distribution explains why the market price of the KY zone under the 2-Zonal (SMP) model remained nearly identical to the Uniform (SMP) price (the slight increase observed in KY prices under the 2-Zonal (SMP) compared to the Uniform (SMP) is owing to numerical effects from the load-weighted average calculation). Conversely, the significant price decrease in the NKY zone was particularly influenced by the concentration of solar PV generation, with 93.1% of such sources located in this zone [38]. To illustrate this effect, Figure 5 depicts the annual hourly average solar PV generation pattern alongside the market price gap between the KY and NKY zones under the 2-Zonal (SMP) throughout the year 2023. This visualization clearly demonstrates the positive correlation between solar power generation in the power system and the price differential between the two zones. Market price separation occurs when the transmission lines become congested. In the current imbalanced structure, NKY generation flowed to KY, and price separation occurred when transmission lines became congested during high-demand periods. This typically occurred between 10:00 and 17:00, when demand peaked. Coincidentally, this timeframe corresponded to a period of rapidly increasing solar PV generation, which was predominantly concentrated in the NKY zone. This temporal overlap between high demand and peak solar PV generation resulted in a unique dynamic of zonal pricing.