# Optimal Shape Design of Direct-Drive Permanent Magnet Generator for 1 kW-Class Wind Turbines
## 4 Optimal Shape Design
### Result and Discussion  
The results obtained from the optimal shape design are presented in Table 5, which includes the results of the initial model as well. The optimal shape design yielded a 25% increase in the active power while maintaining the weight as that of the initial model. In order to validate the results of the optimal shape design, an electromagnetic analysis was performed by using obtained optimized parameters, wherein the circuit and load conditions were taken into account in order to maximize the active power. The results of the electromagnetic analysis for the validation were compared with those obtained by the optimal shape design as shown in Table 6. The error values, which represent the difference of the results from the validation and the optimal shape design, are less than 4%. Figure 12: Prediction profilers of response variables related to shape parameters. The optimal design of the proposed generator successfully satisfied the required active power while maintaining a similar weight difference between the initial and optimal models. This is because the weight-function criteria for the active power in the desirability function was three times higher than that of the weight reduction. If a higher weight-function criteria were imposed on weight minimization, the weight of the generator could be reduced slightly, but the active power of the generator would be lower than the required target specification. Therefore, it is not possible to satisfy the required active power of the generator without increasing its weight under the given shape design parameters. In addition, when determining the shape design parameters, the design parameter for air gap clearance was not considered. The air gap clearance of the proposed generator is 1 mm, which is the same as that of generators with similar specifications [35]. As the air gap clearance decreases by 0.1 mm, the reactance value decreases and the no-load voltage increases by 1% [36]. To conduct a study considering the air gap clearance between the stator and permanent magnets, the deformation and vibration of the rotor should be taken into account during generator operation, and this will be considered in future work. Meanwhile, in order to enable practical utilization of the currents and voltages induced by the proposed generator, a rectifier topology must be included in the circuit diagram as shown in Figure 8. Given that the induced currents and voltages contain harmonic content, an active rectifier, such as a six-switch rectifier [37], is recommended instead of a passive rectifier only to minimize high harmonic content of the currents and voltages. Thus, further research into the implementation of the active rectifier is also necessary. As the weight of the generator is closely related to both mechanical losses and manufacturing costs, high power density enables the generator to be produced at a lower price than a generator with the same rated capacity. Additionally, it increases the efficiency of the generator. To confirm that the optimal design for the proposed generator was conducted reasonably, it was compared with other studies using the power generation/weight ratio, also known as power density (kW/kgf). To facilitate comparison with other generators, the weight of the proposed generator, excluding the bearing and cover, was determined to be 3.44 kgf. Table 7 provides the comparison of the proposed generator with other generators studied in several literatures. The power density increases as the rated capacity increases. For generators with a rated capacity greater than 8 kW, the power density exceeds 100 W/kgf. Some studies [10; 14] have shown that the generator can achieve high power density even with a lower rated capacity. However, since the generator operates at a higher rotation speed, it needs a speed increase gearbox to be installed, which ultimately increases the total weight of the wind turbine.