## 4 Case Study and Proof of Concept
### Test System 1

Table 9: _Cont._The description of results as displayed in Table 13 ( the outcome of implementing CSAOA on all the equations mentioned in Section 2) is as follows:  
1. [label=()]
2. Cost (ECD) minimization performed on test system 2. The minimum generation cost of the system is found to be USD 76,085 without DSM, which further reduces to USD 74,774 with DSM, respectively. Figures 7 and 8 illustrate, respectively, the hourly production of distributed energy resources (DERs) in the graphical representation, when the cost of generating is USD 76,085 and USD 74,774. On comparing Figures 6-8, the hourly load pattern can be easily traced, meaning that the total load demands every hour are fulfilled by the DERs. 3. Emission (EMD) minimization is performed on test system 2. The minimum emissions of the plant could be reduced to 236 tons ultimately when DSM is implemented, and the load demand is restructured. 4. CEED is performed as per the PPF method and FP method. With the PPF method, the cost and emission combination is USD 314,678, 256 tons and, with the FP method, the cost and emission combination is found to be USD 90,775, 249 tons. These values produce much more improved outcomes when the load demand is reorganized utilizing the DSM approach. It can be clearly seen that the FP method of CEED is a better option for obtaining a minimum cost and emission combination compared with PPF-based CEED. 5. Weighted combined economic emissions dispatch with equal weightage to both cost and emissions function is found to be the best measure of CEED, with a minimum value of USD 78,304 and 246 tons for cost and emissions, respectively. These values, as mentioned above, reduce further for the DSM-based load demand model to USD 78,064 and 243 tons. The hourly output of DERs is shown in Figures 9 and 10, \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Without DSM** & **With 40\% DSM** \\ \hline Peak Load Demand (MW) & 225 & 207.385 \\ \hline Ave. Load Demand (MW) & 186.56 & 186.56 \\ \hline Total Load Demand (MW) & 4477.5 & 4477.4990 \\ \hline Load Factor & 0.8291 & 0.8996 \\ \hline Reduction in Peak (\%) & Reference & 7.829\% \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Beneficial effects of DSM applications. Figure 6: Load–demand curve with and without DSM. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \begin{tabular}{c} **Cost and Emission** \\ **Profiles** \\ \end{tabular} & **Without DSM** & **With DSM** \\ \hline \multirow{2}{*}{ECD} & \begin{tabular}{c} Cost minimization \\ (thousands of USD) \\ \end{tabular} & \multirow{2}{*}{76.085} & \multirow{2}{*}{74.774} \\ \hline EMD & \begin{tabular}{c} Emission \\ minimization (tons) \\ \end{tabular} & \multirow{2}{*}{240} & \multirow{2}{*}{236} \\ \hline CEED (PPF) & \begin{tabular}{c} Cost \\ (thousands of USD) \\ \end{tabular} & \multirow{2}{*}{314.678} & \multirow{2}{*}{310.264} \\ \cline{2-2}  & \begin{tabular}{c} Emission (tons) \\ \end{tabular} & \multirow{2}{*}{256} & \multirow{2}{*}{254} \\ \hline CEED (FP) & \begin{tabular}{c} Cost \\ (thousands of USD) \\ \end{tabular} & \multirow{2}{*}{90.775} & \multirow{2}{*}{92.192} \\ \cline{2-2}  & \begin{tabular}{c} Emission (tons) \\ \end{tabular} & \multirow{2}{*}{249} & \multirow{2}{*}{244} \\ \hline \multirow{2}{*}{ECED (\(\mu=0.5\))} & \
\begin{tabular}{c} Cost \\ (thousands of USD) \\ \end{tabular} & \multirow{2}{*}{78.304} & \multirow{2}{*}{78.064} \\ \cline{2-2}  &
\begin{tabular}{c} Emission (tons) \\ \end{tabular} & \multirow{2}{*}{246} & \multirow{2}{*}{243} \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Outcomes of various fitness functions when evaluated using CSAOA. Figure 10: ECED hourly output with DSM. Figure 9: ECED hourly output without DSM. Figure 11: Hourly output of CEED without DSM. Figure 12: Hourly output of CEED with DSM. Figure 13: _Cont._  
Measures of central tendencies are evaluated and displayed in Table 15 to statistically analyze the performance of the proposed CSAOA with CSA and AOA.