## 4 Simulation Results
### Power Flows
For instance, consider a scenario where the CC-JL line is congested, necessitating different prices between these two zones. Simultaneously, if the CC-YN and YN-JL lines are not congested, the SMP mechanism would imply that prices in these zones should remain uniform. This creates a logical contradiction, as the CC and JL zones would be required to have both different and identical prices at the same time, making it impossible to adopt the SMP mechanism in the loop network. Consequently, although the SMP mechanism can be applied to radial systems, such as Australia or a 2-zonal pricing in the Korean power system, it is not applicable to such loop systems. Impact of Zonal and Nodal Pricing on a Transco's Conflicts of Interest in a Combined Transmission-Retail Monopoly  
In the current Korean electricity market, the Korea Electric Power Corporation (KEPCO) acts simultaneously as both a Transco, which should remain neutral to maximize social welfare, and a retail monopoly, which is motivated to minimize power purchase costs [46]. This section investigates the effect of the transition to more granular pricing schemes on the potentially conflicting interests of the Transco in this unique structure. Figure 9: Comparison of interzonal power flows of (**a**) 5-Zonal (ATC, ZMP) and (**b**) 5-Zonal (FBMC, ZMP). In Korea, certain generation and transmission constraints are incorporated into the market-clearing model to address issues such as equipment overload, transient stability, and voltage stability, as listed in Table 4. The Transco bears significant responsibilities for maintaining power system reliability, including expanding transmission lines, increasing energy storage system (ESS) capacity for grid stabilization, reinforcing reactive power compensation equipment, and maintaining transmission facilities [47]. If these investments and improvements could alleviate the generation and transmission constraints outlined in Table 4, a reduction in the generation costs would be anticipated. However, this could paradoxically lead to an increase in power purchase costs, creating a potential conflict of interest for the Transco. To explore this dynamic, we conducted a sensitivity analysis across seven pricing schemes, examining the impact of alleviating generation and transmission constraints. It was assumed that this alleviation resulted from the Transco's efforts to enhance power system reliability. Specifically, we compared the change in generation costs (a proxy for social welfare) to the change in power purchase costs. As presented in Table 4, although the Korean electricity market typically applies 25 generation and transmission constraints, we simplified our sensitivity analysis to manage the computational load. Instead of analyzing each of the 25 constraints individually, we relaxed all constraints applicable to each zone simultaneously. Further, to reduce computational complexity, we set the MIP gap tolerance to 0.1% in the sensitivity analysis. Tables 12 and 13 present the changes in generation and power purchase costs when the generation and transmission constraints were relaxed for each zone under different pricing schemes. For example, the costs listed for the CC zone reflected the results obtained when only the constraints applicable to the CC zone in Table 4 were relaxed. The base case represents the generation and power purchase costs when all constraints listed in Table 4 were applied. The numbers in parentheses indicate the rate of change compared with the base case when the constraints for the applicable zone were relaxed. As presented in Tables 12 and 13, our analysis revealed that, while generation costs invariably decreased with the relaxation of constraints across all cases, power purchase costs may not necessarily exhibit the same trend. In the currently adopted Uniform (SMP), the power purchase costs remain relatively stable despite the relaxation of generation and transmission constraints, owing to the formation of a single price for the entire wholesale electricity market.