# Effective Scheme for Inductive Wireless Power Coil Design Using Scan-and-Zoom Optimization
## 4 Performance Comparison and Verification
### Conventional FEA-Based Coil Design Method  
The conventional FEA-based coil design method in reference [10] is adopted to take this problem as shown in Figure 10. First, \(R_{in}\) is fixed at 10 mm which is a minimum coil radius constraint, and \(R_{in}\) is swept by the step size of 1 mm. The resulting search trajectory is shown in Figure 11a, and the optimal coil radii, maximum PTE, and the number of FEA executions are shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Parameters** & **Value** & **Unit** \\ \hline \(P_{out}\) & Output power & 100 & W \\ \(f_{0}\) & Operating frequency & 100 & kHz \\ \(V_{out}\) & Output voltage & 50 & V \\ \(\eta_{t}\) & Target efficiency & \(\geq\)95 & \% \\ \hline \hline \end{tabular}
\end{table}
Table 1: IPT system design requirements.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Parameters** & **Value** \\ \hline \(R_{out}\) and \(R_{in}\) & Outer and inner radius & 10 mm \(\leq R_{in}<R_{out}\leq\) 200 mm \\ \(g\) & Coil separation/distance & 95 mm \\ \(d_{w}\) & Wire diameter & 3.4 mm \\ \(t_{w}\) & Coil thickness & 3.4 mm \\ \(W\times D\times H\) & Ferrite dimension & 400 mm \(\times\) 400 mm \(\times\) 4 mm \\ \hline \hline \end{tabular}
\end{table}
Table 2: Design constraints for IPT.  
Figure 9: Single-turn coil modeling in ANSYS Maxwell for verification.  
Figure 11: The search trajectory (**a**) Conventional FEA-based coil design (**b**) Proposed coil design method.  
Figure 10: Simplified flow chart of the conventional coil design method.  
Another approach to implementing the optimization is to use the optimization function in ANSYS Maxwell. Pattern search is selected for comparison with the proposed method. This is because the scan-and-zoom algorithm and the Pattern Search algorithm share several similarities such as:  
* Non-Gradient: Both algorithms are derivative-free optimization techniques, meaning they do not require gradient information of the objective function. This makes them suitable for optimizing functions that are non-smooth or non-differentiable.
* Simplicity: Both algorithms are relatively easy to implement compared to more complex optimization techniques. This simplicity makes them accessible choices for solving optimization problems.
* Direct Search: Both algorithms perform a direct exploration of the search space. They systematically evaluate the objective function at different points to locate the optimal or near-optimal solution.
* Global Exploration: Both methods can explore a wide range of the search space. This ability to avoid becoming trapped in local optima makes them suitable for problems with complex landscapes.
* Constraints Handling: Both algorithms can be adapted to handle constrained optimization problems where the solution needs to satisfy certain constraints.  
The optimization results of coil design methods are shown in Table 3. The optimization function in ANSYS Maxwell is embedded in the same software with the finite element analysis (FEA), which makes the speed of data transfer faster than the proposed method. Therefore, the execution time of the optimization function in ANSYS Maxwell is slightly faster compared to the proposed method. However, the power transfer efficiency (PTE) of ANSYS Maxwell optimization is lower compared to the proposed method. This is because the proposed method is implemented in the M-file of MATLAB, which provides high flexibility to optimize the code for the WPT system. Moreover, the proposed method can cooperate with the circuit simulation in MATLAB Simulink. Therefore, all losses from the circuit simulation such as switching losses and conduction losses of MOSFET and diode are fully considered in the proposed optimization method, resulting in a more accurate optimization process.