# Optimal Power Flow Solutions for Power System Considering Electric Market and Renewable Energy
## 1 Introduction  
Optimal power flow (OPF) is a very important for power systems to reach stable and economic operation statuses. Control parameters of electric components in the power system must be set appropriately to assure that other components' parameters can be within an allowable working range [1]. The purpose can be reached by running the OPF program for power systems, so OPF is one of the leading problems in power system operation fields. Basically, the power system is comprised of three major parts, high capacity power plants, transmission power networks and distribution power networks in which the OPF problem has been studied so far for increasing the effectiveness of high capacity power plants and the transmission of power grids [2]. In conventional OPF problems, core power sources are mainly thermal power plants, which are mainly dependent on fossil fuels such as coal, gas, and oil. In recent years, renewable energy-based power plants, such as solar, photovoltaic, and wind power plants, have been concerned as a part of power source in power systems where major thermal power plants had been working stably on their sites. Thus, the newOPF problem with the presence of renewable energy-based power plants focuses on the determination of location and capacity for the renewable energy-based power plants. To solve the conventional OPF problem, optimization tools, such as deterministic algorithms and metaheuristic algorithms, find the control parameters of the power system and voltage of all generators, active power of generators, excluding slack, reactive power output of capacitors, and tap setting of transformers. Then, the Matpower program is run to reach other remaining parameters, such as active power of slack generator, reactive power of all generators, apparent power of lines, and voltage of loads [3]. As all parameters are within a predetermined operation range, the OPF solutions obtained are valid and they can be acknowledged for reaching stable operation status [4]. However, they may not be effective solutions. Derived from an unexpected issue, many methods have been proposed and evaluated so far [5]. For dealing with the new OPF problem, the duty of optimization tools is more difficult, since they must determine three more factors of renewable energy-based power plants, such as the number of added power plants, the location, and the capacity of each added power plant. For solving such conventional OPF problems, classical methods and numerical methods, such as gradient search algorithm [1], quadratic programming [5], Newton method [6; 7], linear programming [8; 9], nonlinear programming [10], and interior point [11], were applied in the past, as metaheuristic algorithms were not highly developed and widely applied. These methods had the same ideal as using an optimization function based on Lagrange multipliers, and they had the objective of taking partial derivative to reach control parameters and dependent parameters of the problem. They are deterministic methods, so they reach the same solutions for different trial runs. Meta-heuristic algorithms differ from the conventional optimization approaches in principle, so their performance for OPF problems is also different from that of the above conventional ones [12]. The metaheuristic optimization approaches are able to implement the non-deterministic optimal search based on randomization and solution update mechanisms without using derivative implementation. The fitness function is a very important factor of these metaheuristic algorithms in dealing with all constraints and reaching high quality of control variables. Normally, the fitness function is comprised of two terms, objective function that needs to be optimized and penalty terms for satisfying all constraints. If the two terms are selected unsuitably, metaheuristic algorithms will not reach valid solutions meeting all constraints and high-quality objective functions.