# Optimal Power Flow Solutions for Power System Considering Electric Market and Renewable Energy
## 4 Numerical Results
### Obtained Results for the IEEE 118-Node System  
In this section, only ISA is run for the IEEE 118-node system for reaching the best profit of different number of wind farms. Each wind farm is supposed to be from 0 MW to 100 MW. The first duty of ISA is to find both location and size of each wind farm. In the second duty, ISA must find all control parameters of the IEEE 118-node system, as shown in Section 3. The solutions of wind farms placement are given in Table 4. Meanwhile, the profit of each case is given in Figure 20. Table 4 can see the important order of nodes for placing wind farms. The order of nodes arranged from the most to the least importance is nodes 29, 31, 71, 45 and 47.  
As shown in Figure 20, the profit is increased as the number of wind farms is increased. The lowest profit of $35,777.8 and the highest profit of $70,548.2 are obtained for the cases without wind farms and with five wind farms. Five wind farms can help the system reach greater than the base system without wind farms by $34,770.4. This greater profit is equivalent to 97.2% of the base system. So, the contribution of ISA for improving profit is significant.  
On the other hand, the increase in profit as using higher number of wind farms is also seen clearly in Figure 20. One wind farm can reach higher profit than without wind farm  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline Case 2: without WTs & Position & - & - & - & - \\  & Power (MW) & 0 & - & - & - \\ \hline Case 3: 1 WT & Position & 5 & - & - & - \\  & Power (MW) & 10 & - & - & - \\ \hline Case 5.1: 2 WTs & Position & 5 & 2 & - & - \\  & Power (MW) & 10 & 10 & - & - \\ \hline Case 5.2: 3 WTs & Position & 5 & 2 & 1 & - \\  & Power (MW) & 10 & 10 & 10 & - \\ \hline Case 5.3: 4 WTs & Position & 5 & 2 & 1 & 10 \\  & Power (MW) & 10 & 10 & 10 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Optimal solutions of Case 2, Case 3, and Case 5 for the IEEE 30-node system.  
Figure 19: Comparison of profits from Case 2, Case 3, and Case 5.  
by $10,620.9, equivalent to 29.69%. Similarly, two wind farms can reach greater profit than one wind farm $9553.9, equivalent to 20.59%. Other comparisons also indicate the same manner, but the values are smaller. The greater profits are, respectively, $4574.6, $5076, and $4944.9, equivalent to 8.18%, 8.39%, and 7.54%. The smaller percent values can reveal the greater profit is proportional to the number of wind farms. The most effective number of wind farms can be two wind farms. However, the wind power cost is free due to the availability of wind speed. So, more wind power generated can lead to higher benefit if the initial investment cost is neglectable. In fact, the initial investment cost for installing wind farms is very high. Meanwhile, the fuel cost of wind farms is zero. This characteristic is opposite to thermal power plants, with not very high investment cost, but with very high cost of fossil fuels. The power system with 118 nodes has 54 thermal units, and all loads are supplied by the power sources. If the fossil fuel is not enough to run generating units, demand of loads must be cut intentionally. So, the investment of wind farms is essential.