## 1 Introduction  
The power system can be separated into three parts: power generation system, power transmission system and distribution system. At present, most of the power generation systems are power plants such as gas power plants, thermal power plants, hydroelectric power plants and nuclear power plants. In addition, it could be a renewable energy power plant such as a solar power plant, wind power plant, wave power plant, etc. Most of the power transmission systems use an alternating current (AC) transmission system with conversion between the voltage level of sending and receiving; power plants have to step-up voltage to high voltage and connect by a transmission system to the distribution system. The distribution system receives a high voltage from the transmission line and steps-down voltage to distribute it to various consumers. In addition, the consumer requires different voltage levels such as a high voltage level or medium voltage level for the industrial sector or low voltage for housing. Therefore, the power system requires voltage levels to be different in order to suit each type of load. The equipment that changes the AC voltage level is a transformer. Thus, it can be seen that in a power system, there are several transformers that must be used. At present, the distribution transformer manufacturing industry has a higher competitive rate. In order to increase industrial competitiveness, manufacturers must have appropriate measures to reduce production costs in order to increase their turnover and be more competitive with other manufacturers. Therefore, in the design of distribution transformers, it must be designed at a low cost of production in order to maintain the competitiveness of the transformer manufacturing industry. The design of a transformer, due to the specifications and costs of production, is sometimes difficult due to the many parameters for the transformer's design [1; 2]. In the past, transformer design was based mainly on the designer's experience with using a trial-and-error method of modifying a lot of variables as appropriate. In addition, there are many owners' specific requirements, such as maximum loss, maximum weight, width, length and height, etc., that result in it being difficult to design. Furthermore, when the designer is inexperienced, they cannot meet target characteristics and a low cost of production, in terms of the price of the main material, such as the laminate of steel core and conductor wire when imported from abroad, of which the price is uncertain. Thus, the design for the optimum production cost has to be redesigned every time when the material price changes, which makes the design difficult [3; 4]. The distribution transformer's design using the original design results to develop a redesign results in a trial-and-error method according to the experience of the designers in order to obtain a new design result that is more suitable. The design results of the regularly produced distribution transformers, therefore, have a relatively reasonable design effect. On the other hand, if the design of the transformer is a new design, this results in it being difficult to calculate a suitable transformer [5; 6]. Currently, there are many techniques for optimization such as Local Search (LS), Particle Swarm Optimization (PSO), Bat-Inspired Algorithm (BA), Cuckoo Search (CS) and Firefly Algorithm (FA). However, the techniques mentioned have different advantages and disadvantages. The Area Elimination Method (AE) has advantages in speed and flexibility and can be easily applied to transformer designs. Therefore, AE techniques are suitable for use in transformer design [7; 8]. The AE Method is a numerical method used for searching for the optimization of conditions of an objective function.