## 5 Numerical Results
### Investigation of the Proposed Method's Performance on the IEEE 30-Bus System
The further comparison indicates that the proposed ICOA method can improve the result from 0.01% to 8.3%. For the case of discrete variables, the study [37] employed three methods in which the best HAS method reported 4.9059 MW. The best ALO method among four applied methods in [44] reported 4.59 MW, while that of JA [47] was 4.5495 MW. Clearly, these methods found less effective solutions than the proposed method, and the improvement of result from the proposed method over other ones was from 0.79% to 8.6%. The comparison with six other implemented methods also indicates the outstanding performance of the proposed method. The best power loss of WCA, SSA, SFOA, COA1, and COA2 are 4.58218, 4.7175, 4.7364, 4.5777, 4.5340, and 4.5328 MW, which are higher than that of the proposed method by 0.068, 0.204, 0.222, 0.064, 0.020, and 0.019 MW corresponding to the improvement of 1.488%, 4.314%, 4.696%, 1.392%, 0.441%, and 0.415%. Clearly, COA1 and COA2 can improve the result relatively well as compared with COA, while the improvement of the proposed method over COA is highly significant. Thus, it can lead to a conclusion that the proposed ICOA method is really highly effective for minimizing TPL objective of the IEEE 30-bus system. For comparison of the TVD objective shown in Table 6, all compared methods have considered only continuous values for all control parameters. Therefore, the comparison is only carried out for continuous variables. However, we have also reported obtained results from the proposed method for the case of discrete variables. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Min.**} & \multirow{2}{*}{**Avg.**} & \multicolumn{2}{c}{**Average**} & \multirow{2}{*}{**\(N_{\text{age}}\)**} & \multirow{2}{*}{**\(\text{{Ti (pu)}}\)**} & \multirow{2}{*}{**CV**} & \multirow{2}{*}{**DV**} & \multirow{2}{*}{**SR (\%)**} \\  & & & & & & & & \\ \hline PSO-PG [19] & 4.6425 & 4.732 & 8.216 & 4000 & 1.35 & X & - \\ PSO-SWT [19] & 4.6578 & 4.9413 & 7.995 & 4000 & 1.31 & X & - \\ PSO-PGSWT [19] & 4.7914 & 5.2349 & 7.912 & 4000 & 1.30 & X & - \\ PSO-IPG [19] & 4.5256 & 4.5508 & 7.852 & 4000 & 1.29 & X & - \\ HPSO-TS [23] & 4.5213 & - & - & - & - & X & - \\ TS [23] & 4.9203 & - & - & - & - & X & - \\ PSO [23] & 4.6862 & - & - & - & - & X & - \\ DE [24] & 4.555 & - & - & 75,000 & - & X & - \\ GSA [29] & 4.51431 & - & - & 20,000 & - & X & - \\ QOTLBO [33] & 4.5594 & 4.5601 & - & 10,000 & - & X & - \\ TLDO [33] & 4.5629 & 4.5695 & - & 10,000 & - & X & - \\ SGA [37] & 4.9408 & 5.0378 & - & - & - & X & - \\ PSO [37] & 4.9239 & 4.972 & - & - & - & X & - \\ HAS [37] & 4.9059 & 4.924 & - & - & - & & X & - \\ ALO [44] & 4.59 & - & 119.3 & 4000 & 14.07 & & X & - \\ BA [44] & 4.628 & - & 129.4 & 4000 & 15.26 & & X & - \\ GWO [44] & 4.6119 & - & 127.2 & 4000 & 15.00 & & X & - \\ ABC [44] & 4.611 & - & 130.6 & 8000 & 15.40 & & X & - \\ JA [47] & 4.5495 & - & - & 15,000 & - & & X & - \\ PSO [50] & 4.7779 & - & - & - & - & X & - \\ PSO-AAC [50] & 4.6469 & - & - & - & - & X & - \\ WOA [50] & 4.5943 & - & - & - & - & X & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._As seen from Table 6, the best TVD of the proposed method, which is 0.0888 pu, is better than that of six other implemented methods and almost all methods in other studies excluding GSA [29] and QOTLBO [33], which reported 0.0676 and 0.0856 pu. Because taking control variables included generator voltages, tap setting of transformers, and power output of shunt capacitor banks of GSA and QOTLBO as the input parameters to run the Matpower program, the recalculated value of TVD is equal to 0.18622 and 0.10313 pu. Clearly, the two recalculated values are much higher than 0.0888 pu from the proposed method. The comparisons with other remaining methods imply that the proposed method can improve the best optimal solution quality from 0.45% to 57%, and the improvement is 27.2% as compared to COA method.