## 4 Simulation Results and Discussion  
Figure 4 shows a power system used for the numerical simulation to evaluate the proposed method. This system consists of three separate locations. Location-1 contains three GENCOs (\(G_{1},\ G_{3}\), and \(G_{2}\)) with a total load of DISCOs of 480 MW. Location-2 contains three GENCOs (\(G_{4},\ G_{5}\), and \(G_{6}\)) with a total load of DISCOs of 430 MW. Location-3 only consists of DISCOs with a total load of 300 MW. In contrast, losses will be supplied by a separated generator \(G_{L}\). Furthermore, Table 2 contains the offer data of GENCOs with four supply blocks (\(\alpha\), \(\beta\), \(\gamma\), and \(\pi\)). Table 3 assumes the demand for power every hour for 24 h, where the B-loss matrix is presented in (21). The calculation of B-loss matrix components in this paper is not the main discussion. The values of the B-loss matrix components are obtained from separate calculations in the paper. \[B=10^{-3}\left[ \begin{array}{rrrrrr}1.7&1.2&0.7&-0.1&-0.5&-0.2\\ 1.2&1.4&0.9&0.1&-0.6&-0.1\\ 0.7&0.9&3.1&0.0&-0.1&-0.6\\ -0.1&0.1&0.0&0.24&-0.6&-0.8\\ -0.5&-0.6&-0.1&-0.6&12.9&-0.2\\ -0.2&-0.1&-0.6&-0.8&-0.2&15.0\\ \end{array} \right] \tag{21}\]  
Figure 4: The system consisting of three locations. In this competition, \(G_{6}\) is declared losing, so the quota is zero. This is due to a very high offer, which is above $52/MWh (see Table 2). For the competition at the 12 th hour, Location-1 has a surplus of 495.6 MW, of which 180 MW are exported to Location-2, and the remaining is exported to Location-3. Therefore, \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multicolumn{2}{c}{**Total Generating**} & \multirow{2}{*}{**Load (MW)**} & \multirow{2}{*}{**Power Balance (MW)**} \\  & & **Power (MW)** & & & \\ \hline Location-1 & 960 & 480 & +495.6 \\ Location-2 & 250 & 430 & \(-180\) \\ Location-3 & 0 & 300 & \(-300\) \\ \hline Losses & 15.6 & 15.6 & 0 \\ \hline \end{tabular}
\end{table} 
Table 6: Power Balance. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Hour**} & \multicolumn{2}{c}{**Demand**} & \multirow{2}{*}{**Hour**} & \multicolumn{2}{c}{**Demand**} & \multirow{2}{*}{**Hour**} & \multicolumn{2}{c}{**Demand**} & \multirow{2}{*}{**Hour**} & \multicolumn{2}{c}{**Demand**} \\  & & **Load (MW)** & & & & **Load (MW)** & & **Load (MW)** \\ \hline
1 & 955 & 7 & 989 & 13 & 1220 & 19 & 1159 \\
2 & 942 & 8 & 1023 & 14 & 1311 & 20 & 1092 \\
3 & 935 & 9 & 1126 & 15 & 1320 & 21 & 1023 \\
4 & 930 & 10 & 1180 & 16 & 1350 & 22 & 984 \\
5 & 935 & 11 & 1198 & 17 & 1321 & 23 & 975 \\
6 & 965 & 12 & 1210 & 18 & 1262 & 24 & 960 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: 24 h Power on Demand Throughput. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Hcm**} & \multicolumn{2}{c}{**Location-1**} & \multicolumn{2}{c}{**Location-2**} & \multirow{2}{*}{**Location-3**} \\  & & **Total Generating** & & **Load (MW)** & & **Power Balance (MW)** \\ \hline Location-1 & 960 & 480 & +495.6 \\ Location-2 & 250 & 430 & \(-180\) \\ Location-3 & 0 & 300 & \(-300\) \\ \hline Losses & 15.6 & 15.6 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Power Balance. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Hcm**} & \multicolumn{2}{c}{**Demand**} & \multirow{2}{*}{**Hour**} & \multicolumn{2}{c}{**Demand**} & \multirow{2}{*}{**Hour**} & \multicolumn{2}{c}{**Demand**} & \multirow{2}{*}{**Hour**} & \multicolumn{2}{c}{**Demand**} \\  & & **Load (MW)** & & & **Load (MW)** & & **Load (MW)** \\ \hline
1 & 955 & 7 & 989 & 13 & 1220 & 19 & 1159 \\
2 & 942 & 8 & 1023 & 14 & 1311 & 20 & 1092 \\
3 & 935 & 9 & 1126 & 15 & 1320 & 21 & 1023 \\
4 & 930 & 10 & 1180 & 16 & 1350 & 22 & 984 \\
5 & 935 & 11 & 1198 & 17 & 1321 & 23 & 975 \\
6 & 965 & 12 & 1210 & 18 & 1262 & 24 & 960 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Result of Quota Analysis of Genco Losses and Nodal Price.