# Optimal Power Flow Solutions for Power System Considering Electric Market and Renewable Energy
## 5 Conclusions  
This paper has studied optimal power flow for the IEEE 30-node and 118-node transmission power networks considering electric market and renewable energies, namely, nodal prices and wind turbine placement. Electricity prices at different nodes were given by different values. Meanwhile, wind turbines in the range from 0 MW to 10 MW for the first system and wind farms from 0 to 100 MW for the second system were placed at different nodes. For the first system, three cases, including (1) the same prices for all nodes, (2) different prices for different nodes, and (3) different prices for different nodes and the \begin{table}
\begin{tabular}{c c c c c c c} \hline
1 wind & Position & 29 & - & - & - & - \\ farm & Power (MW) & 100 & - & - & - & - \\ \hline
2 wind & Position & 29 & 31 & - & - & - \\ farms & Power (MW) & 100 & 100 & - & - & - \\ \hline
3 wind & Position & 29 & 31 & 71 & - & - \\ farms & Power (MW) & 100 & 100 & 100 & - & - \\ \hline
4 wind & Position & 29 & 31 & 71 & 45 & - \\ farms & Power (MW) & 100 & 100 & 100 & 100 & - \\ \hline
5 wind & Position & 29 & 31 & 71 & 45 & 47 \\ farms & Power (MW) & 100 & 100 & 100 & 100 & 100 \\ \hline \end{tabular}
\end{table} 
Table 4: Optimal solutions for the IEEE 118-node system. Figure 20: Comparison of profits from different cases of the IEEE 118-node system. placement of one wind turbine, were implemented by using six applied algorithms, PSO, GA, MSA, SSA, WCA, and JSA. The results from the three cases are summarized as follows:  
1. For Case 1, JSA obtained greater profit than MSA, SSA, WCA, PSO, and GA by 0.4%, 1.2%, 0.2%, 0.7%, and 0.75%, respectively. For Case 2 and Case 3, these values are 0.04%, 2.44%, 1.7%, 0.46%, and 1.02% and 1.2%, 1.52%, 0.4%, 1.3%, and 0.1%, respectively. 2. Approximately all fifty solutions of JSA had a small deviation of profit, and its number of high-quality solutions was high. However, five remaining algorithms had big deviation and a small number of good solutions. 3. JSA is much faster than others at least two times. The final solution of others at the last iteration was worse than a solution of JSA at a half iteration number. The results above indicates that JSA is more effective than PSO, GA, MSA, SSA, and WCA in finding the best solutions for OPF problem considering electric market and renewable energy. Thus, JSA has been selected to implement Case 4 and Case 5 of the first system and six other cases of the second system. For the first system, Case 4 used the optimal location and rated power of the added wind turbine in Case 3 to optimize all parameters of transmission power network. Case 5 optimized the placement of two, three, and four wind turbines in three subcases 5.1, 5.2, and 5.3. For the second system, JSA has been run for optimizing zero, one, two, three, four, and five wind farms. The results and indications are as follows:  
1. For the first system, JSA had approximately the same profit for Case 3 and Case 4, although Case 3 was more complicated. Case 3 optimized two factors of wind turbine and all parameters of transmission power network, but only all parameters of transmission network were optimized in Case 4. This result indicated that JSA was very effective for the complex problem with transmission network and renewable power plants. Three subcases in Case 5 indicated that higher profits could be reached when more wind turbines were placed. The effectiveness order of nodes for placing wind turbines was Node 5, Node 2, Node 1, and Node 10. 2. For the second system, the order of nodes arranged from the most to the least importance is nodes 29, 31, 71, 45, and 47. As following the order, the profit can be reached effectively. In fact, the system with one wind farm can reach higher profit than the base system without wind farm by 29.69%. When increasing the wind farms to two, three, four, and five, the profit is greater by 20.59%, 8.18%, 8.39%, and 7.54%. Clearly, the important nodes have high impact on the increase in profit.