## 3 Methodology and Simulation Framework
### Proposed Pricing Schemes and Korean Electricity Market Overview  
As explained in Section 2, pricing schemes encompass both the market-clearing model (specifically, the transmission flow model) and pricing mechanisms. Therefore, we proposed and constructed seven comprehensive pricing schemes, including currently adopted schemes, by combining these two factors, as presented in Table 2.  
For nodal pricing, the DC-OPF with marginal loss factors is commonly used as the transmission flow model to account for both transmission losses and congestion while ensuring computational efficiency. Adhering to this common practice, this study applied the DC-OPF to model nodal pricing schemes. In addition, LMP and ELMP were considered as pricing mechanisms, categorizing nodal pricing into two schemes: Nodal (LMP) and Nodal (ELMP). Zonal pricing can be implemented using various bidding zone configurations. Although the determination of optimal bidding zone configurations is an important research area [3; 6; 12; 24], this study did not focus on this aspect. Instead, this study adopted two \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Category**} & \multirow{2}{*}{\
\begin{tabular}{c} **Transmission** \\ **Flow Models** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Pricing** \\ **Mechanisms** \\ \end{tabular} } & \multirow{2}{*}{**Pricing Schemes**} \\ \cline{4-5}  & & & & LMP & Nodal (LMP) \\ \cline{4-5}  & & & ELMP & Nodal (ELMP) \\ \cline{4-5}  & & FBMC & & 5-Zonal (FBMC, ZMP) \\ \cline{4-5}  & & ATC & ZMP & 5-Zonal (ATC, ZMP) \\ \cline{4-5}  & & & ZMP & 2-Zonal (ZMP) \\ \cline{4-5}  & & & SMP & 2-Zonal (SMP) \\ \hline As-Is & Uniform Pricing & ATC & SMP & Uniform (SMP) \\ \hline \hline \end{tabular} Note: The pricing schemes are named as Category (Transmission Flow Model, Pricing Mechanism). If only one transmission flow model is used in a specific pricing scheme, it is simplified to Category (Pricing Mechanism). For example, “5-Zonal (FBMC, ZMP)” indicates 5-zonal pricing with FBMC and ZMP, while “Uniform (SMP)” represents uniform pricing with SMP.  
\end{table} 
Table 2: Overview of proposed pricing schemes. specific bidding zone configurations for the Korean electricity market, as illustrated in Figure 2. These configurations represent the most prominent options currently under discussion in Korea. They were selected for their relevance to ongoing policy debates and their potential for practical implementation. The first configuration, shown in Figure 2a, divides South Korea into two bidding zones: the capital region (KY) and non-capital region (NKY) (KY, derived from the Korean term \"Kyongin\", encompasses Seoul, Incheon, and Gyeonggi province, while NKY represents the rest of the country). The second configuration, illustrated in Figure 2b, delineates five bidding zones based on administrative districts, with certain modifications to consider the power system characteristics: the capital region (KY), Chungcheong (CC), Yeungnam (YN), Gangwon (GW), and Jeolla (JL) (these abbreviations are derived from Korean province names. Note that the Gangwon (GW) zone slightly differs from the standard administrative district, incorporating parts of Gyeongbuk province to reflect the distribution of nuclear power plants in the zone). In Figure 2, the red dotted lines indicate the interconnections between zones in our market model. For 5-zonal pricing, both FBMC and ATC were considered as transmission flow models, with ZMP applied as the pricing mechanism. For 2-zonal pricing, only the ATC was considered because the benefits of the FBMC are limited owing to the single transmission interface connecting the two bidding zones. Both the ZMP and SMP can be applied as pricing mechanisms for 2-zonal pricing. The reasons why the SMP cannot be applied to 5-zonal pricing are elucidated in Section 4. Consequently, this study configured zonal pricing into four pricing schemes: 5-Zonal (FBMC and ZMP), 5-Zonal (ATC and ZMP), 2-Zonal (ZMP), and 2-Zonal (SMP).