# Optimal Shape Design of Direct-Drive Permanent Magnet Generator for 1 kW-Class Wind Turbines
## 5 Conclusions  
In this study, an optimal shape design of the axial-flux permanent magnet generator for 1 kW-class small-scale wind turbines was conducted to minimize the weight under the constraint of required active power. The electromagnetic analysis and sensitivity analysis for seven shape design parameters were carried out, which have an influence on the active power and weight of the generator. A response surface methodology was conducted based on the obtained results from the sensitivity analysis, and then the optimal shape design parameters of the generator were determined using the desirability function. The obtained results are as follows:  
1. A proposed outer-rotor type generator with axial-flux permanent magnets was suitable for a vertical-axis wind turbine, due to its ability to be vertically stacked in the center of a tower. The proposed generator was designed with a rated capacity of 1 kW, taking into consideration the sweep area of the wind turbine and its operation condition. Under the rated-load condition, each stage of the generator was required to generate 500 W with a torque of 48 Nm. 2. The finite element method, based on the electromagnetic analysis, was used to estimate the electromagnetic characteristics of a half geometry of a single stage for the proposed generator. The induced currents and voltages obtained under the rated-load condition provided an active power of 199 W, which was corrected to consider a power factor of 0.8. 3. Since the obtained active power was insufficient for the target specification, the optimal shape design was carried out to meet the target specification, including an active power of 250 W with weight minimization. The design space exploration was conducted using a sensitivity analysis to quantify variations in performance regarding changes in seven design parameters. 4. The inner diameter, length of the stator and slot height were considered as the main shape parameters that influence both the active power and weight of the generator. Based on the results of the sensitivity analysis, a response surface model was constructed to establish the functional relationship between the weight, active power and design parameters. 5. The optimal design parameters were identified using the desirability function based on the response surface model, resulting in an active power of 252 W and a weight of 5.04 kgf. The results indicate a 25% increase in active power while maintaining the weight of the initial model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**References** & **Rated Rotation Speed** & **Rated Capacity** & **Power Density** \\  & **[rpm]** & **[kW]** & **[kW/kgf]** \\ \hline Proposed in this study & 100 & 1 & 73.4 \\
[10] & 3000 & 0.39 & 130 \\
[42] & 100 & 0.4 & 48 \\
[40] & 129 & 1 & 62.5 \\
[41] & 300 & 2 & 59 \\
[38] & 200 & 3 & 75 \\
[39] & 300 & 3 & 85.7 \\
[14]\({}^{*}\) & 2000 & 3.6 & 600 \\
[4] & 100 & 7.5 & 51.4 \\
[15] & 210 & 8.1 & 143 \\
[43] & 100 & 12 & 109 \\
[44]\({}^{*}\) & 375 & 16.6 & 130 \\
[5]\({}^{*}\) & 211 & 20 & 178.6 \\ \hline \hline \end{tabular}  
* only consider weight of coppers and permanent magnets (active mass).  
\end{table} 
Table 7: Comparison of the results for the generator with different rated capacity and power density. 6. As a result of the comparison with other studies based on power density, the optimized generator provided a higher power generation/weight ratio for generators with a rated capacity of 3 kW. It is expected that an even higher power density can be achieved when the optimal design proposed in this study is applied to generators for wind turbines with higher rated capacities. All authors contributed to this work by collaboration. Conceptualization, H.J.P. and D.G.A. ; methodology, H.J.P. and D.G.A. ; software, H.J.P. ; validation, H.J.P. and H.L.K. ; formal analysis, H.J.P. and D.G.A. ; investigation, H.L.K. ; resources, H.L.K. ; writing--original draft preparation, H.J.P. ; writing--review and editing, S.H.H. ; supervision, S.H.H. ; project administration, S.H.H.