# Optimal Power Flow Solutions for Power System Considering Electric Market and Renewable Energy
## 1 Introduction
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Algorithm and Reference** & \begin{tabular}{c} **Applied IEEE** \\ **System** \\ \end{tabular} & **Objective Function** & **Number of WFs, PVSs,–Location for Each** \\ \hline Modified cuckoo search algorithm [22] & 30 nodes & Fuel cost & 2 WFs at nodes 10 and 24 \\ \hline Artificial bee colony [23] & 30 nodes & \begin{tabular}{c} Operating cost; \\ active power loss; \\ voltage deviation \\ \end{tabular} & 2 WFs at nodes 10 and 24 \\ \hline Jaya algorithm [24] & 30 nodes & \begin{tabular}{c} Fuel cost; \\ active power loss; \\ voltage stability \\ \end{tabular} & 2 WFs at nodes 3 and 30 \\ \hline Modified Jaya algorithm [25] & 30 nodes; 118 nodes & \begin{tabular}{c} Fuel cost; \\ active power loss; \\ voltage stability \\ \end{tabular} & 2 WFs at nodes 3 and 30 for both IEEE 30-node and 118-node systems \\ \hline Modified equilibrium & 30 nodes; 57 nodes; 118 nodes & \begin{tabular}{c} Fuel cost; \\ Power loss \\ \end{tabular} & 2 WFs at nodes 3 and 30 for both IEEE 30-node systems \\ \hline Hybrid of firefly and Jaya algorithm [28] & 30 nodes & \begin{tabular}{c} Fuel cost; \\ active power loss; \\ voltage stability; \\ emission \\ \end{tabular} & 2 WFs at nodes 5 and 11; 1 PVS at nodes 5 and 13 \\ \hline Multi-objective Coronavirus herd immunity algorithm [29] & 30 nodes; 57 nodes & \begin{tabular}{c} Fuel cost; \\ active power loss; \\ voltage stability \\ \end{tabular} & \
\begin{tabular}{c} 1 WF at node 5 and 1 PVS at node 11 for the \\ IEEE 30-node system \\ 1 WF at node 2 and 1 PVS at node 3 for the \\ IEEE 57-node system \\ \end{tabular} \\ \hline Non-dominated sort grey wolf algorithm [30] & 30 nodes & Fuel cost & 2 WFs at nodes 5 and 11; 1 PVS at node 13 \\ \hline Equilibrium optimizer algorithm [31] & 30 nodes &
\begin{tabular}{c} Fuel cost; \\ active power loss; \\ emission index; \\ \end{tabular} & 1 WF at node 11; 2 PVSs at nodes 5 and 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The summary of previous studies on solving OPF problems considering renewable energy sources. Another topic of the OPF problem is to consider the stochastic participation of renewable energy sources in transmission power networks. The flow direction algorithm was applied in [39] to reduce the total operating cost for all power plants, such as thermal, small hydro, wind, and solar photovoltaic power plants. The study has suggested that the total cost could be minimum if the energy efficiency was maximized by increasing stochastic participation of the renewable power plants, wind farms, and photovoltaic fields. Three standard IEEE systems with 30, 57, and 118 nodes were employed for simulation. The study [40] has applied the mayfly algorithm to minimize several single objectives, such as total cost of wind, solar and thermal power plants, voltage deviation, power loss, and emission for a 30-node transmission power network. In one study [41], the gorilla troop algorithm was run for two systems with 30 and 118 nodes for reaching the smallest cost of thermal units only. In general, the three algorithms have tried to reduce the total generation cost, but they had different ideas of cost. The two studies [39; 40] have considered the cost of renewable energies, but another study [41] has ignored the cost. However, the three studies have pointed out that, as the uncertainty of renewable energies was high, the cost of generation could be higher due to the use of more power from thermal power plants. In this study, we optimized power flow for the IEEE 30-node and IEEE-118 node power networks considering nodal prices and placement of wind energy-based generators. The different nodal prices are considered to optimize the location and rated power of wind farms installed in the system. The study [42] has built a set of generators and run nodal price program to calculate electricity price for the first system.