## Appendix A  
The optimal system state variables when each objective is selected to be the objective function in the IEEE 30- and 118-bus systems can be seen in Tables A1-A5.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Variables** & **Value** & **Variables** & **Value** & **Variables** & **Value** & **Variables** & **Value** & **Variables** & **Value** \\ \hline \(p_{g1}\) & 79.2962 & \(P_{g65}\) & 39.7697 & \(V_{g1}\) & 0.9986 & \(V_{g65}\) & 1.0445 & \(T_{8.5}\) & 1.0250 \\ \(P_{g4}\) & 41.9684 & \(P_{g66}\) & 82.4272 & \(V_{g4}\) & 1.0113 & \(V_{g66}\) & 1.0178 & \(T_{26.25}\) & 1.0022 \\ \(p_{g6}\) & 93.4360 & \(P_{g69}\) & 48.0714 & \(V_{g66}\) & 1.0134 & \(V_{g69}\) & 1.0178 & \(T_{30.17}\) & 1.0095 \\ \(p_{g8}\) & 67.2358 & \(P_{g70}\) & 62.5577 & \(V_{g8}\) & 1.0317 & \(V_{g70}\) & 1.0172 & \(T_{38.37}\) & 1.0156 \\ \(P_{g10}\) & 25.2477 & \(P_{g72}\) & 4.8808 & \(V_{g10}\) & 1.0318 & \(V_{g72}\) & 1.0184 & \(T_{63.99}\) & 1.0240 \\ \(P_{g12}\) & 141.1926 & \(P_{g73}\) & 14.9595 & \(V_{g12}\) & 1.0085 & \(V_{g73}\) & 1.0184 & \(T_{64.61}\) & 1.0198 \\ \(P_{g15}\) & 98.8427 & \(P_{g74}\) & 100.0000 & \(V_{g15}\) & 1.0127 & \(V_{g74}\) & 1.0166 & \(T_{65.66}\) & 1.0116 \\ \(P_{g18}\) & 62.8468 & \(P_{g76}\) & 99.9963 & \(V_{g18}\) & 1.0138 & \(V_{g76}\) & 1.0046 & \(T_{68.69}\) & 1.0776 \\ \(P_{g19}\) & 56.2988 & \(P_{g77}\) & 99.9994 & \(V_{g19}\) & 1.0130 & \(V_{g77}\) & 1.0152 & \(T_{81.80}\) & 1.0069 \\ \(P_{g24}\) & 37.1550 & \(P_{g80}\) & 343.6913 & \(V_{g24}\) & 1.0200 & \(V_{g80}\) & 1.0214 & \(Q_{5}\) & 23.6248 \\ \(P_{g25}\) & 23.9125 & \(P_{g85}\) & 82.7307 & \(V_{g25}\) & 1.0194 & \(V_{g85}\) & 1.0191 & \(Q_{534}\) & 7.1127 \\ \(P_{g26}\) & 11.2993 & \(P_{g87}\) & 17.3755 & \(V_{g26}\) & 1.0317 & \(V_{g87}\) & 1.0195 & \(Q_{537}\) & 1.8497 \\ \(P_{g27}\) & 88.5769 & \(P_{g89}\) & 93.5984 & \(V_{g27}\) & 1.0180 & \(V_{g89}\) & 1.0183 & \(Q_{544}\) & 0.6465 \\ \(P_{g31}\) & 71.8922 & \(P_{g80}\) & 100.0000 & \(V_{g31}\) & 1.0179 & \(V_{g90}\) & 1.0117 & \(Q_{545}\) & 25.9688 \\ \(P_{g32}\) & 70.6395 & \(P_{g91}\) & 32.7792 & \(V_{g32}\) & 1.0175 & \(V_{g91}\) & 1.0165 & \(Q_{546}\) & 27.4017 \\ \(P_{g34}\) & 75.6676 & \(P_{g92}\) & 96.7686 & \(V_{g34}\) & 1.0163 & \(V_{g20}\) & 1.0155 & \(Q_{548}\) & 14.9718 \\ \(P_{g36}\) & 92.0627 & \(P_{g99}\) & 55.4364 & \(V_{g36}\) & 1.0142 & \(V_{g99}\) & 1.0207 & \(Q_{74}\) & 29.9529 \\ \(P_{g42}\) & 99.9950 & \(P_{g103}\) & 68.3646 & \(V_{g42}\) & 1.0167 & \(V_{g103}\) & 1.0233 & \(Q_{532}\) & 29.9963 \\ \(P_{g46}\) & 77.5342 & \(P_{g104}\) & 68.1967 & \(V_{g46}\) & 1.0211 & \(V_{g104}\) & 1.0214 & \(Q_{533}\) & 9.1679 \\ \(P_{g49}\) & 202.3555 & \(P_{g105}\) & 21.5187 & \(V_{g49}\) & 1.0203 & \(V_{g105}\) & 1.0189 & \(Q_{105}\) & 6.1990 \\ \(P_{g54}\) & 143.4796 & \(P_{g107}\) & 61.9437 & \(V_{g54}\) & 1.0183 & \(V_{g107}\) & 1.0217 & \(Q_{107}\) & 6.1352 \\ \(P_{g55}\) & 89.7263 & \(P_{g110}\) & 60.6194 & \(V_{g55}\) & 1.0188 & \(V_{g110}\) & 1.0223 & \(Q_{5110}\) & 29.9901 \\ \(P_{g56}\) & 86.9104 & \(P_{g111}\) & 5.6696 & \(V_{g56}\) & 1.0180 & \(V_{g111}\) & 1.0229 & Cost (USD/h) & 163,295.7775 \\ \(P_{g59}\) & 240.2069 & \(P_{g112}\) & 52.2977 & \(V_{g59}\) & 1.0175 & \(V_{g112}\) & 1.0183 & Emis (ton/h) & 2.6964 \\ \(P_{g61}\) & 158.5317 & \(P_{g113}\) & 44.9178 & \(V_{g61}\) & 1.0210 & \(V_{g113}\) & 1.0188 & \(\mathbf{Loss}\) (MW) & 1.8268 \\ \(P_{g62}\) & 64.8718 & \(P_{g116}\) & 29.0120 & \(V_{g62}\) & 1.0200 & \(V_{g116}\) & 1.0392 & \(V\)SI & 0.0665 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Optimal solutions provided by MaMPA when considering transmission loss as the objective function in the IEEE 118-bus system (case 7).