## 3 Methodology and Simulation Framework
### Simulation Design and Input Data  
This study applied the seven pricing schemes proposed in Section 3.1 to the Korean electricity market. The simulation results were analyzed based on actual power system data for the entire year 2023. To ensure consistency and minimize distortions, we used a common dataset and topology across all simulations, capturing only the effects caused by changes in pricing schemes. The power system was modeled at various levels of granularity, yielding detailed 4579-node representation, as illustrated in Figure 3. The topology included 3322 transformers (considering 3-winding transformers), 3056 transmission lines, 4579 buses (including auxiliary buses for 3-winding transformers), and 1597 generators (including distributed energy resources). To enhance the reliability of our modeling approach, we utilized PLEXOS, an advanced software tool for power-system modeling and simulation. The UCED problem and pricing processes were implemented using the CPLEX solver, which is a typical MILP and LP solver available in PLEXOS. The mixed-integer programming (MIP) gap tolerance was set to 0.0001%. Our simulation methodology performed 24 h optimizations with hourly time steps. Each day's results informed the subsequent day's initial conditions, creating a continuous chain of linked optimizations throughout the simulation period. Figure 3: Simplified visualization of the Korean power system (345 kV and above). The simulation model incorporated comprehensive input data and detailed modeling techniques to accurately reflect the Korean power system. Hourly demand data for 2023 were included, with a peak demand of 94,529 MW and an annual consumption of 566,160 GWh [37; 38; 39]. The load distribution was modeled at a detailed nodal level, with the demand allocated to individual nodes based on node-specific load participation factors relative to the total system demand. The generator data, including the installed capacities (totaling 150.4 GW), average generation costs, and average annual maintenance days for the various types of power plants are summarized in Table 3[37; 38; 39]. Conventional power sources were modeled with detailed technical characteristics, including output ranges, ramp rates, minimum up-and down-times, cost functions, and start-up costs. For renewable energy sources, hourly time-series data were employed to capture generation profiles, with annual average capacity factors of 14.4% and 19.7% for solar and wind power, respectively. The transmission network model incorporated transmission line and transformer parameters, such as thermal limits, reactance, and resistance, thereby enabling an accurate representation of network topology. In this study, the ATC model employed relatively slack transfer capacities, with predefined limits set to the thermal limits of the transmission lines connecting different zones. While these values represent theoretical maximum transmission interface limits, actual transfer capabilities could be lower, depending on network conditions and topology. For the FBMC model, all transmission lines connecting bidding zones were considered as CBs. The model implemented a co-optimization of energy and 4.5 GW of operating reserves, as practiced in the Korean electricity market. In addition, following the same market practices, it incorporated 25 key generation and transmission constraints that address various system security aspects: some constraints are derived from transient and voltage stability analyses, while others are determined through external security contingency analyses, as listed in Table 4[41]. Although specific data values are subject to confidentiality requirements, our approach aimed to provide a reliable representation of the Korean power system by using comprehensive input data and detailed modeling techniques. Additional information about our modeling is available upon reasonable request and is subject to data protection agreements.