# Optimal Shape Design of Direct-Drive Permanent Magnet Generator for 1 kW-Class Wind Turbines
## 1 Introduction  
Wind turbines are highly effective devices that convert the kinetic energy of wind into mechanical and eventually electrical energy. They are commonly categorized into two types based on their rated capacities and intended applications. Large-scale wind turbines have rated capacities ranging up to several MWs and are designed for use in power plants that are typically deployed in wind farms. In contrast, small-scale wind turbines can be grid-connected for residential or industrial electricity generation or can be used in off-grid applications such as water pumping or battery charging. Small-scale wind turbines are typically installed as a single unit or in small numbers [1]. In particular, wind turbines with a rated capacity of 1 kW have gained attention for their excellent adaptability to the urban environment in terms of lower manufacturing and maintenance costs [2, 3]. The 1 kW-class wind turbine utilizes a vertical-axis generator with Darrieu-type blades to facilitate operation even under highly turbulent and irregular wind conditions [4]. To ensure high-efficiency power generation even under weak wind conditions, a direct-drive generator using the axial-flux permanent magnet (AFPM) has been adopted to reduce additional mechanical and electrical losses during power generation. This design allows for operation under rapidly changing wind speed conditions without the use of gearboxes [5]. Moreover, the rated capacity of the generator can be easily adjusted by stacking disk-shaped compact features in the axial-direction [6]. The use of a permanent magnet in the rotor eliminates the need for a field current, which is supplied to the field windings of the generator, resulting in a simple structure and low costs. However, the disadvantages of AFPM machines have been reported in comparison to other applications, such as a lower torque/mass ratio, large outer diameter, coggingtorque and power losses [7]. Much research regarding cogging torque and electrical losses, which reduce the performance of the machine, have been carried out in the past years to define strategies in the design stage of machines [8]. [PERSON] [9] investigated an effective cogging torque mitigation method for AFPM machines with a yokeless and segmented armature. By implementing the response surface methodology, optimal design factors are determined to mitigate the cogging torque. [PERSON] et al. [10] designed and analyzed the performance of an AFPM generator with a non-ferromagnetic permanent magnet holder on the rotor disc. The generator's performance and efficiency were evaluated analytically and experimentally, considering power loss. The results showed an improvement in performance even at high rotating speeds without an increase in the number of pole pairs. [PERSON] et al. [6] demonstrated the reduction of the no-load momentum of the AFPM generator using skewed magnets. This approach provided a significant advantage for the AFPM generator in terms of low cogging torque, high efficiency and compact size. [PERSON] [11] used the Taguchi experimental method for the optimal design of the AFPM generator. A sensitivity analysis based on the electromagnetic analysis results was conducted to identify optimum values for six independent design parameters and five levels. As a result, the degree of influence of the design parameters on the performance of the generator was determined by a regression model. The preceding literature reviews elucidated the design approaches for reducing cogging torque and power losses to increase efficiency and output power of the AFPM generator. However, the weight reduction of the generator should be considered for the generator design, since the performance of the AFPM machine's efficiency is influenced not only by the electromagnetic characteristics, but also by the weight and shape of mechanical parts of the generator, leading to excessive rotational momentum and friction losses in the stator and rotor [12; 13].