## 4 Case Study and Proof of Concept
### Test System 1
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Unit**} & \multicolumn{4}{c}{**Emission Coefficients of \(\mathbf{NO_{x}}\)**} & \multicolumn{2}{c}{**Penalty Factor of \(\mathbf{NO_{x}}\)**} \\ \cline{2-6}  & \(\mathbf{\alpha_{\text{NOX}}}\) & \(\mathbf{\beta_{\text{NOX}}}\) & \(\mathbf{\gamma_{\text{NOX}}}\) & \(\mathbf{\xi_{\text{NOX}}}\) & \(\mathbf{h_{n}}\) \\ \cline{2-6}  & **tons/kW** & **tons/kW** & **tons/kW** & **tons/kW** & **tons/kW** \\ \hline
1 & \(1.2000\times 10^{-3}\) & \(5.2000\times 10^{-2}\) & \(1.8500\times 10^{1}\) & \(-2.6000\times 10^{1}\) & \(9.4070\times 10^{-1}\) \\ \hline
2 & \(4.0000\times 10^{-4}\) & \(4.5000\times 10^{-2}\) & \(1.2000\times 10^{1}\) & \(-3.5000\times 10^{1}\) & \(1.4962\times 10^{0}\) \\ \hline
3 & \(1.6000\times 10^{-3}\) & \(5.0000\times 10^{-2}\) & \(1.3000\times 10^{1}\) & \(-1.5000\times 10^{1}\) & \(1.3870\times 10^{0}\) \\ \hline
4 & \(1.2000\times 10^{-3}\) & \(7.0000\times 10^{-2}\) & \(1.7500\times 10^{1}\) & \(-7.4000\times 10^{1}\) & \(8.3080\times 10^{-1}\) \\ \hline
5 & \(3.0000\times 10^{-4}\) & \(4.0000\times 10^{-2}\) & \(8.5000\times 10^{0}\) & \(-8.9000\times 10^{1}\) & \(2.1705\times 10^{0}\) \\ \hline
6 & \(1.4000\times 10^{-3}\) & \(2.4000\times 10^{-2}\) & \(1.5500\times 10^{1}\) & \(-7.5000\times 10^{1}\) & \(1.0930\times 10^{0}\) \\ \hline \end{tabular}
\end{table} 
Table 10: Maximum \(\mathbf{NO_{x}}\) penalty factor and emission coefficient in 6 generator sets. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Unit**} & \multicolumn{4}{c}{**Emission Coefficients of \(\mathbf{NO_{x}}\)**} & \multicolumn{2}{c}{**Penalty Factor of \(\mathbf{NO_{x}}\)**} \\ \cline{2-6}  & \(\mathbf{\alpha_{\text{NOX}}}\) & \(\mathbf{\beta_{\text{NOX}}}\) & \(\mathbf{\gamma_{\text{NOX}}}\) & \(\mathbf{\xi_{\text{NOX}}}\) & \(\mathbf{h_{n}}\) \\ \cline{2-6}  & **tons/kW** & **tons/kW** & **tons/kW** & **tons/kW** & **tons/kW** \\ \hline
1 & \(1.5000\times 10^{-3}\) & \(9.2000\times 10^{-2}\) & \(1.4000\times 10^{1}\) & \(-16.00\) & \(7.8230\times 10^{-1}\) \\ \hline
2 & \(1.4000\times 10^{-3}\) & \(2.5000\times 10^{-2}\) & \(1.2500\times 10^{1}\) & \(-93.50\) & \(1.1895\times 10^{0}\) \\ \hline
3 & \(1.6000\times 10^{-3}\) & \(5.5000\times 10^{-2}\) & \(1.3500\times 10^{1}\) & \(-85.00\) & \(1.4356\times 10^{0}\) \\ \hline
4 & \(1.2000\times 10^{-3}\) & \(1.0000\times 10^{-2}\) & \(1.3500\times 10^{1}\) & \(-24.50\) & \(1.1333\times 10^{0}\) \\ \hline
5 & \(2.3000\times 10^{-3}\) & \(4.0000\times 10^{-2}\) & \(2.1000\times 10^{1}\) & \(-59.00\) & \(7.4560\times 10^{-1}\) \\ \hline
6 & \(1.4000\times 10^{-3}\) & \(8.0000\times 10^{-2}\) & \(2.2000\times 10^{1}\) & \(-70.00\) & \(7.1580\times 10^{-1}\) \\ \hline \end{tabular}
\end{table} 
Table 11: Maximum \(\mathbf{CO_{2}}\) penalty factor and emission coefficient in 6 generator sets. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Unit**} & \multicolumn{4}{c}{**Emission Coefficients of \(\mathbf{SO_{2}}\)**} & \multicolumn{2}{c}{**Penalty Factor of \(\mathbf{SO_{2}}\)**} \\ \cline{2-6}  & \(\mathbf{\alpha_{\text{SO2}}}\) & \(\mathbf{\beta_{\text{SO2}}}\) & \(\mathbf{\gamma_{\text{SO2}}}\) & \(\mathbf{\xi_{\text{SO2}}}\) & \(\mathbf{h_{s}}\) \\ \cline{2-6}  & **tons/kW** & **tons/kW** & **tons/kW** & **tons/kW** & **tons/kW** \\ \hline
3 & \(1.0000\times 10^{-3}\) & \(3.5000\times 10^{-2}\) & \(1.0000\times 10^{1}\) & \(-8.0000\times 10^{1}\) & \(2.1051\times 10^{0}\) \\ \hline
4 & \(2.0000\times 10^{-3}\) & \(7.0000\times 10^{-2}\) & \(2.3500\times 10^{1}\) & \(-3.4500\times 10^{1}\) & \(5.9760\times 10^{-1}\) \\ \hline
5 & \(1.3000\times 10^{-3}\) & \(1.2000\times 10^{-1}\) & \(2.1500\times 10^{1}\) & \(-1.9750\times 10^{1}\) & \(6.7720\times 10^{-1}\) \\ \hline
6 & \(2.1000\times 10^{-3}\) & \(8.0000\times 10^{-2}\) & \(2.2500\times 10^{1}\) & \(-2.5600\times 10^{1}\) & \(6.1920\times 10^{-1}\) \\ \hline \end{tabular}
\end{table}