# Optimization Design of Planar Circle Coil for Limited-Size Wireless Power Transfer System
## 3 Parameters Optimization Design Based on TSEMO Algorithm  
In the last section, we take the S-S topology as an example to determine the PTE and TP of the WPT system to obtain the normalized design objectives \(K\) and \(\eta\). Next, we investigate the influence of various system parameters on \(K\) and \(\eta\), and merge and delete some parameters to obtain the final design variables and their ranges. Obviously, it is time-consuming to calculate all the variable design combinations. The intelligent optimization algorithm can solve this problem well. It can explore the solution space intelligently and dramatically minimize the calculation times. Figure 7 shows the flowchart of the Thompson sampling efficient multi-objective optimization (TSEMO) algorithm. TSEMO algorithm is an optimization algorithm based on a proxy model. The proxy model of the Gaussian process is established for the actual problem through the current data set, and the next sampling point is determined. After the next sampling point is calculated, update the proxy model, choose the next point, and enter the next round of optimization until it reaches the maximum number of iterations. The introduction of the proxy model avoids the large number of calculations required for random sampling in the sampling space and accelerates the optimization process very well. The TSEMO algorithm's process building in MATLAB is based on [23]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Symbol** & **Ranges** \\ \hline Inverter frequency & \(f\) & 200–800 kHz \\ Inner diameter of coils & \(D_{in}\) & 20–240 mm \\ Turn pitch & \(p\) & 2–12 \\ Turns & \(N\) & 2–50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The final design variables and ranges. Figure 6: The cross-sectional structure model of the planar coil. When taking \(K\) and \(\eta\) as optimization objectives, the optimal solution of the S-S coupling mechanism is no longer unique. It will exist in the form of a solution set. The optimal data solution set is called the Pareto front, also called the non-inferior solution set. The parameter value in the Pareto front maximizes one object while maintaining the maximum possible value of other conflicting objects. Solutions suitable to enter the Pareto front are picked by the criteria named Pareto dominance. Pareto dominance can be explained by considering that \(x_{1}\) and \(x_{2}\) both represent arbitrary solutions. For a minimization problem, Pareto dominance states that \(x_{1}\) dominates \(x_{2}\) if their objective function satisfies the following:  
\[ \begin{array}{l}f_{i}(x_{1})\leq f_{i}(x_{2})\text{ for all }i^{\prime}s\\ f_{i}(x_{1})<f_{i}(x_{2})\text{ for at least one }i\end{array}  \tag{17}\]  
where \(f_{i}\) represents the value of the \(i\)th objective function, namely, \(x_{2}\)'s all objective function values are not better than \(x_{1}\)'s objective function values, and at least one objective function value of \(x_{2}\) is worse than \(x_{1}\)'s. Thus, Pareto advantage is essentially comparing solutions and deciding which solution is non-advantageous. The non-dominant solution is then added to the Pareto front. After obtaining Pareto front data, the conflicts between multiple design objectives can be well weighed by using Pareto front visualization. Then the optimal solution and corresponding design parameters can be obtained. When the coils are around the environment of magnetic material and conductive material, it is difficult to use the empirical formula to calculate the accurate coils inductance, mutual inductance, and AC resistance. Researchers typically estimate those data in the finite element analysis software after building a simplified model. In COMSOL, the physical field of the model is the magnetic field, and a 2-dimensional axisymmetric model is adopted,  
Figure 7: Algorithm flowchart for TSEMO algorithm. so the coupler is usually half-drawn, and the distance between couplers is fixed at 5 cm. The material data is given according to the actual model.