# Optimal Power Flow Solutions for Power System Considering Electric Market and Renewable Energy
## 1 Introduction
Researchers can find new fitness functions for reducing difficulty for applied algorithms or reaching more effective solutions more easily. Therefore, the applications of the metaheuristics are more and wider than other deterministic conventional algorithms. Almost metaheuristic algorithms can solve the OPF successfully, in which modified or hybrid algorithms can reach better results, such as the lightning attachment procedure algorithm [13], pattern search technique based particle swarm optimization [14], hybrid evolutionary algorithm [15], modified crossover based differential evolution [16], manta ray foraging optimizer [17], hybrid whale algorithm, moth-flame algorithm [18], improved Archimedes optimization algorithm [19], moth-flame optimization algorithm [20], and adaptive Gaussian teaching-learning algorithm [21]. In general, these studies focused on improving original metaheuristic algorithms for better performance or improving constraint handling methods for satisfying limitation of dependent variables, rather than improving power flow tools, such as Newton-Raphson and Gauss-Seidel. Different objective functions were optimized for comparison and evaluation of performance. Recently, researchers have concerned renewable power plants in transmission power grids, and the OPF problem has become more complicated by the presence of the plants. Major factors of the renewable plants are the number of added plants, installed location, and rated power for each added plant. So, to solve the OPF problem with the installation of renewable energies, there are major factors that must be accomplished before finding important parameters of basic electric components, such as thermal units, capacitors, transformers, loads, and transmission branches, as mentioned above. Basically, researchersare supposed to install small WFs and PVSs from some to tens of megawatts. The studies focused on two topics, including (1) the placement of WFs [22; 23; 24; 25; 26; 27] and (2) the placement of both PVSs and WFs [28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. These studies have used different metaheuristic algorithms and solved at least one standard IEEE transmission network with 30 nodes and at most three standard IEEE systems with 30, 57, and 118 nodes. Information of the studies consisting of algorithms, applied systems, objective function, number of renewable units, location, and power of each unit is given in Table 1. Almost all studies used only WFs or both WFs and PVSs rather than only PVSs. Popular nodes for the placement of renewable energy are 3 and 30, or 10 and 24 for the IEEE 30-node system. For the IEEE 57 and 118-nodes systems, the location is not the same for studies. One study [24] used the loss sensitivity factor-based method to determine node 30 and node 3, which are the most and the least important for installing distributed generators based on solar radiation or wind. Then, the Java algorithm was applied to optimize rated power of WFs and parameters of other electric components. The results indicated that node 30 was more suitable than node 3 for placing WFs. Some of the studies used the determined locations to optimize size of WFs [25; 26], meanwhile others optimized both location and size [27; 28; 29], and others optimized three factors, including the number of units, location, and power of each unit [33; 34; 35; 36; 37; 38]. Almost all methods focused on fuel cost minimization, loss minimization, and voltage improvement.