# Optimal Power Flow Solutions for Power System Considering Electric Market and Renewable Energy
## 1 Introduction
To simulate the two systems, JSA [43], MSA [44], SSA [45], WCA [46], PSO [47], and GA [48] are implemented for find the most solutions. In summary, the novelties of the paper can be expressed as follows:  
1. Applying different nodal prices for nodes in transmission power networks and considering wind energy. The study is more complicated than previous studies [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38] by considering the node prices, and it is also more complicated than the previous study [38] by considering wind energy. 2. Consider different number of wind turbines and wind farms. In the first system with 30 nodes, four study cases of WTs placement with one, two, three and four WTs in range between 0 MW and 10 MW are implemented. In the second system with 118 nodes, five study case of WFs placement, from one to five WTs in range from 0 to 100 MW are simulated. Two factors of each wind turbine as well as each wind farm must be determined, including the placed location and rated power. The different \begin{table}
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**Algorithm and Reference** & **Applied IEEE System** & **Objective Function** & **Number of WFs, PVSs,—Location for Each** \\ \hline Modified Rao algorithm [32] & 30 nodes; 118 nodes & Fuel cost & 1 WF at node 30 for the IEEE 30-node system 1 WF at node 31 and 1 PVS at node 54 for the IEEE 118-node system \\ \hline Barnacle mating optimizer [33]; Enhanced genetic algorithm [34]; White shark algorithm [35]; Crow search algorithm [36] & 30 nodes & Fuel cost; power loss; fuel cost and emission & 2 WFs at nodes 5 and 11; 1 PVS at node 13 \\ \hline Manta ray foraging optimization [37] & 30 nodes; 118 nodes & Fuel cost; active power loss; voltage stability; emission & 2 WFs at nodes 30 and 11; 3 PVSs at nodes 5, 13 and 24 \\ \hline Differential evolution [38] & 30 nodes; 57 nodes; 118 nodes & Fuel cost; fuel cost and emission; voltage stability & 2 WFs at nodes 5 and 11; 1 PVS at node 13 for the IEEE 30-node system 2 WFs at nodes 6 and 9; 1 PVS at node 2 for the IEEE 57-node system 3 PVSs at nodes 6, 15 and 34 for the IEEE 118-node system \\ \hline \hline \end{tabular}
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Table 1: _Cont._study cases aim to determine the most suitable nodes to place wind energy as joining electric market. The target has not been concerned in all previous studies. 3. Applying recent and effective metaheuristic algorithms, including JSA [43], MSA [44], SSA [45], WCA [46], PSO [47], and GA [48]. There are conventional and novel algorithms in the six applied ones. The contributions of the paper are as follows: 1. Reach optimal solutions of placing wind turbines in the IEEE 30-node and the IEEE 118-node transmission power networks in electric market. 2. Find the maximum profit of electricity sale for the case without and with wind energy. The obtained maximum profits indicate the most suitable nodes for installing wind turbines and the most effective number of WTs and WFs for reaching the highest profit. On the other hand, the priority order of nodes for placing wind energy-based generators can be used to plan stability improvement for the transmission power networks. 3. Find one suitable metaheuristic algorithm for all study cases with electric market and wind energy. The six algorithms have applied for different optimization problems so far; however, the most powerful one should be recommended for other similar studies. Other parts of the paper are as follows: Section 2 shows objective function and all requirement conditions. Section 3 presents the structure of JSA and the whole solution process of JSA for the problem. Section 4 presents the results obtained by four applied algorithms for study cases. Section 5 summarizes the obtained results, contributions, shortcomings, and proposes future work to tackle the shortcomings.