## 4 Simulation Results
### IEEE 30 Bus Test System
#### 4.1.1 Simple Objective OPF  
The first five case studies have been used to solve simple objective OPF problems. **Case 1: Fuel Cost**  
This first single objective function considers minimizing the total fuel cost of power generation. It is modeled by the quadratic cost curve given in Equation (14). Simulation results, illustrated in Table 4, show that the fuel cost using the HIC-GWA is 798.20 ($/h).  
Compared with solutions from state-of-the-art existing optimization approaches in Table 5, the proposed HIC-GWA has significantly reduced the total fuel cost.  
The convergence curve of the total cost ($/h) for case 1 is shown in Figure 2. Note that it converged in less than 30 iterations. **Case 2: Piecewise quadratic fuel cost**  
Thermal generators produce electricity by burning fuels such as coal, petroleum, or natural gas. The model for the fuel cost curve is given by Equation (15). Simulation results, illustrated in \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Solutions** & **Case 1** & **Case 2** & **Case 3** & **Case4** & **Case 5** \\ \hline Fuel cost ($/h) & 798.20 & 645.85 & 902.25 & 959.54 & 1000.30 \\ Emission (t/h) & 0.37 & 0.28 & 0.45 & 0.20 & 0.21 \\ \(R_{\text{loss}}\) (MW) & 8.86 & 6.59 & 11.18 & 2.67 & 2.61 \\ VD (p.u.) & 1.15 & 1.25 & 0.96 & 1.68 & 1.41 \\ \(L\) index & 0.13 & 0.13 & 0.17 & 0.13 & 0.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal solution of IEEE 30 bus power system for case studies 1 to 5. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Fuel Cost ($/h)** & **Emission (t/h)** & **\(P_{\text{loss}}\) (MW)** & **VD (p.u.)** & \(L\) **Index** \\ \hline MSA & 800.51 & 0.37 & 9.03 & 0.90 & 0.14 \\ MPSO & 800.52 & 0.37 & 9.04 & 0.90 & 0.14 \\ MDE & 800.84 & 0.36 & 808365.00 & 0.78 & 0.14 \\ MFO & 800.69 & 0.37 & 9.15 & 0.76 & 0.14 \\ FPA & 802.80 & 0.36 & 9.54 & 0.37 & 0.15 \\ ARCBO & 800.52 & 0.37 & 9.03 & 0.89 & 0.14 \\ HSFLA-SA & 801.79 & & & & \\ HIC-GWA & 798.20 & 0.37 & 8.86 & 1.15 & 0.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of HIC-GWA with the literature for case study 1. Figure 2: Total cost convergence curve during iterations for case 1. Table 4, show that the fuel cost using the proposed approach is 645.85 ($/h). Compared with existing optimization methods in Table 6, HIC-GWA has significantly reduced the total fuel cost.  
In cases 1 and 2, the proposed metaheuristic has a better convergence than recently published optimization methods.  
**Case 3: Piecewise quadratic fuel cost with valve point loading**  
The valve point loading effect is included in the cost function of Equation (17). Simulation results, illustrated in Table 4, show that the fuel cost using HIC-GWA is 902.25 ($/h). Compared with existing optimization methods in Table 7, HIC-GWA has significantly reduced the fuel cost in this case. **Case 4: Emission**  
The objective, in this case, is to reduce the emission level of important air pollutants like NOx and SOx, using the emission function described in Equation (18). Simulation results, illustrated in Table 4, show that the emission using HIC-GWA is 0.2009 (ton/h). Compared with existing optimization methods in Table 8, HIC-GWA has significantly reduced the emission level. **Case 5: Emission**  
The objective, in this case, is to reduce the emission level of important air pollutants like NOx and SOx, using the emission function described in Equation (18). Simulation results, illustrated in Table 4, show that the emission using HIC-GWA is 0.2009 (ton/h). Compared with existing optimization methods in Table 8, HIC-GWA has significantly reduced the emission level.