# Effective Scheme for Inductive Wireless Power Coil Design Using Scan-and-Zoom Optimization
## 4 Performance Comparison and Verification
### Proposed Coil Design Method  
The input parameters of the optimization algorithm are \(R_{in}\) and \(R_{out}\) as shown in Table 2 and the PTE is the output parameter of the optimization algorithm. To apply the proposed coil design method, nL is set to 10, and \(nP\) is set to 4. The scan-and-zoom algorithm is terminated at level 5 by the termination criterion of \(\varepsilon_{1}=10^{-4}\) % and \(\varepsilon_{2}=5\) mm as shown in Figure 12. The results are summarized in Table 3, and the search trajectory is shown in Figure 11b.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Conventional [(10)]** & \
\begin{tabular}{c} **ANSYS Maxwell** \\ **(Pattern Search)** \\ \end{tabular} &
\begin{tabular}{c} **Proposed** \\ **Co-Simulation** \\ \end{tabular} \\ \hline Outer radius \(R_{out}\) & 120 mm & 146.25 mm & 174.271 mm \\ Inner radius \(R_{in}\) & 52 mm & 102.5 mm & 138.646 mm \\  & 99.88\%/99.25\% & & \\ PTE (coil) & (without/with Litz & 99.406\% (with Litz & 99.448\% (with Litz \\  & wire option) & wire option) & wire option) \\ \# of FEA executions & 299 & 56 & 64 \\ Simulation time * & 14, 950 s & 2800 s & 3200 s \\ PTE (overall) & 99.76\%/99.13\% & N/A & 99.3353\% \\ \hline \hline \end{tabular}  
* In both the conventional and proposed methods, simulation time is recorded using the MATLAB tic-toc function, while the ANSYS simulation time is determined through actual execution. All evaluations were conducted on an Intel Core i7-8600K processor.  
\end{table}
Table 3: The optimization results of coil design methods.  
The number of FEA executions of the proposed coil design method is much lower than the conventional coil design method as shown in Table 3. The PTE of the conventional coil design method without the Litz wire option is higher than the proposed coil design method because the internal resistance of the coil is underestimated by ignoring the skin and proximity effects. The PTE calculated by the Litz wire option in the conventional coil design method is 99.25%. Because of these results, the conventional coil design method not only takes a long time to extract the coil shape parameter values but also reaches non-optimal solutions.  
Semiconductor losses are a crucial factor that significantly affects power transfer efficiency. However, most existing optimization methods do not take these losses into account. In the proposed optimization method, it becomes effortless to consider semiconductor losses by utilizing circuit simulation in MATLAB. This allows for the inclusion of all losses from the circuit simulation, leading to a more comprehensive and accurate optimization process. To further substantiate the superiority of the proposed method, we implemented MATLAB Simulink circuit schematics in Figure 13, which calculates the overall PTE by the time simulation. The detailed non-ideal MOSFET and diode device characteristics are shown in Table 4. By incorporating the circuit simulation tool, we can more accurately evaluate the impact of semiconductor losses on the overall system performance, providing a comprehensive analysis that enhances the reliability and effectiveness of the optimization process. This capability further reinforces the superiority of the proposed method in capturing real-world performance aspects that might be overlooked using ANSYS Maxwell alone.  
Figure 12: Convergence rate of (**a**) the radius increment per level (**b**) the PTE increment per level.  
Figure 13: MATLAB Simulink circuit schematics.